1 Boolean Operations {#occt_user_guides__boolean_operations}
2 =========================
6 @section occt_algorithms_1 Introduction
8 This document provides a comprehensive description of the Boolean Operation Algorithm (BOA) as it is implemented in Open CASCADE Technology. The Boolean Component contains:
10 * General Fuse Operator (GFA),
11 * Boolean Operator (BOA),
12 * Section Operator (SA),
13 * Partition Operator (PA).
15 GFA is the base algorithm for BOA, PA, SA.
17 GFA has a history-based architecture designed to allow using OCAF naming functionality. The architecture of GFA is expandable, that allows creating new algorithms basing on it.
20 @section occt_algorithms_2 Overview
22 @subsection occt_algorithms_2_1 Operators
24 @subsubsection occt_algorithms_2_1_1 Boolean operator
26 The Boolean operator provides the operations (Common, Fuse, Cut) between two groups: *Objects* and *Tools*. Each group consists of an arbitrary number of arguments in terms of *TopoDS_Shape*.
28 The operator can be represented as:
30 <i>R<sub>B</sub>=B<sub>j</sub> (G<sub>1</sub>, G<sub>2</sub>),</i>
33 * *R<sub>B</sub>* - result of the operation;
34 * *B<sub>j</sub>* - operation of type *j* (Common, Fuse, Cut);
35 * *G<sub>1</sub>={S<sub>11</sub>, S<sub>12</sub> ... S<sub>1n1</sub>}* group of arguments (Objects);
36 * *G<sub>2</sub>={S<sub>21</sub>, S<sub>22</sub> ... S<sub>2n2</sub>}* group of arguments (Tools);
37 * *n<sub>1</sub>* - Number of arguments in *Objects* group;
38 * *n<sub>2</sub>* - Number of arguments in *Tools* group.
41 **Note** There is an operation *Cut21*, which is an extension for forward Cut operation, i.e <i>Cut21=Cut(G2, G1)</i>.
43 @subsubsection occt_algorithms_2_1_2 General Fuse operator
45 The General fuse operator can be applied to an arbitrary number of arguments in terms of *TopoDS_Shape*.
47 The GFA operator can be represented as:
49 <i>R<sub>GF</sub> = GF (S<sub>1</sub>, S<sub>2</sub> ... S<sub>n</sub>), </i>
52 * *R<sub>GF</sub>* - result of the operation,
53 * *S<sub>1</sub>, S<sub>2</sub> ... S<sub>n</sub>* - arguments of the operation,
54 * *n* - number of arguments.
56 The result of the Boolean operator, *R<sub>B</sub>*, can be obtained from *R<sub>GF</sub>*.
58 For example, for two arguments *S<sub>1</sub>* and *S<sub>2</sub>* the result *R<sub>GF</sub>* is
60 <i>R<sub>GF</sub> = GF (S<sub>1</sub>, S<sub>2</sub>) = S<sub>p1</sub> + S<sub>p2</sub> + S<sub>p12</sub></i>
62 @figure{/user_guides/boolean_operations/images/operations_image001.svg, "Operators"}
64 This Figure shows that
65 * <i>B<sub>common</sub> (S<sub>1</sub>, S<sub>2</sub>) = S<sub>p12</sub>;</i>
66 * <i>B<sub>cut12</sub> (S<sub>1</sub>, S<sub>2</sub>) = S<sub>p1</sub>;</i>
67 * <i>B<sub>cut21</sub> (S<sub>1</sub>, S<sub>2</sub>) = S<sub>p2</sub>;</i>
68 * <i>B<sub>fuse</sub> (S<sub>1</sub>, S<sub>2</sub>) = S<sub>p1</sub>+S<sub>p2</sub>+S<sub>p12</sub></i>
70 <i>R<sub>GF</sub>=GF (S<sub>1</sub>, S<sub>2</sub>) = B<sub>fuse</sub> = B<sub>common</sub>+ B<sub>cut12</sub>+ B<sub>cut21</sub>.</i>
72 The fact that *R<sub>GF</sub>* contains the components of *R<sub>B</sub>* allows considering GFA as the general case of BOA. So it is possible to implement BOA as a subclass of GFA.
74 @subsubsection occt_algorithms_2_1_3 Partition operator
76 The Partition operator can be applied to an arbitrary number of arguments in terms of *TopoDS_Shape*. The arguments are divided on two groups: Objects, Tools. The result of PA contains all parts belonging to the Objects but does not contain the parts that belongs to the Tools only.
78 The PA operator can be represented as follows:
80 <i>R<sub>PA</sub>=PA (G<sub>1</sub>, G<sub>2</sub>),</i>
82 * <i>R<sub>PA</sub></i> - is the result of the operation;
83 * *G<sub>1</sub>={S<sub>11</sub>, S<sub>12</sub> ... S<sub>1n1</sub>}* group of arguments (Objects);
84 * *G<sub>2</sub>={S<sub>21</sub>, S<sub>22</sub> ... S<sub>2n2</sub>}* group of arguments (Tools);
85 * *n<sub>1</sub>* - Number of arguments in *Objects* group;
86 * *n<sub>2</sub>* - Number of arguments in *Tools* group.
88 The result *R<sub>PA</sub>* can be obtained from *R<sub>GF</sub>* .
90 For example, for two arguments *S<sub>1</sub>* and *S<sub>2</sub>* the result *R<sub>PA</sub>* is
92 <i>R<sub>PA</sub>=PA(S<sub>1</sub>,S<sub>2</sub>)=S<sub>p1</sub>+S<sub>p12</sub>.</i>
94 In case when all arguments of the PA are Objects (no Tools), the result of PA is equivalent to the result of GFA.
96 For example, when *G<sub>1</sub>* consists of shapes *S<sub>1</sub>* and *S<sub>2</sub>* the result of *R<sub>PA</sub>* is
98 <i>R<sub>PA</sub>=PA(S<sub>1</sub>, S<sub>2</sub>) = S<sub>p1</sub> + S<sub>p2</sub> + S<sub>p12</sub> = GF (S<sub>1</sub>, S<sub>2</sub>)</i>
100 The fact that the *R<sub>GF</sub>* contains the components of *R<sub>PA</sub>* allows considering GFA as the general case of PA. Thus, it is possible to implement PA as a subclass of GFA.
103 @subsubsection occt_algorithms_2_1_4 Section operator
105 The Section operator *SA* can be applied to arbitrary number of arguments in terms of *TopoDS_Shape*. The result of *SA* contains vertices and edges in accordance with interferences between the arguments
106 The SA operator can be represented as follows:
107 <i>R<sub>SA</sub>=SA(S1, S2… Sn)</i>, where
108 * <i>R<sub>SA</sub></i> – is result of the operation;
109 * <i>S1, S2 … Sn</i> - Arguments of the operation;
110 * *n* - Number of arguments.
112 @subsection occt_algorithms_2_2 Parts of algorithms
114 GFA, BOA, PA and SA have the same Data Structure (DS). The main goal of the Data Structure is to store all necessary information for input data and intermediate results.
116 The operators consist of two main parts:
117 * Intersection Part (IP). The main goal of IP is to compute the interferences between sub-shapes of arguments. The IP uses DS to retrieve input data and store the results of intersections.
118 * Building Part (BP). The main goal of BP is to build required result of an operation. This part also uses DS to retrieve data and store the results.
120 As it follows from the definition of operator results, the main differences between GFA, BOA, PA and SA are in the Building Part. The Intersection Part is the same for the algorithms.
122 @section occt_algorithms_3 Terms and Definitions
124 This chapter provides the background terms and definitions that are necessary to understand how the algorithms work.
126 @subsection occt_algorithms_3_1 Interferences
128 There are two groups of interferences.
130 At first, each shape having a boundary representation (vertex, edge, face) has an internal value of geometrical tolerance. The shapes interfere with each other in terms of their tolerances. The shapes that have a boundary representation interfere when there is a part of 3D space where the distance between the underlying geometry of shapes is less or equal to the sum of tolerances of the shapes. Three types of shapes - vertex, edge and face - produce six types of **BRep interferences:**
138 At second, there are interferences that occur between a solid *Z1* and a shape *S2* when *Z1* and *S2* have no BRep interferences but *S2* is completely inside of *Z1*. These interferences are **Non-BRep interferences**. There are four possible cases:
144 @subsubsection occt_algorithms_3_1_1 Vertex/Vertex interference
146 For two vertices *Vi* and *Vj*, the distance between their corresponding 3D points is less than the sum of their tolerances *Tol(Vi)* and *Tol(Vj)*.
148 @figure{/user_guides/boolean_operations/images/operations_image002.svg, "Vertex/vertex interference"}
150 The result is a new vertex *Vn* with 3D point *Pn* and tolerance value <i>Tol(Vn)</i>.
152 The coordinates of *Pn* and the value <i>Tol(Vn)</i> are computed as the center and the radius of the sphere enclosing the tolerance spheres of the source vertices <i>(V1, V2)</i>.
154 @subsubsection occt_algorithms_3_1_2 Vertex/Edge interference
156 For a vertex *Vi* and an edge *Ej*, the distance *D* between 3D point of the vertex and its projection on the 3D curve of edge *Ej* is less or equal than sum of tolerances of vertex *Tol(Vi)* and edge *Tol(Ej)*.
158 @figure{/user_guides/boolean_operations/images/operations_image003.svg, "Vertex/edge interference"}
160 The result is vertex *Vi* with the corresponding tolerance value <i>Tol(Vi)=Max(Tol(Vi), D+Tol(Ej))</i>, where <i>D = distance (Pi, PPi)</i>;
162 and parameter *t<sub>i</sub>* of the projected point *PPi* on 3D curve *Cj* of edge *Ej*.
164 @subsubsection occt_algorithms_3_1_3 Vertex/Face interference
166 For a vertex *Vi* and a face *Fj* the distance *D* between 3D point of the vertex and its projection on the surface of the face is less or equal than sum of tolerances of the vertex *Tol(Vi)* and the face *Tol(Fj)*.
168 @figure{/user_guides/boolean_operations/images/operations_image004.svg, "Vertex/face interference"}
170 The result is vertex *Vi* with the corresponding tolerance value <i>Tol(Vi)=Max(Tol(Vi), D+Tol(Fj))</i>, where <i>D = distance (Pi, PPi)</i>
172 and parameters <i>u<sub>i</sub>, v<sub>i</sub></i> of the projected point *PPi* on surface *Sj* of face *Fj*.
174 @subsubsection occt_algorithms_3_1_4 Edge/Edge interference
176 For two edges *Ei* and *Ej* (with the corresponding 3D curves *Ci* and *Cj*) there are some places where the distance between the curves is less than (or equal to) sum of tolerances of the edges.
178 Let us examine two cases:
180 In the first case two edges have one or several common parts of 3D curves in terms of tolerance.
182 @figure{/user_guides/boolean_operations/images/operations_image005.svg, "Edge/edge interference: common parts"}
185 * Parametric range <i>[t<sub>i1</sub>, t<sub>i2</sub> ]</i> for 3D curve *Ci* of edge *Ei*.
186 * Parametric range <i>[t<sub>j1</sub>, t<sub>j2</sub> ]</i> for 3D curve *Cj* of edge *Ej*.
188 In the second case two edges have one or several common points in terms of tolerance.
190 @image html /user_guides/boolean_operations/images/operations_image006.svg "Edge/edge interference: common points"
191 @image latex /user_guides/boolean_operations/images/operations_image006.svg "Edge/edge interference: common points"
193 The result is a new vertex *Vn* with 3D point *Pn* and tolerance value *Tol(Vn)*.
195 The coordinates of *Pn* and the value *Tol(Vn)* are computed as the center and the radius of the sphere enclosing the tolerance spheres of the corresponding nearest points *Pi*, *Pj* of 3D curves *Ci*, *Cj* of source edges *Ei*, *Ej*.
197 * Parameter *t<sub>i</sub>* of *Pi* for the 3D curve *Ci*.
198 * Parameter *t<sub>j</sub>* of *Pj* for the 3D curve *Cj*.
200 @subsubsection occt_algorithms_3_1_5 Edge/Face interference
202 For an edge *Ei* (with the corresponding 3D curve *Ci*) and a face *Fj* (with the corresponding 3D surface *Sj*) there are some places in 3D space, where the distance between *Ci* and surface *Sj* is less than (or equal to) the sum of tolerances of edge *Ei* and face *Fj*.
204 Let us examine two cases:
206 In the first case Edge *Ei* and Face *Fj* have one or several common parts in terms of tolerance.
208 @figure{/user_guides/boolean_operations/images/operations_image007.svg, "Edge/face interference: common parts"}
210 The result is a parametric range <i>[t<sub>i1</sub>, t<sub>i2</sub>]</i> for the 3D curve *Ci* of the edge *Ei*.
212 In the second case Edge *Ei* and Face *Fj* have one or several common points in terms of tolerance.
214 @figure{/user_guides/boolean_operations/images/operations_image008.svg, "Edge/face interference: common points"}
216 The result is a new vertex *Vn* with 3D point *Pn* and tolerance value *Tol(Vn)*.
218 The coordinates of *Pn* and the value *Tol(Vn)* are computed as the center and the radius of the sphere enclosing the tolerance spheres of the corresponding nearest points *Pi*, *Pj* of 3D curve *Ci* and surface *Sj* of source edges *Ei*, *Fj*.
220 * Parameter *t<sub>i</sub>* of *Pi* for the 3D curve *Ci*.
221 * Parameters *u<sub>i</sub>* and *v<sub>i</sub>* of the projected point *PPi* on the surface *Sj* of the face *Fj*.
223 @subsubsection occt_algorithms_3_1_6 Face/Face Interference
225 For a face *Fi* and a face *Fj* (with the corresponding surfaces *Si* and *Sj*) there are some places in 3D space, where the distance between the surfaces is less than (or equal to) sum of tolerances of the faces.
227 @figure{/user_guides/boolean_operations/images/operations_image009.svg, "Face/face interference: common curves"}
229 In the first case the result contains intersection curves *C<sub>ijk</sub> (k = 0, 1, 2…k<sub>N</sub>,* where *k<sub>N</sub>* is the number of intersection curves with corresponding values of tolerances *Tol(C<sub>ijk</sub>)*.
231 @figure{/user_guides/boolean_operations/images/operations_image010.svg, "Face/face interference: common points"}
233 In the second case Face *Fi* and face *Fj* have one or several new vertices *V<sub>ijm</sub>*, where <i>m=0,1,2, ... mN, mN </i> is the number of intersection points.
235 The coordinates of a 3D point *P<sub>ijm</sub>* and the value *Tol(V<sub>ijm</sub>)* are computed as the center and the radius of the sphere enclosing the tolerance spheres of the corresponding nearest points *Pi*, *Pj* of the surface *Si*, *Sj* of source shapes *Fi*, *Fj*.
237 * Parameters *u<sub>j</sub>*, *v<sub>j</sub>* belong to point *PPj* projected on surface *Sj* of face *Fj*.
238 * Parameters *u<sub>i</sub>* and *v<sub>i</sub>* belong to point *PPi* projected on surface *Si* of face *Fi*.
240 @subsubsection occt_algorithms_3_1_7 Vertex/Solid Interference
242 For a vertex *Vi* and a solid *Zj* there is Vertex/Solid interference if the vertex *Vi* has no BRep interferences with any sub-shape of *Zj* and *Vi* is completely inside the solid *Zj*.
244 @figure{/user_guides/boolean_operations/images/operations_image060.png, "Vertex/Solid Interference"}
246 @subsubsection occt_algorithms_3_1_8 Edge/Soild Interference
248 For an edge *Ei* and a solid *Zj* there is Edge/Solid interference if the edge *Ei* and its sub-shapes have no BRep interferences with any sub-shape of *Zj* and *Ei* is completely inside the solid *Zj*.
250 @figure{/user_guides/boolean_operations/images/operations_image061.png, "Edge/Solid Interference"}
252 @subsubsection occt_algorithms_3_1_9 Face/Soild Interference
254 For a face *Fi* and a solid *Zj* there is Face/Solid interference if the face *Fi* and its sub-shapes have no BRep interferences with any sub-shape of *Zj* and *Fi* is completely inside the solid *Zj*.
256 @figure{/user_guides/boolean_operations/images/operations_image062.png, "Face/Solid Interference"}
258 @subsubsection occt_algorithms_3_1_10 Solid/Soild Interference
260 For a solid *Zi* and a solid *Zj* there is Solid/Solid interference if the solid *Zi* and its sub-shapes have no BRep interferences with any sub-shape of *Zj* and *Zi* is completely inside the solid *Zj*.
262 @figure{/user_guides/boolean_operations/images/operations_image063.png, "Solid/Solid Interference"}
265 @subsubsection occt_algorithms_3_1_11 Computation Order
267 The interferences between shapes are computed on the basis of increasing of the dimension value of the shape in the following order:
279 This order allows avoiding the computation of redundant interferences between upper-level shapes *Si* and *Sj* when there are interferences between lower sub-shapes *Sik* and *Sjm*.
281 @subsubsection occt_algorithms_3_1_12 Results
283 * The result of the interference is a shape that can be either interfered shape itself (or its part) or a new shape.
284 * The result of the interference is a shape with the dimension value that is less or equal to the minimal dimension value of interfered shapes. For example, the result of Vertex/Edge interference is a vertex, but not an edge.
285 * The result of the interference splits the source shapes on the parts each time as it can do that.
287 @subsection occt_algorithms_3_2 Paves
289 The result of interferences of the type Vertex/Edge, Edge/Edge and Edge/Face in most cases is a vertex (new or old) lying on an edge.
291 The result of interferences of the type Face/Face in most cases is intersection curves, which go through some vertices lying on the faces.
293 The position of vertex *Vi* on curve *C* can be defined by a value of parameter <i>t<sub>i</sub></i> of the 3D point of the vertex on the curve.
294 Pave *PVi* on curve *C* is a structure containing the vertex *Vi* and correspondent value of the parameter <i>t<sub>i</sub></i> of the 3D point of the vertex on the curve. Curve *C* can be a 3D or a 2D curve.
296 @figure{/user_guides/boolean_operations/images/operations_image011.svg, "Paves"}
298 Two paves *PV1* and *PV2* on the same curve *C* can be compared using the parameter value @code PV1 > PV2 if t1 > t2 @endcode
300 The usage of paves allows binding of the vertex to the curve (or any structure that contains a curve: edge, intersection curve).
303 @subsection occt_algorithms_3_3 Pave Blocks
305 A set of paves *PVi (i=1, 2...nPV)*, where *nPV* is the number of paves] of curve *C* can be sorted in the increasing order using the value of parameter *t* on curve *C*.
307 A pave block *PBi* is a part of the object (edge, intersection curve) between neighboring paves.
309 @figure{/user_guides/boolean_operations/images/operations_image012.svg, "Pave Blocks"}
311 Any finite source edge *E* has at least one pave block that contains two paves *PVb* and *PVe*:
312 * Pave *PVb* corresponds to the vertex *Vb* with minimal parameter <i>t<sub>b</sub></i> on the curve of the edge.
313 * Pave *PVe* corresponds to the vertex *Ve* with maximal parameter <i>t<sub>e</sub></i> on the curve of the edge.
315 @subsection occt_algorithms_3_4 Shrunk Range
317 Pave block *PV* of curve *C* is bounded by vertices *V1* and *V2* with tolerance values *Tol(V1)* and *Tol(V2)*. Curve *C* has its own tolerance value *Tol(C)*:
318 * In case of edge, the tolerance value is the tolerance of the edge.
319 * In case of intersection curve, the tolerance value is obtained from an intersection algorithm.
321 @figure{/user_guides/boolean_operations/images/operations_image013.svg, "Shrunk Range"}
323 The theoretical parametric range of the pave block is <i>[t1C, t2C]</i>.
325 The positions of the vertices *V1* and *V2* of the pave block can be different. The positions are determined by the following conditions:
327 Distance (P1, P1c) is equal or less than Tol(V1) + Tol(C)
328 Distance (P2, P2c) is equal or less than Tol(V2) + Tol(C)
330 The Figure shows that each tolerance sphere of a vertex can reduce the parametric range of the pave block to a range <i>[t1S, t2S]</i>. The range <i>[t1S, t2S]</i> is the shrunk range of the pave block.
332 The shrunk range of the pave block is the part of 3D curve that can interfere with other shapes.
334 @subsection occt_algorithms_3_5 Common Blocks
336 The interferences of the type Edge/Edge, Edge/Face produce results as common parts.
338 In case of Edge/Edge interference the common parts are pave blocks that have different base edges.
340 @figure{/user_guides/boolean_operations/images/operations_image014.svg, "Common Blocks: Edge/Edge interference"}
342 If the pave blocks <i>PB<sub>1</sub>, PB<sub>2</sub>…PB<sub>NbPB</sub></i> , where *NbPB* is the number of pave blocks have the same bounding vertices and geometrically coincide, the pave blocks form common block *CB*.
345 In case of Edge/Face interference the common parts are pave blocks lying on a face(s).
347 @figure{/user_guides/boolean_operations/images/operations_image015.svg, "Common Blocks: Edge/Face interference"}
349 If the pave blocks *PBi* geometrically coincide with a face *Fj*, the pave blocks form common block *CB*.
351 In general case a common block *CB* contains:
352 * Pave blocks *PBi (i=0,1,2, 3… NbPB)*.
353 * A set of faces *Fj (j=0,1... NbF), NbF* - number of faces.
356 @subsection occt_algorithms_3_6 FaceInfo
358 The structure *FaceInfo* contains the following information:
359 * Pave blocks that have state **In** for the face;
360 * Vertices that have state **In** for the face;
361 * Pave blocks that have state **On** for the face;
362 * Vertices that have state **On** for the face;
363 * Pave blocks built up from intersection curves for the face;
364 * Vertices built up from intersection points for the face.
366 @figure{/user_guides/boolean_operations/images/operations_image016.svg, "Face Info"}
368 In the figure, for face *F1*:
369 * Pave blocks that have state **In** for the face: *PB<sub>in1</sub>*.
370 * Vertices that have state **In** for the face: *V<sub>in1</sub>*.
371 * Pave blocks that have state **On** for the face: *PB<sub>on11</sub>*, *PB<sub>on12</sub>*, *PB<sub>on2</sub>*, *PB<sub>on31</sub>*, *PB<sub>on32</sub>*, *PB<sub>on4</sub>*.
372 * Vertices that have state **On** for the face: *V1, V2, V3, V4, V5, V6*.
373 * Pave blocks built up from intersection curves for the face: *PB<sub>sc1</sub>*.
374 * Vertices built up from intersection points for the face: none
377 @section occt_algorithms_4 Data Structure
379 Data Structure (DS) is used to:
380 * Store information about input data and intermediate results;
381 * Provide the access to the information;
382 * Provide the links between the chunks of information.
384 This information includes:
391 Data Structure is implemented in the class *BOPDS_DS*.
393 @subsection occt_algorithms_4_1 Arguments
395 The arguments are shapes (in terms of *TopoDS_Shape*):
396 * Number of arguments is unlimited.
397 * Each argument is a valid shape (in terms of *BRepCheck_Analyzer*).
398 * Each argument can be of one of the following types (see the Table):
400 | No | Type | Index of Type |
401 | :----- | :----- | :----- |
403 | 2 | COMPSOLID | 1 |
411 * The argument of type *0 (COMPOUND)* can include any number of shapes of an arbitrary type (0, 1…7).
412 * The argument should not be self-interfered, i.e. all sub-shapes of the argument that have geometrical coincidence through any topological entities (vertices, edges, faces) must share these entities.
413 * There are no restrictions on the type of underlying geometry of the shapes. The faces or edges of arguments *S<sub>i</sub>* can have underlying geometry of any type supported by Open CASCADE Technology modeling algorithms (in terms of *GeomAbs_CurveType* and *GeomAbs_SurfaceType*).
414 * The faces or edges of the arguments should have underlying geometry with continuity that is not less than C1.
416 @subsection occt_algorithms_4_2 Shapes
418 The information about Shapes is stored in structure *BOPDS_ShapeInfo*. The objects of type *BOPDS_ShapeInfo* are stored in the container of array type. The array allows getting the access to the information by an index (DS index).
419 The structure *BOPDS_ShapeInfo* has the following contents:
423 | :-------- | :----- |
424 | *myShape* | Shape itself |
425 | *myType* | Type of shape |
426 | *myBox* | 3D bounding box of the shape |
427 | *mySubShapes* | List of DS indices of sub-shapes |
428 | *myReference* | Storage for some auxiliary information |
429 | *myFlag* | Storage for some auxiliary information |
431 @subsection occt_algorithms_4_3 Interferences
433 The information about interferences is stored in the instances of classes that are inherited from class <i>BOPDS_Interf</i>.
437 | *BOPDS_Interf* | Root class for interference |
438 | *Index1* | DS index of the shape 1 |
439 | *Index2* | DS index of the shape 2 |
440 | *BOPDS_InterfVV* | Storage for Vertex/Vertex interference |
441 | *BOPDS_InterfVE* | Storage for Vertex/Edge interference |
442 | *myParam* | The value of parameter of the point of the vertex on the curve of the edge |
443 | *BOPDS_InterfVF* | Storage for Vertex/Face interference |
444 | *myU, myV* | The value of parameters of the point of the vertex on the surface of the face |
445 | *BOPDS_InterfEE* | Storage for Edge/Edge interference |
446 | *myCommonPart* | Common part (in terms of *IntTools_CommonPart* ) |
447 | *BOPDS_InterfEF* | Storage for Edge/Face interference |
448 | *myCommonPart* | Common part (in terms of *IntTools_CommonPart* ) |
449 | *BOPDS_InterfFF* | Storage for Face/Face interference |
450 | *myTolR3D, myTolR2D* | The value of tolerances of curves (points) reached in 3D and 2D |
451 | *myCurves* | Intersection Curves (in terms of *BOPDS_Curve*) |
452 | *myPoints* | Intersection Points (in terms of *BOPDS_Point*) |
453 | *BOPDS_InterfVZ* | Storage for Vertex/Solid interference |
454 | *BOPDS_InterfEZ* | Storage for Edge/Solid interference |
455 | *BOPDS_InterfFZ* | Storage for Face/Solid interference |
456 | *BOPDS_InterfZZ* | Storage for Solid/Solid interference |
462 The Figure shows inheritance diagram for *BOPDS_Interf* classes.
464 @figure{/user_guides/boolean_operations/images/operations_image017.svg, "BOPDS_Interf classes"}
467 @subsection occt_algorithms_4_4 Pave, PaveBlock and CommonBlock
469 The information about the pave is stored in objects of type *BOPDS_Pave*.
474 | *myIndex* | DS index of the vertex |
475 | *myParam* | Value of the parameter of the 3D point of vertex on curve. |
477 The information about pave blocks is stored in objects of type *BOPDS_PaveBlock*.
481 | *BOPDS_PaveBlock* | |
482 | *myEdge* | DS index of the edge produced from the pave block |
483 | *myOriginalEdge* | DS index of the source edge |
484 | *myPave1* | Pave 1 (in terms of *BOPDS_Pave*) |
485 | *myPave2* | Pave 2 (in terms of *BOPDS_Pave*) |
486 | *myExtPaves* | The list of paves (in terms of *BOPDS_Pave*) that is used to store paves lying inside the pave block during intersection process |
487 | *myCommonBlock* | The reference to common block (in terms of *BOPDS_CommonBlock*) if the pave block is a common block |
488 | *myShrunkData* | The shrunk range of the pave block |
490 * To be bound to an edge (or intersection curve) the structures of type *BOPDS_PaveBlock* are stored in one container of list type <i>(BOPDS_ListOfPaveBlock)</i>.
491 * In case of edge, all the lists of pave blocks above are stored in one container of array type. The array allows getting the access to the information by index of the list of pave blocks for the edge. This index (if exists) is stored in the field *myReference*.
493 The information about common block is stored in objects of type *BOPDS_CommonBlock*.
497 | *BOPDS_CommonBlock* | |
498 | *myPaveBlocks* | The list of pave blocks that are common in terms of @ref occt_algorithms_3_5 "Common Blocks" |
499 | *myFaces* | The list of DS indices of the faces, on which the pave blocks lie. |
502 @subsection occt_algorithms_4_5 Points and Curves
503 The information about intersection point is stored in objects of type *BOPDS_Point*.
508 | *myPnt* | 3D point |
509 | *myPnt2D1* | 2D point on the face1 |
510 | *myPnt2D2* | 2D point on the face2 |
512 The information about intersection curve is stored in objects of type *BOPDS_Curve*.
517 | *myCurve* | The intersection curve (in terms of *IntTools_Curve* ) |
518 | *myPaveBlocks* | The list of pave blocks that belong to the curve |
519 | *myBox* | The bounding box of the curve (in terms of *Bnd_Box* ) |
521 @subsection occt_algorithms_4_6 FaceInfo
522 The information about *FaceInfo* is stored in a structure *BOPDS_FaceInfo*.
523 The structure *BOPDS_FaceInfo* has the following contents.
527 | *BOPDS_FaceInfo* | |
528 | *myPaveBlocksIn* | Pave blocks that have state In for the face |
529 | *myVerticesIn* | Vertices that have state In for the face |
530 | *myPaveBlocksOn* | Pave blocks that have state On for the face |
531 | *myVerticesOn* | Vertices that have state On for the face |
532 | *myPaveBlocksSc* | Pave blocks built up from intersection curves for the face |
533 | *myVerticesSc* | Vertices built up from intersection points for the face +
535 The objects of type *BOPDS_FaceInfo* are stored in one container of array type. The array allows getting the access to the information by index. This index (if exists) is stored in the field *myReference*.
537 @section occt_algorithms_5 Intersection Part
539 Intersection Part (IP) is used to
540 * Initialize the Data Structure;
541 * Compute interferences between the arguments (or their sub-shapes);
542 * Compute same domain vertices, edges;
544 * Build section edges;
546 * Store all obtained information in DS.
548 IP is implemented in the class *BOPAlgo_PaveFiller*.
550 @figure{/user_guides/boolean_operations/images/operations_image064.svg, "Diagram for Class BOPAlgo_PaveFiller"}
552 @subsection occt_algorithms_5_1a Class BOPAlgo_Algo
553 The class *BOPAlgo_Algo* provides the base interface for all algorithms to provide the possibility to:
555 * Get Warning status;
556 * Turn on/off the parallel processing
557 * Break the operations by user request
560 * Set the appropriate memory allocator.
562 The description provided in the next paragraphs is coherent with the implementation of the method *BOPAlgo_PaveFiller::Perform()*.
564 @subsection occt_algorithms_5_1 Initialization
565 The input data for the step is the Arguments. The description of initialization step is shown in the Table.
567 | No | Contents | Implementation |
568 | :--- | :----- | :----- |
569 | 1 | Initialization the array of shapes (in terms of @ref occt_algorithms_4_2 "Shapes"). Filling the array of shapes. | *BOPDS_DS::Init()* |
570 | 2 | Initialization the array pave blocks (in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock, CommonBlock") | *BOPDS_DS::Init()* |
571 | 3 | Initialization of intersection Iterator. The intersection Iterator is the object that computes intersections between sub-shapes of the arguments in terms of bounding boxes. The intersection Iterator provides approximate number of the interferences for given type (in terms of @ref occt_algorithms_3_1 "Interferences") | *BOPDS_Iterator* |
572 | 4 | Initialization of intersection Context. The intersection Context is an object that contains geometrical and topological toolkit (classifiers, projectors, etc). The intersection Context is used to cache the tools to increase the algorithm performance. | *IntTools_Context* |
575 @subsection occt_algorithms_5_2 Compute Vertex/Vertex Interferences
577 The input data for this step is the DS after the @ref occt_algorithms_5_1 "Initialization". The description of this step is shown in the table :
580 | No | Contents | Implementation |
581 | :--- | :---- | :----- |
582 | 1 | Initialize array of Vertex/Vertex interferences. | *BOPAlgo_PaveFiller::PerformVV()* |
583 | 2 | Access to the pairs of interfered shapes <i>(nVi, nVj)k, k=0, 1…nk,</i> where *nVi* and *nVj* are DS indices of vertices *Vi* and *Vj* and *nk* is the number of pairs. | *BOPDS_Iterator* |
584 | 3 | Compute the connexity chains of interfered vertices *nV1C, nV2C… nVnC)k, C=0, 1…nCs*, where *nCs* is the number of the connexity chains | *BOPAlgo_Tools::MakeBlocksCnx()* |
585 | 4 | Build new vertices from the chains *VNc. C=0, 1…nCs.* | *BOPAlgo_PaveFiller::PerformVV()* |
586 | 5 | Append new vertices in DS. | *BOPDS_DS::Append()* |
587 | 6 | Append same domain vertices in DS. | *BOPDS_DS::AddShapeSD()* |
588 | 7 | Append Vertex/Vertex interferences in DS. | *BOPDS_DS::AddInterf()* |
590 * The pairs of interfered vertices are: <i>(nV11, nV12), (nV11, nV13), (nV12, nV13), (nV13, nV15), (nV13, nV14), (nV14, nV15), (nV21, nV22), (nV21, nV23), (nV22, nV23);</i>
591 * These pairs produce two chains: <i>(nV11, nV12, nV13, nV14, nV15)</i> and <i>(nV21, nV22, nV23);</i>
592 * Each chain is used to create a new vertex, *VN1* and *VN2*, correspondingly.
594 The example of connexity chains of interfered vertices is given in the image:
596 @figure{/user_guides/boolean_operations/images/operations_image018.svg, "Connexity chains of interfered vertices"}
599 @subsection occt_algorithms_5_3 Compute Vertex/Edge Interferences
601 The input data for this step is the DS after computing Vertex/Vertex interferences.
603 | No | Contents | Implementation |
604 | :--- | :--- | :--- |
605 | 1 | Initialize array of Vertex/Edge interferences | *BOPAlgo_PaveFiller::PerformVE()* |
606 | 2 | Access to the pairs of interfered shapes <i>(nVi, nEj)k k=0, 1…nk,</i> where *nVi* is DS index of vertex *Vi*, *nEj* is DS index of edge *Ej* and *nk* is the number of pairs. | *BOPDS_Iterator* |
607 | 3 | Compute paves. See @ref occt_algorithms_3_1_2 "Vertex/Edge Interference" | *BOPInt_Context::ComputeVE()* |
608 | 4 | Initialize pave blocks for the edges *Ej* involved in the interference | *BOPDS_DS:: ChangePaveBlocks()* |
609 | 5 | Append the paves into the pave blocks in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock" | *BOPDS_PaveBlock:: AppendExtPave()* |
610 | 6 | Append Vertex/Edge interferences in DS | *BOPDS_DS::AddInterf()* |
612 @subsection occt_algorithms_5_4 Update Pave Blocks
613 The input data for this step is the DS after computing Vertex/Edge Interferences.
615 | No | Contents | Implementation |
616 | :--- | :---- | :--- |
617 | 1 | Each pave block PB containing internal paves is split by internal paves into new pave blocks *PBN1, PBN2… PBNn*. PB is replaced by new pave blocks *PBN1, PBN2… PBNn* in the DS. | *BOPDS_DS:: UpdatePaveBlocks()* |
619 @subsection occt_algorithms_5_5 Compute Edge/Edge Interferences
621 The input data for this step is the DS after updating Pave Blocks.
623 | No | Contents | Implementation |
624 | :---- | :---- | :----- |
625 | 1 | Initialize array of Edge/Edge interferences | *BOPAlgo_PaveFiller::PerformEE()* |
626 | 2 | Access to the pairs of interfered shapes <i>(nEi, nEj)k, k=0, 1…nk,</i> where *nEi* is DS index of the edge *Ei*, *nEj* is DS index of the edge *Ej* and *nk* is the number of pairs. | *BOPDS_Iterator* |
627 | 3 | Initialize pave blocks for the edges involved in the interference, if it is necessary. | *BOPDS_DS:: ChangePaveBlocks()* |
628 | 4 | Access to the pave blocks of interfered shapes: <i>(PBi1, PBi2…PBiNi)</i> for edge *Ei* and <i>(PBj1, PBj2…PBjNj)</i> for edge *Ej* | *BOPAlgo_PaveFiller::PerformEE()* |
629 | 5 | Compute shrunk data for pave blocks in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock", if it is necessary. | *BOPAlgo_PaveFiller::FillShrunkData()* |
630 | 6 | Compute Edge/Edge interference for pave blocks *PBix* and *PBiy*. The result of the computation is a set of objects of type *IntTools_CommonPart* | *IntTools_EdgeEdge* |
631 | 7.1 | For each *CommonPart* of type *VERTEX:* Create new vertices *VNi (i =1, 2…,NbVN),* where *NbVN* is the number of new vertices. Intersect the vertices *VNi* using the steps Initialization and compute Vertex/Vertex interferences as follows: a) create a new object *PFn* of type *BOPAlgo_PaveFiller* with its own DS; b) use new vertices *VNi (i=1, 2…,NbVN), NbVN* as arguments (in terms of *TopoDs_Shape*) of *PFn*; c) invoke method *Perform()* for *PFn*. The resulting vertices *VNXi (i=1, 2…,NbVNX)*, where *NbVNX* is the number of vertices, are obtained via mapping between *VNi* and the results of *PVn*. | *BOPTools_Tools::MakeNewVertex()* |
632 | 7.2 | For each *CommonPart* of type *EDGE:* Compute the coinciding connexity chains of pave blocks <i>(PB1C, PB2C… PNnC)k, C=0, 1…nCs,</i> where *nCs* is the number of the connexity chains. Create common blocks <i>(CBc. C=0, 1…nCs)</i> from the chains. Attach the common blocks to the pave blocks. | *BOPAlgo_Tools::PerformCommonBlocks()* |
633 | 8 | Post-processing. Append the paves of *VNXi* into the corresponding pave blocks in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock" | *BOPDS_PaveBlock:: AppendExtPave()* |
634 | 9 | Split common blocks CBc by the paves. | *BOPDS_DS:: UpdateCommonBlock()* |
635 | 10 | Append Edge/Edge interferences in the DS. | *BOPDS_DS::AddInterf()* |
637 The example of coinciding chains of pave blocks is given in the image:
639 @figure{/user_guides/boolean_operations/images/operations_image019.png, "Coinciding chains of pave blocks"}
641 * The pairs of coincided pave blocks are: <i>(PB11, PB12), (PB11, PB13), (PB12, PB13), (PB21, PB22), (PB21, PB23), (PB22, PB23).</i>
642 * The pairs produce two chains: <i>(PB11, PB12, PB13)</i> and <i>(PB21, PB22, PB23).</i>
644 @subsection occt_algorithms_5_6 Compute Vertex/Face Interferences
646 The input data for this step is the DS after computing Edge/Edge interferences.
648 | No | Contents | Implementation |
649 | :---- | :--- | :---- |
650 | 1 | Initialize array of Vertex/Face interferences | *BOPAlgo_PaveFiller::PerformVF()* |
651 | 2 | Access to the pairs of interfered shapes <i>(nVi, nFj)k, k=0, 1…nk,</i> where *nVi* is DS index of the vertex *Vi*, *nFj* is DS index of the edge *Fj* and *nk* is the number of pairs. | *BOPDS_Iterator* |
652 | 3 | Compute interference See @ref occt_algorithms_3_1_3 "Vertex/Face Interference" | *BOPInt_Context::ComputeVF()* |
653 | 4 | Append Vertex/Face interferences in the DS | *BOPDS_DS::AddInterf()* |
654 | 5 | Repeat steps 2-4 for each new vertex *VNXi (i=1, 2…,NbVNX),* where *NbVNX* is the number of vertices. | *BOPAlgo_PaveFiller::TreatVerticesEE()* |
656 @subsection occt_algorithms_5_7 Compute Edge/Face Interferences
657 The input data for this step is the DS after computing Vertex/Face Interferences.
659 | No | Contents | Implementation |
660 | :---- | :---- | :---- |
661 | 1 | Initialize array of Edge/Face interferences | *BOPAlgo_PaveFiller::PerformEF()* |
662 | 2 | Access to the pairs of interfered shapes <i>(nEi, nFj)k, k=0, 1…nk,</i> where *nEi* is DS index of edge *Ei*, *nFj* is DS index of face *Fj* and *nk* is the number of pairs. | *BOPDS_Iterator* |
663 | 3 | Initialize pave blocks for the edges involved in the interference, if it is necessary. | *BOPDS_DS::ChangePaveBlocks()* |
664 | 4 | Access to the pave blocks of interfered edge <i>(PBi1, PBi2…PBiNi)</i> for edge *Ei* | *BOPAlgo_PaveFiller::PerformEF()* |
665 | 5 | Compute shrunk data for pave blocks (in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock") if it is necessary. | *BOPAlgo_PaveFiller::FillShrunkData()* |
666 | 6 | Compute Edge/Face interference for pave block *PBix*, and face *nFj*. The result of the computation is a set of objects of type *IntTools_CommonPart* | *IntTools_EdgeFace* |
667 | 7.1 | For each *CommonPart* of type *VERTEX:* Create new vertices *VNi (i=1, 2…,NbVN),* where *NbVN* is the number of new vertices. Merge vertices *VNi* as follows: a) create new object *PFn* of type *BOPAlgo_PaveFiller* with its own DS; b) use new vertices *VNi (i=1, 2…,NbVN), NbVN* as arguments (in terms of *TopoDs_Shape*) of *PFn*; c) invoke method *Perform()* for *PFn*. The resulting vertices *VNXi (i=1, 2…,NbVNX)*, where *NbVNX* is the number of vertices, are obtained via mapping between *VNi* and the results of *PVn*. | *BOPTools_Tools::MakeNewVertex()* and *BOPAlgo_PaveFiller::PerformVertices1()* |
668 | 7.2 | For each *CommonPart* of type *EDGE:* Create common blocks <i>(CBc. C=0, 1…nCs)</i> from pave blocks that lie on the faces. Attach the common blocks to the pave blocks. | *BOPAlgo_Tools::PerformCommonBlocks()* |
669 | 8 | Post-processing. Append the paves of *VNXi* into the corresponding pave blocks in terms of @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock". | *BOPDS_PaveBlock:: AppendExtPave()* |
670 | 9 | Split pave blocks and common blocks *CBc* by the paves. | *BOPAlgo_PaveFiller::PerformVertices1()*, *BOPDS_DS:: UpdatePaveBlock()* and *BOPDS_DS:: UpdateCommonBlock()* |
671 | 10 | Append Edge/Face interferences in the DS | *BOPDS_DS::AddInterf()* |
672 | 11 | Update *FaceInfo* for all faces having EF common parts. | *BOPDS_DS:: UpdateFaceInfoIn()* |
675 @subsection occt_algorithms_5_8 Build Split Edges
677 The input data for this step is the DS after computing Edge/Face Interferences.
679 For each pave block *PB* take the following steps:
681 | No | Contents | Implementation |
682 | :--- | :--- | :--- |
683 | 1 | Get the real pave block *PBR*, which is equal to *PB* if *PB* is not a common block and to *PB<sub>1</sub>* if *PB* is a common block. *PB<sub>1</sub>* is the first pave block in the pave blocks list of the common block. See @ref occt_algorithms_4_4 "Pave, PaveBlock and CommonBlock". | *BOPAlgo_PaveFiller::MakeSplitEdges()* |
684 | 2 | Build the split edge *Esp* using the information from *DS* and *PBR*. | *BOPTools_Tools::MakeSplitEdge()* |
685 | 3 | Compute *BOPDS_ShapeInfo* contents for Esp | *BOPAlgo_PaveFiller::MakeSplitEdges()* |
686 | 4 | Append *BOPDS_ShapeInfo* contents to the DS | *BOPDS_DS::Append()* |
688 @subsection occt_algorithms_5_9 Compute Face/Face Interferences
690 The input data for this step is DS after building Split Edges.
692 | No | Contents | Implementation |
693 | :--- | :--- | :--- |
694 | 1 | Initialize array of Face/Face interferences | *BOPAlgo_PaveFiller::PerformFF()* |
695 | 2 | Access to the pairs of interfered shapes <i>(nFi, nFj)k, k=0, 1…nk,</i> where *nFi* is DS index of edge *Fi*, *nFj* is DS index of face *Fj* and *nk* is the number of pairs. | *BOPDS_Iterator* |
696 | 3 | Compute Face/Face interference | *IntTools_FaceFace* |
697 | 4 | Append Face/Face interferences in the DS. | *BOPDS_DS::AddInterf()* |
699 @subsection occt_algorithms_5_10 Build Section Edges
701 The input data for this step is the DS after computing Face/Face interferences.
703 | No | Contents | Implementation |
704 | :---- | :---- | :---- |
705 | 1 | For each Face/Face interference *nFi, nFj*, retrieve @ref occt_algorithms_4_6 "FaceInfo". Create draft vertices from intersection points *VPk (k=1, 2…, NbVP)*, where *NbVP* is the number of new vertices, and the draft vertex *VPk* is created from an intersection point if *VPk ≠ Vm (m = 0, 1, 2… NbVm)*, where *Vm* is an existing vertex for the faces *nFi* and *nF,j* (*On* or *In* in terms of *TopoDs_Shape*), *NbVm* is the number of vertices existing on faces *nFi* and *nF,j* and ≠ - means non-coincidence in terms of @ref occt_algorithms_3_1_1 "Vertex/Vertex interference". | *BOPAlgo_PaveFiller::MakeBlocks()* |
706 | 2 | For each intersection curve *Cijk* | |
707 | 2.1 | Create paves PVc for the curve using existing vertices, i.e. vertices On or In (in terms of *FaceInfo*) for faces *nFi* and *nFj*. Append the paves *PVc* | *BOPAlgo_PaveFiller::PutPaveOnCurve()* and *BOPDS_PaveBlock::AppendExtPave()* |
708 | 2.2 | Create technological vertices *Vt*, which are the bounding points of an intersection curve (with the value of tolerance *Tol(Cijk)*). Each vertex *Vt* with parameter *Tt* on curve *Cijk* forms pave *PVt* on curve *Cijk*. Append technological paves. | *BOPAlgo_PaveFiller::PutBoundPaveOnCurve()* |
709 | 2.3 | Create pave blocks *PBk* for the curve using paves <i>(k=1, 2…, NbPB)</i>, where *NbPB* is the number of pave blocks | *BOPAlgo_PaveFiller::MakeBlocks()* |
710 | 2.4 | Build draft section edges *ESk* using the pave blocks <i>(k=1, 2…, NbES)</i>, where *NbES* is the number of draft section edges The draft section edge is created from a pave block *PBk* if *PBk* has state *In* or *On* for both faces *nFi* and *nF,j* and *PBk ≠ PBm (m=0, 1, 2… NbPBm)*, where *PBm* is an existing pave block for faces *nFi* and *nF,j* (*On* or *In* in terms of *FaceInfo*), *NbVm* is the number of existing pave blocks for faces *nFi* and *nF,j* and ≠ - means non-coincidence (in terms of @ref occt_algorithms_3_1_3 "Vertex/Face interference"). | *BOPTools_Tools::MakeEdge()* |
711 | 3 | Intersect the draft vertices *VPk (k=1, 2…, NbVP)* and the draft section edges *ESk (k=1, 2…, NbES)*. For this: a) create new object *PFn* of type *BOPAlgo_PaveFiller* with its own DS; b) use vertices *VPk* and edges *ESk* as arguments (in terms of @ref occt_algorithms_4_1 "Arguments") of *PFn*; c) invoke method *Perform()* for *PFn*. Resulting vertices *VPXk (k=1, 2… NbVPX)* and edges *ESXk (k=1, 2… NbESX)* are obtained via mapping between *VPk, ESk* and the results of *PVn*. | *BOPAlgo_PaveFiller::PostTreatFF()* |
712 | 4 | Update face info (sections about pave blocks and vertices) | *BOPAlgo_PaveFiller::PerformFF()* |
714 @subsection occt_algorithms_5_11 Build P-Curves
715 The input data for this step is the DS after building section edges.
717 | No | Contents | Implementation |
718 | :---- | :---- | :---- |
719 | 1 | For each Face/Face interference *nFi* and *nFj* build p-Curves on *nFi* and *nFj* for each section edge *ESXk*. | *BOPAlgo_PaveFiller::MakePCurves()* |
720 | 2 | For each pave block that is common for faces *nFi* and *nFj* build p-Curves on *nFi* and *nFj*. | *BOPAlgo_PaveFiller::MakePCurves()* |
722 @subsection occt_algorithms_5_12 Process Degenerated Edges
723 The input data for this step is the DS after building P-curves.
725 | No | Contents | Implementation |
726 | :---- | :---- | :---- |
727 | | For each degenerated edge *ED* having vertex *VD* | BOPAlgo_PaveFiller::ProcessDE() |
728 | 1 | Find pave blocks *PBi (i=1,2… NbPB)*, where *NbPB* is the number of pave blocks, that go through vertex *VD*. | *BOPAlgo_PaveFiller::FindPaveBlocks()* |
729 | 2 | Compute paves for the degenerated edge *ED* using a 2D curve of *ED* and a 2D curve of *PBi*. Form pave blocks *PBDi (i=1,2… NbPBD)*, where *NbPBD* is the number of the pave blocks for the degenerated edge *ED* | *BOPAlgo_PaveFiller::FillPaves()* |
730 | 3 | Build split edges *ESDi (i=1,2…NbESD)*, where *ESD* is the number of split edges, using the pave blocks *PBDi* | *BOPAlgo_PaveFiller:: MakeSplitEdge()* |
732 @section occt_algorithms_6 General description of the Building Part
734 Building Part (BP) is used to
735 * Build the result of the operation
736 * Provide history information (in terms of <i>\::Generated(), \::Modified()</i> and <i>\::IsDeleted()</i>)
737 BP uses the DS prepared by *BOPAlgo_PaveFiller* described at chapter 5 as input data.
738 BP is implemented in the following classes:
739 * *BOPAlgo_Builder* - for the General Fuse operator (GFA).
740 * *BOPAlgo_BOP* - for the Boolean Operation operator (BOA).
741 * *BOPAlgo_Section* - for the Section operator (SA).
743 @figure{/user_guides/boolean_operations/images/operations_image020.svg, "Diagram for BP classes"}
745 The class *BOPAlgo_BuilderShape* provides the interface for algorithms that have:
746 * A Shape as the result;
747 * History information (in terms of <i>\::Generated(), \::Modified()</i> and <i>\::IsDeleted()).</i>
749 @section occt_algorithms_7 General Fuse Algorithm
750 @subsection occt_algorithms_7_1 Arguments
751 The arguments of the algorithm are shapes (in terms of *TopoDS_Shape*). The main requirements for the arguments are described in @ref occt_algorithms_4 "Data Structure" chapter.
753 @subsection occt_algorithms_7_2 Results
755 During the operation argument *Si* can be split into several parts *Si1, Si2… Si1NbSp*, where *NbSp* is the number of parts. The set <i>(Si1, Si2… Si1NbSp)</i> is an image of argument *Si*.
756 * The result of the General Fuse operation is a compound. Each sub-shape of the compound corresponds to the certain argument shape S1, S2…Sn and has shared sub-shapes in accordance with interferences between the arguments.
757 * For the arguments of the type EDGE, FACE, SOLID the result contains split parts of the argument.
758 * For the arguments of the type WIRE, SHELL, COMPSOLID, COMPOUND the result contains the image of the shape of the corresponding type (i.e. WIRE, SHELL, COMPSOLID or COMPOUND).
759 The types of resulting shapes depend on the type of the corresponding argument participating in the operation. See the table below:
761 | No | Type of argument | Type of resulting shape | Comments |
762 | :--- | :---- | :--- | :--- |
763 | 1 | COMPOUND | COMPOUND | The resulting COMPOUND is built from images of sub-shapes of type COMPOUND COMPSOLID, SHELL, WIRE and VERTEX. Sets of split sub-shapes of type SOLID, FACE, EDGE. |
764 | 2 | COMPSOLID | COMPSOLID | The resulting COMPSOLID is built from split SOLIDs. |
765 | 3 | SOLID | Set of split SOLIDs | |
766 | 4 | SHELL | SHELL | The resulting SHELL is built from split FACEs |
767 | 5 | FACE | Set of split FACEs | |
768 | 6 | WIRE | WIRE | The resulting WIRE is built from split EDGEs |
769 | 7 | EDGE | Set of split EDGEs | |
770 | 8 | VERTEX | VERTEX | |
772 @subsection occt_algorithms_7_3 Examples
774 Please, have a look at the examples, which can help to better understand the definitions.
776 @subsubsection occt_algorithms_7_3_1 Case 1: Three edges intersecting at a point
778 Let us consider three edges: *E1, E2* and *E3* that intersect in one 3D point.
780 @figure{/user_guides/boolean_operations/images/operations_image021.svg, "Three Intersecting Edges"}
782 The result of the GFA operation is a compound containing 6 new edges: *E11, E12, E21, E22, E31*, and *E32*. These edges have one shared vertex *Vn1*.
785 * The argument edge *E1* has resulting split edges *E11* and *E12* (image of *E1*).
786 * The argument edge *E2* has resulting split edges *E21* and *E22* (image of *E2*).
787 * The argument edge *E3* has resulting split edges *E31* and *E32* (image of *E3*).
789 @subsubsection occt_algorithms_7_3_2 Case 2: Two wires and an edge
791 Let us consider two wires *W1 (Ew11, Ew12, Ew13)* and *W2 (Ew21, Ew22, Ew23)* and edge *E1*.
793 @figure{/user_guides/boolean_operations/images/operations_image022.svg, "Two wires and an edge"}
795 The result of the GF operation is a compound consisting of 2 wires: *Wn1 (Ew11, En1, En2, En3, Ew13)* and *Wn2 (Ew21, En2, En3, En4, Ew23)* and two edges: *E11* and *E12*.
798 * The argument *W1* has image *Wn1*.
799 * The argument *W2* has image *Wn2*.
800 * The argument edge *E1* has split edges *E11* and *E12*. (image of *E1*).
801 The edges *En1, En2, En3, En4* and vertex *Vn1* are new shapes created during the operation. Edge *Ew12* has split edges *En1, En2* and *En3* and edge *Ew22* has split edges *En2, En3* and *En4*.
803 @subsubsection occt_algorithms_7_3_3 Case 3: An edge intersecting with a face
805 Let us consider edge *E1* and face *F2*:
807 @figure{/user_guides/boolean_operations/images/operations_image023.svg, "An edge intersecting with a face"}
809 The result of the GF operation is a compound consisting of 3 shapes:
810 * Split edge parts *E11* and *E12* (image of *E1*).
811 * New face *F21* with internal edge *E12* (image of *F2*).
813 @subsubsection occt_algorithms_7_3_4 Case 4: An edge lying on a face
815 Let us consider edge *E1* and face *F2*:
817 @figure{/user_guides/boolean_operations/images/operations_image024.svg, "An edge lying on a face"}
819 The result of the GF operation is a compound consisting of 5 shapes:
820 * Split edge parts *E11, E12* and *E13* (image of *E1*).
821 * Split face parts *F21* and *F22* (image of *F2*).
824 @subsubsection occt_algorithms_7_3_5 Case 5: An edge and a shell
826 Let us consider edge *E1* and shell *Sh2* that consists of 2 faces: *F21* and *F22*
828 @figure{/user_guides/boolean_operations/images/operations_image025.svg, "An edge and a shell"}
830 The result of the GF operation is a compound consisting of 5 shapes:
831 * Split edge parts *E11, E12 , E13* and *E14* (image of *E1*).
832 * Image shell *Sh21* (that contains split face parts *F211, F212, F221* and *F222*).
834 @subsubsection occt_algorithms_7_3_6 Case 6: A wire and a shell
836 Let us consider wire *W1 (E1, E2, E3, E4)* and shell *Sh2 (F21, F22)*.
837 @figure{/user_guides/boolean_operations/images/operations_image026.svg, "A wire and a shell"}
839 The result of the GF operation is a compound consisting of 2 shapes:
841 * Image wire *W11* that consists of split edge parts from wire *W1: E11, E12, E13* and *E14*.
842 * Image shell *Sh21* that contains split face parts: *F211, F212, F213, F221, F222* and *F223*.
844 @subsubsection occt_algorithms_7_3_7 Case 7: Three faces
846 Let us consider 3 faces: *F1, F2* and *F3*. @figure{/user_guides/boolean_operations/images/operations_image027.png, "Three faces"}
848 The result of the GF operation is a compound consisting of 7 shapes:
849 * Split face parts: *Fn1, Fn2, Fn3, Fn4, Fn5, Fn6* and *Fn7*.
851 @subsubsection occt_algorithms_7_3_8 Case 8: A face and a shell
853 Let us consider shell *Sh1 (F11, F12, F13)* and face *F2*.
854 @figure{/user_guides/boolean_operations/images/operations_image028.png, "A face and a shell"}
856 The result of the GF operation is a compound consisting of 4 shapes:
857 * Image shell *Sh11* that consists of split face parts from shell *Sh1: Fn1, Fn2, Fn3, Fn4, Fn5* and *Fn6*.
858 * Split parts of face *F2: Fn3, Fn6* and *Fn7*.
860 @subsubsection occt_algorithms_7_3_9 Case 9: A shell and a solid
862 Let us consider shell *Sh1 (F11, F12…F16)* and solid *So2*. @figure{/user_guides/boolean_operations/images/operations_image029.png, "A shell and a solid: arguments"}
864 The result of the GF operation is a compound consisting of 2 shapes:
865 * Image shell *Sh11* consisting of split face parts of *Sh1: Fn1, Fn2 ... Fn8.*
866 * Solid *So21* with internal shell. (image of *So2*).
867 @figure{/user_guides/boolean_operations/images/operations_image030.png, "A shell and a solid: results"}
869 @subsubsection occt_algorithms_7_3_10 Case 10: A compound and a solid
871 Let us consider compound *Cm1* consisting of 2 solids *So11* and *So12*) and solid *So2*.
872 @figure{/user_guides/boolean_operations/images/operations_image031.png, "A compound and a solid: arguments"}
874 The result of the GF operation is a compound consisting of 4 shapes:
875 * Image compound *Cm11* consisting of split solid parts from *So11* and *So12 (Sn1, Sn2, Sn3, Sn4)*.
876 * Split parts of solid *So2 (Sn2, Sn3, Sn5)*.
878 @figure{/user_guides/boolean_operations/images/operations_image032.png, "A compound and a solid: results"}
880 @subsection occt_algorithms_7_4 Class BOPAlgo_Builder
882 GFA is implemented in the class *BOPAlgo_Builder*.
884 @subsubsection occt_algorithms_7_4_1 Fields
886 The main fields of the class are described in the Table:
890 | *myPaveFiller* | Pointer to the *BOPAlgo_PaveFiller* object |
891 | *myDS* | Pointer to the *BOPDS_DS* object |
892 | *myContext* | Pointer to the intersection Context |
893 | *myImages* | The Map between the source shape and its images |
894 | *myShapesSD* | The Map between the source shape (or split part of source shape) and the shape (or part of shape) that will be used in result due to same domain property. |
896 @subsubsection occt_algorithms_7_4_2 Initialization
898 The input data for this step is a *BOPAlgo_PaveFiller* object (in terms of @ref occt_algorithms_5 "Intersection") at the state after @ref occt_algorithms_5_12 "Processing of degenerated edges" with the corresponding DS.
900 | No | Contents | Implementation |
901 | :---- | :---- | :---- |
902 | 1 | Check the readiness of the DS and *BOPAlgo_PaveFiller*. | *BOPAlgo_Builder::CheckData()* |
903 | 2 | Build an empty result of type Compound. | *BOPAlgo_Builder::Prepare()* |
905 @subsubsection occt_algorithms_7_4_3 Build Images for Vertices
907 The input data for this step is *BOPAlgo_Builder* object after Initialisation.
909 | No | Contents | Implementation |
910 | :--- | :--- | :--- |
911 | 1 | Fill *myShapesSD* by SD vertices using the information from the DS. | *BOPAlgo_Builder::FillImagesVertices()* |
913 @subsubsection occt_algorithms_7_4_4 Build Result of Type Vertex
915 The input data for this step is *BOPAlgo_Builder* object after building images for vertices and *Type*, which is the shape type (*TopAbs_VERTEX*).
917 | No | Contents | Implementation |
918 | :--- | :--- | :----- |
919 | 1 | For the arguments of type *Type*. If there is an image for the argument: add the image to the result. If there is no image for the argument: add the argument to the result. | *BOPAlgo_Builder::BuildResult()* |
921 @subsubsection occt_algorithms_7_4_5 Build Images for Edges
923 The input data for this step is *BOPAlgo_Builder object* after building result of type vertex.
925 | No | Contents | Implementation |
926 | :---- | :---- | :----- |
927 | 1 | For all pave blocks in the DS. Fill *myImages* for the original edge *E* by split edges *ESPi* from pave blocks. In case of common blocks on edges, use edge *ESPSDj* that corresponds to the leading pave block and fill *myShapesSD* by the pairs *ESPi/ESPSDj*. | *BOPAlgo_Builder::FillImagesEdges()* |
929 @subsubsection occt_algorithms_7_4_6 Build Result of Type Edge
931 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex", but for the type *Edge*.
933 @subsubsection occt_algorithms_7_4_7 Build Images for Wires
935 The input data for this step is:
936 * *BOPAlgo_Builder* object after building result of type *Edge*;
937 * Original Shape - Wire
938 * *Type* - the shape type <i>(TopAbs_WIRE).</i>
940 | No | Contents | Implementation |
941 | :---- | :---- | :----- |
942 | 1 | For all arguments of the type *Type*. Create a container C of the type *Type*. | *BOPAlgo_Builder::FillImagesContainers()* |
943 | 2 | Add to C the images or non-split parts of the *Original Shape*, taking into account its orientation. | *BOPAlgo_Builder::FillImagesContainers()* *BOPTools_Tools::IsSplitToReverse()* |
944 | 3 | Fill *myImages* for the *Original Shape* by the information above. | *BOPAlgo_Builder::FillImagesContainers()* |
946 @subsubsection occt_algorithms_7_4_8 Build Result of Type Wire
948 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex" but for the type *Wire*.
950 @subsubsection occt_algorithms_7_4_9 Build Images for Faces
952 The input data for this step is *BOPAlgo_Builder* object after building result of type *Wire*.
954 | No | Contents | Implementation |
955 | :--- | :--- | :--- |
956 | 1 | Build Split Faces for all interfered DS shapes *Fi* of type *FACE*. | |
957 | 1.1 | Collect all edges or their images of *Fi(ESPij)*. | *BOPAlgo_Builder::BuildSplitFaces()* |
958 | 1.2 | Impart to ESPij the orientation to be coherent with the original one. | *BOPAlgo_Builder::BuildSplitFaces()* |
959 | 1.3 | Collect all section edges *SEk* for *Fi*. | *BOPAlgo_Builder::BuildSplitFaces()* |
960 | 1.4 | Build split faces for *Fi (Fi1, Fi2…FiNbSp)*, where *NbSp* is the number of split parts (see @ref occt_algorithms_7_2 "Building faces from a set of edges" for more details). | *BOPAlgo_BuilderFace* |
961 | 1.5 | Impart to <i>(Fi1, Fi2…FiNbSp)</i> the orientation coherent with the original face *Fi*. | *BOPAlgo_Builder::BuildSplitFaces()* |
962 | 1.6 | Fill the map mySplits with *Fi/(Fi1, Fi2…FiNbSp)* | *BOPAlgo_Builder::BuildSplitFaces()* |
963 | 2 | Fill Same Domain faces | *BOPAlgo_Builder::FillSameDomainFaces* |
964 | 2.1 | Find and collect in the contents of *mySplits* the pairs of same domain split faces <i>(Fij, Fkl)m</i>, where *m* is the number of pairs. | *BOPAlgo_Builder::FillSameDomainFaces* *BOPTools_Tools::AreFacesSameDomain()* |
965 | 2.2 | Compute the connexity chains 1) of same domain faces <i>(F1C, F2C… FnC)k, C=0, 1…nCs,</i> where *nCs* is the number of connexity chains. | *BOPAlgo_Builder::FillSameDomainFaces()* |
966 | 2.3 | Fill *myShapesSD* using the chains <i>(F1C, F2C… FnC)k</i> | *BOPAlgo_Builder::FillSameDomainFaces()* |
967 | 2.4 | Add internal vertices to split faces. | *BOPAlgo_Builder::FillSameDomainFaces()* |
968 | 2.5 | Fill *myImages* using *myShapesSD* and *mySplits*. | *BOPAlgo_Builder::FillSameDomainFaces()* |
971 The example of chains of same domain faces is given in the image:
973 @figure{/user_guides/boolean_operations/images/operations_image033.svg, "Chains of same domain faces"}
975 * The pairs of same domain faces are: <i>(F11, F21), (F22, F31), (F41, F51) , (F41, F6)</i> and <i>(F51, F6)</i>.
976 * The pairs produce the three chains: <i>(F11, F21), (F22, F31)</i> and <i>(F41, F51, F6)</i>.
978 @subsubsection occt_algorithms_7_4_10 Build Result of Type Face
979 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex" but for the type *Face*.
981 @subsubsection occt_algorithms_7_4_11 Build Images for Shells
982 The input data for this step is:
983 * *BOPAlgo_Builder* object after building result of type face;
984 * *Original Shape* - Shell;
985 * *Type* - the type of the shape <i>(TopAbs_SHELL)</i>.
987 The procedure is the same as for building images for wires.
989 @subsubsection occt_algorithms_7_4_12 Build Result of Type Shell
990 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex" but for the type *Shell*.
992 @subsubsection occt_algorithms_7_4_13 Build Images for Solids
994 The input data for this step is *BOPAlgo_Builder* object after building result of type *Shell*.
996 The following procedure is executed for all interfered DS shapes *Si* of type *SOLID*.
998 | No | Contents | Implementation |
999 | :--- | :--- | :--- |
1000 | 1 | Collect all images or non-split parts for all faces <i>(FSPij)</i> that have 3D state *In Si*. | *BOPAlgo_Builder::FillIn3DParts ()* |
1001 | 2 | Collect all images or non-split parts for all faces of *Si* | *BOPAlgo_Builder::BuildSplitSolids()* |
1002 | 3 | Build split solids for *Si -> (Si1, Si2…SiNbSp)*, where *NbSp* is the number of split parts (see @ref occt_algorithms_7_2 "Building faces from a set of edges" for more details) | *BOPAlgo_BuilderSolid* |
1003 | 4 | Fill the map Same Domain solids *myShapesSD* | *BOPAlgo_Builder::BuildSplitSolids()* |
1004 | 5 | Fill the map *myImages* | *BOPAlgo_Builder::BuildSplitSolids()* |
1005 | 6 | Add internal vertices to split solids | *BOPAlgo_Builder::FillInternalShapes()* |
1007 @subsubsection occt_algorithms_7_4_14 Build Result of Type Solid
1008 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex", but for the type Solid.
1010 @subsubsection occt_algorithms_7_4_15 Build Images for Type CompSolid
1012 The input data for this step is:
1013 * *BOPAlgo_Builder* object after building result of type solid;
1014 * *Original Shape* - Compsolid;
1015 * *Type* - the type of the shape <i>(TopAbs_COMPSOLID)</i>.
1017 The procedure is the same as for building images for wires.
1019 @subsubsection occt_algorithms_7_4_16 Build Result of Type Compsolid
1020 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex", but for the type Compsolid.
1022 @subsubsection occt_algorithms_7_4_17 Build Images for Compounds
1023 The input data for this step is as follows:
1024 * *BOPAlgo_Builder* object after building results of type compsolid;
1025 * *Original Shape* - Compound;
1026 * *Type* - the type of the shape <i>(TopAbs_COMPOUND)</i>.
1028 The procedure is the same as for building images for wires.
1030 @subsubsection occt_algorithms_7_4_18 Build Result of Type Compound
1032 This step is the same as @ref occt_algorithms_7_4_4 "Building Result of Type Vertex", but for the type Compound.
1034 @subsubsection occt_algorithms_7_4_19 Post-Processing
1035 The purpose of the step is to correct tolerances of the result to provide its validity in terms of *BRepCheck_Analyzer.*
1037 The input data for this step is a *BOPAlgo_Builder* object after building result of type compound.
1039 | No | Contents | Implementation |
1040 | :---- | :---- | :----- |
1041 | 1 | Correct tolerances of vertices on curves | *BOPTools_Tools::CorrectPointOnCurve()* |
1042 | 2 | Correct tolerances of edges on faces | *BOPTools_Tools::CorrectCurveOnSurface()* |
1045 @section occt_algorithms_9 Boolean Operations Algorithm
1047 @subsection occt_algorithms_9_1 Arguments
1049 * The arguments of BOA are shapes in terms of *TopoDS_Shape*. The main requirements for the arguments are described in the @ref occt_algorithms_4 "Data Structure"
1050 * There are two groups of arguments in BOA:
1051 * Objects <i>(S1=S11, S12, ...)</i>;
1052 * Tools <i>(S2=S21, S22, ...)</i>.
1053 * The following table contains the values of dimension for different types of arguments:
1055 | No | Type of Argument | Index of Type | Dimension |
1056 | :---- | :---- | :----- | :---- |
1057 | 1 | COMPOUND | 0 | One of 0, 1, 2, 3 |
1058 | 2 | COMPSOLID | 1 | 3 |
1059 | 3 | SOLID | 2 | 3 |
1060 | 4 | SHELL | 3 | 2 |
1061 | 5 | FACE | 4 | 2 |
1062 | 6 | WIRE | 5 | 1 |
1063 | 7 | EDGE | 6 | 1 |
1064 | 8 | VERTEX | 7 | 0 |
1066 * For Boolean operation Fuse all arguments should have equal dimensions.
1067 * For Boolean operation Cut the minimal dimension of *S2* should not be less than the maximal dimension of *S1*.
1068 * For Boolean operation Common the arguments could have any dimension.
1070 @subsection occt_algorithms_9_3 Results. General Rules
1072 * The result of the Boolean operation is a compound (if defined). Each sub-shape of the compound has shared sub-shapes in accordance with interferences between the arguments.
1073 * The content of the result depends on the type of the operation (Common, Fuse, Cut12, Cut21) and the dimensions of the arguments.
1074 * The result of the operation Fuse is defined for arguments *S1* and *S2* that have the same dimension value : *Dim(S1)=Dim(S2)*. If the arguments have different dimension values the result of the operation Fuse is not defined. The dimension of the result is equal to the dimension of the arguments. For example, it is impossible to fuse an edge and a face.
1075 * The result of the operation Fuse for arguments *S1* and *S2* contains the parts of arguments that have states **OUT** relative to the opposite arguments.
1076 * The result of the operation Fuse for arguments *S1* and *S2* having dimension value 3 (Solids) is refined by removing all possible internal faces to provide minimal number of solids.
1077 * The result of the operation Common for arguments *S1* and *S2* is defined for all values of the dimensions of the arguments. The result can contain the shapes of different dimension, but the minimal dimension of the result will be equal to the minimal dimension of the arguments. For example, the result of the operation Common between edges cannot be a vertex.
1078 * The result of the operation Common for the arguments *S1* and *S2* contains the parts of the argument that have states **IN** and **ON** relative to the opposite argument.
1079 * The result of the operation Cut is defined for arguments *S1* and *S2* that have values of dimensions *Dim(S2)* that should not be less than *Dim(S1)*. The result can contain the shapes of different dimension, but the minimal dimension of the result will be equal to the minimal dimension of the objects *Dim(S1)*. The result of the operation *Cut12* is not defined for other cases. For example, it is impossible to cut an edge from a solid, because a solid without an edge is not defined.
1080 * The result of the operation *Cut12* for arguments *S1* and *S2* contains the parts of argument *S1* that have state **OUT** relative to the opposite argument *S2*.
1081 * The result of the operation *Cut21* for arguments *S1* and *S2* contains the parts of argument *S2* that have state **OUT** relative to the opposite argument *S1*.
1082 * For the argumenst of collection type (WIRE, SHELL, COMPSOLID) the type will be passed in the result. For example, the result of Common operation between Shell and Wire will be compound containing Wire.
1084 @subsection occt_algorithms_9_4 Examples
1086 @subsubsection occt_algorithms_9_4_1 Case 1: Two Vertices
1088 Let us consider two interfering vertices *V1* and *V2*:
1090 @figure{/user_guides/boolean_operations/images/boolean_image001.svg}
1092 * The result of *Fuse* operation is the compound that contains new vertex *V*.
1094 @figure{/user_guides/boolean_operations/images/boolean_image002.svg}
1096 * The result of *Common* operation is a compound containing new vertex *V*.
1098 * The result of *Cut12* operation is an empty compound.
1099 * The result of *Cut21* operation is an empty compound.
1101 @subsubsection occt_algorithms_9_4_2 Case 2: A Vertex and an Edge
1103 Let us consider vertex *V1* and the edge *E2*, that intersect in a 3D point:
1105 @figure{/user_guides/boolean_operations/images/boolean_image004.png}
1107 * The result of *Fuse* operation is result is not defined because the dimension of the vertex (0) is not equal to the dimension of the edge (1).
1109 * The result of *Common* operation is a compound containing vertex *V<sub>1</sub>* as the argument *V<sub>1</sub>* has a common part with edge *E2*.
1111 @figure{/user_guides/boolean_operations/images/boolean_image005.png}
1113 * The result of *Cut12* operation is an empty compound.
1114 * The result of *Cut21* operation is not defined because the dimension of the vertex (0) is less than the dimension of the edge (1).
1116 @subsubsection occt_algorithms_9_4_3 Case 3: A Vertex and a Face
1118 Let us consider vertex *V1* and face *F2*, that intersect in a 3D point:
1120 @figure{/user_guides/boolean_operations/images/boolean_image006.png}
1122 * The result of *Fuse* operation is not defined because the dimension of the vertex (0) is not equal to the dimension of the face (2).
1124 * The result of *Common* operation is a compound containing vertex *V<sub>1</sub>* as the argument *V<sub>1</sub>* has a common part with face *F2*.
1126 @figure{/user_guides/boolean_operations/images/boolean_image007.png}
1128 * The result of *Cut12* operation is an empty compound.
1129 * The result of *Cut21* operation is not defined because the dimension of the vertex (0) is less than the dimension of the face (2).
1131 @subsubsection occt_algorithms_9_4_4 Case 4: A Vertex and a Solid
1133 Let us consider vertex *V1* and solid *S2*, that intersect in a 3D point:
1135 @figure{/user_guides/boolean_operations/images/boolean_image008.png}
1137 * The result of *Fuse* operation is not defined because the dimension of the vertex (0) is not equal to the dimension of the solid (3).
1139 * The result of *Common* operation is a compound containing vertex *V<sub>1</sub>* as the argument *V<sub>1</sub>* has a common part with solid *S2*.
1141 @figure{/user_guides/boolean_operations/images/boolean_image009.png}
1143 * The result of *Cut12* operation is an empty compound.
1144 * The result of *Cut21* operation is not defined because the dimension of the vertex (0) is less than the dimension of the solid (3).
1146 @subsubsection occt_algorithms_9_4_5 Case 5: Two edges intersecting at one point
1148 Let us consider edges *E1* and *E2* that intersect in a 3D point:
1150 @figure{/user_guides/boolean_operations/images/boolean_image010.svg}
1152 * The result of *Fuse* operation is a compound containing split parts of arguments i.e. 4 new edges *E11, E12, E21*, and *E22*. These edges have one shared vertex *Vn1*.
1154 * argument edge *E1* has resulting split edges *E11* and *E12* (image of *E1*);
1155 * argument edge *E2* has resulting split edges *E21* and *E22* (image of *E2*).
1157 @figure{/user_guides/boolean_operations/images/boolean_image011.svg}
1159 * The result of *Common* operation is an empty compound because the dimension (0) of the common part between the edges (vertex) is less than the dimension of the arguments (1).
1161 * The result of *Cut12* operation is a compound containing split parts of the argument *E1*, i.e. 2 new edges *E11* and *E12*. These edges have one shared vertex *Vn1*.
1163 In this case the argument edge *E1* has resulting split edges *E11* and *E12* (image of *E1*).
1165 @figure{/user_guides/boolean_operations/images/boolean_image012.svg}
1167 * The result of *Cut21* operation is a compound containing split parts of the argument *E2*, i.e. 2 new edges *E21* and *E12*. These edges have one shared vertex *Vn1*.
1169 In this case the argument edge *E2* has resulting split edges *E21* and *E22* (image of *E2*).
1171 @figure{/user_guides/boolean_operations/images/boolean_image013.svg}
1173 @subsubsection occt_algorithms_9_4_6 Case 6: Two edges having a common block
1175 Let us consider edges *E1* and *E2* that have a common block:
1177 @figure{/user_guides/boolean_operations/images/boolean_image014.svg}
1179 * The result of *Fuse* operation is a compound containing split parts of arguments i.e. 3 new edges *E11*, *E12* and *E22*. These edges have two shared vertices.
1181 * argument edge *E1* has resulting split edges *E11* and *E12* (image of *E1*);
1182 * argument edge *E2* has resulting split edges *E21* and *E22* (image of *E2*);
1183 * edge *E12* is common for the images of *E1* and *E2*.
1185 @figure{/user_guides/boolean_operations/images/boolean_image015.svg}
1187 * The result of *Common* operation is a compound containing split parts of arguments i.e. 1 new edge *E12*. In this case edge *E12* is common for the images of *E1* and *E2*.
1188 The common part between the edges (edge) has the same dimension (1) as the dimension of the arguments (1).
1190 @figure{/user_guides/boolean_operations/images/boolean_image016.svg}
1192 * The result of *Cut12* operation is a compound containing a split part of argument *E1*, i.e. new edge *E11*.
1194 @figure{/user_guides/boolean_operations/images/boolean_image017.svg}
1196 * The result of *Cut21* operation is a compound containing a split part of argument *E2*, i.e. new edge *E22*.
1198 @figure{/user_guides/boolean_operations/images/boolean_image018.svg}
1201 @subsubsection occt_algorithms_9_4_7 Case 7: An Edge and a Face intersecting at a point
1203 Let us consider edge *E1* and face *F2* that intersect at a 3D point:
1205 @figure{/user_guides/boolean_operations/images/boolean_image019.png}
1207 * The result of *Fuse* operation is not defined because the dimension of the edge (1) is not equal to the dimension of the face (2).
1209 * The result of *Common* operation is an empty compound because the dimension (0) of the common part between the edge and face (vertex) is less than the dimension of the arguments (1).
1211 * The result of *Cut12* operation is a compound containing split parts of the argument *E1*, i.e. 2 new edges *E11* and *E12*.
1213 In this case the argument edge *E1* has no common parts with the face *F2* so the whole image of *E1* is in the result.
1215 @figure{/user_guides/boolean_operations/images/boolean_image020.png}
1217 * The result of *Cut21* operation is not defined because the dimension of the edge (1) is less than the dimension of the face (2).
1219 @subsubsection occt_algorithms_9_4_8 Case 8: A Face and an Edge that have a common block
1221 Let us consider edge *E1* and face *F2* that have a common block:
1223 @figure{/user_guides/boolean_operations/images/boolean_image021.png}
1225 * The result of *Fuse* operation is not defined because the dimension of the edge (1) is not equal to the dimension of the face (2).
1227 * The result of *Common* operation is a compound containing a split part of the argument *E1*, i.e. new edge *E12*.
1229 In this case the argument edge *E1* has a common part with face *F2* so the corresponding part of the image of *E1* is in the result. The yellow square is not a part of the result. It only shows the place of *F2*.
1231 @figure{/user_guides/boolean_operations/images/boolean_image022.png}
1233 * The result of *Cut12* operation is a compound containing split part of the argument *E1*, i.e. new edge *E11*.
1235 In this case the argument edge *E1* has a common part with face *F2* so the corresponding part is not included into the result. The yellow square is not a part of the result. It only shows the place of F2.
1237 @figure{/user_guides/boolean_operations/images/boolean_image023.png}
1239 * The result of *Cut21* operation is not defined because the dimension of the edge (1) is less than the dimension of the face (2).
1241 @subsubsection occt_algorithms_9_4_9 Case 9: An Edge and a Solid intersecting at a point
1243 Let us consider edge *E1* and solid *S2* that intersect at a point:
1245 @figure{/user_guides/boolean_operations/images/boolean_image024.png}
1247 * The result of *Fuse* operation is not defined because the dimension of the edge (1) is not equal to the dimension of the solid (3).
1249 * The result of *Common* operation is a compound containing a split part of the argument *E1*, i.e. new edge *E12*.
1251 In this case the argument edge *E1* has a common part with solid *S2* so the corresponding part of the image of *E1* is in the result. The yellow square is not a part of the result. It only shows the place of *S2*.
1253 @figure{/user_guides/boolean_operations/images/boolean_image025.png}
1255 * The result of *Cut12* operation is a compound containing split part of the argument *E1*, i.e. new edge *E11*.
1257 In this case the argument edge *E1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow square is not a part of the result. It only shows the place of *S2*.
1259 @figure{/user_guides/boolean_operations/images/boolean_image071.png}
1261 * The result of *Cut21* operation is not defined because the dimension of the edge (1) is less than the dimension of the solid (3).
1263 @subsubsection occt_algorithms_9_4_10 Case 10: An Edge and a Solid that have a common block
1265 Let us consider edge *E1* and solid *S2* that have a common block:
1267 @figure{/user_guides/boolean_operations/images/boolean_image072.png}
1269 * The result of *Fuse* operation is not defined because the dimension of the edge (1) is not equal to the dimension of the solid (3).
1271 * The result of *Common* operation is a compound containing a split part of the argument *E1*, i.e. new edge *E12*.
1273 In this case the argument edge *E1* has a common part with solid *S2* so the corresponding part of the image of *E1* is in the result. The yellow square is not a part of the result. It only shows the place of *S2*.
1275 @figure{/user_guides/boolean_operations/images/boolean_image073.png}
1277 * The result of *Cut12* operation is a compound containing split part of the argument *E1*, i.e. new edge *E11*.
1279 In this case the argument edge *E1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow square is not a part of the result. It only shows the place of *S2*.
1281 @figure{/user_guides/boolean_operations/images/boolean_image026.png}
1283 * The result of *Cut21* operation is not defined because the dimension of the edge (1) is less than the dimension of the solid (3).
1285 @subsubsection occt_algorithms_9_4_11 Case 11: Two intersecting faces
1287 Let us consider two intersecting faces *F1* and *F2*:
1289 @figure{/user_guides/boolean_operations/images/boolean_image027.png}
1291 * The result of *Fuse* operation is a compound containing split parts of arguments i.e. 2 new faces *F11* and *F21*. These faces have one shared edge *En1*.
1293 @figure{/user_guides/boolean_operations/images/boolean_image028.png}
1296 * The result of *Common* operation is an empty compound because the dimension (1) of the common part between *F1* and *F2* (edge) is less than the dimension of arguments (2).
1298 * The result of *Cut12* operation is a compound containing split part of the argument *F1*, i.e. new face *F11*.
1300 @figure{/user_guides/boolean_operations/images/boolean_image029.png}
1302 * The result of *Cut21* operation is a compound containing split parts of the argument *F2*, i.e. 1 new face *F21*.
1304 @figure{/user_guides/boolean_operations/images/boolean_image030.png}
1306 @subsubsection occt_algorithms_9_4_12 Case 12: Two faces that have a common part
1308 Let us consider two faces *F1* and *F2* that have a common part:
1310 @figure{/user_guides/boolean_operations/images/boolean_image031.png}
1312 * The result of *Fuse* operation is a compound containing split parts of arguments, i.e. 3 new faces: *F11*, *F12* and *F22*. These faces are shared through edges In this case:
1313 * the argument edge *F1* has resulting split faces *F11* and *F12* (image of *F1*)
1314 * the argument face *F2* has resulting split faces *F12* and *F22* (image of *F2*)
1315 * the face *F12* is common for the images of *F1* and *F2*.
1317 @figure{/user_guides/boolean_operations/images/boolean_image032.png}
1319 * The result of *Common* operation is a compound containing split parts of arguments i.e. 1 new face *F12*.
1320 In this case: face *F12* is common for the images of *F1* and *F2*.
1321 The common part between the faces (face) has the same dimension (2) as the dimension of the arguments (2).
1324 @figure{/user_guides/boolean_operations/images/boolean_image033.png}
1326 * The result of *Cut12* operation is a compound containing split part of the argument *F1*, i.e. new face *F11*.
1328 @figure{/user_guides/boolean_operations/images/boolean_image034.png}
1330 * The result of *Cut21* operation is a compound containing split parts of the argument *F2*, i.e. 1 new face *F21*.
1332 @figure{/user_guides/boolean_operations/images/boolean_image035.png}
1334 @subsubsection occt_algorithms_9_4_13 Case 13: Two faces that have a common edge
1336 Let us consider two faces *F1* and *F2* that have a common edge:
1338 @figure{/user_guides/boolean_operations/images/boolean_image036.png}
1340 * The result of *Fuse* operation is a compound containing split parts of arguments, i.e. 2 new faces: *F11* and *F21*. These faces have one shared edge *En1*.
1342 @figure{/user_guides/boolean_operations/images/boolean_image037.png}
1344 * The result of *Common* operation is an empty compound because the dimension (1) of the common part between *F1* and *F2* (edge)is less than the dimension of the arguments (2)
1346 * The result of *Cut12* operation is a compound containing split part of the argument *F1*, i.e. new face *F11*. The vertices are shown just to clarify the fact that the edges are spitted.
1348 @figure{/user_guides/boolean_operations/images/boolean_image038.png}
1350 * The result of *Cut21* operation is a compound containing split parts of the argument *F2*, i.e. 1 new face *F21*. The vertices are shown just to clarify the fact that the edges are spitted.
1352 @figure{/user_guides/boolean_operations/images/boolean_image039.png}
1354 @subsubsection occt_algorithms_9_4_14 Case 14: Two faces that have a common vertex
1356 Let us consider two faces *F1* and *F2* that have a common vertex:
1358 @figure{/user_guides/boolean_operations/images/boolean_image040.png}
1360 * The result of *Fuse* operation is a compound containing split parts of arguments, i.e. 2 new faces: *F11* and *F21*. These faces have one shared vertex *Vn1*.
1362 @figure{/user_guides/boolean_operations/images/boolean_image041.png}
1364 * The result of *Common* operation is an empty compound because the dimension (0) of the common part between *F1* and *F2* (vertex) is less than the dimension of the arguments (2)
1366 * The result of *Cut12* operation is a compound containing split part of the argument *F1*, i.e. new face *F11*.
1368 @figure{/user_guides/boolean_operations/images/boolean_image042.png}
1370 * The result of *Cut21* operation is a compound containing split parts of the argument *F2*, i.e. 1 new face *F21*.
1372 @figure{/user_guides/boolean_operations/images/boolean_image043.png}
1375 @subsubsection occt_algorithms_9_4_15 Case 15: A Face and a Solid that have an intersection curve.
1377 Let us consider face *F1* and solid *S2* that have an intersection curve:
1379 @figure{/user_guides/boolean_operations/images/boolean_image044.png}
1381 * The result of *Fuse* operation is not defined because the dimension of the face (2) is not equal to the dimension of the solid (3).
1383 * The result of *Common* operation is a compound containing split part of the argument *F1*. In this case the argument face *F1* has a common part with solid *S2*, so the corresponding part of the image of *F1* is in the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1385 @figure{/user_guides/boolean_operations/images/boolean_image045.png}
1387 * The result of *Cut12* operation is a compound containing split part of the argument *F1*. In this case argument face *F1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1389 @figure{/user_guides/boolean_operations/images/boolean_image046.png}
1391 * The result of *Cut21* operation is is not defined because the dimension of the face (2) is less than the dimension of the solid (3).
1393 @subsubsection occt_algorithms_9_4_16 Case 16: A Face and a Solid that have overlapping faces.
1395 Let us consider face *F1* and solid *S2* that have overlapping faces:
1397 @figure{/user_guides/boolean_operations/images/boolean_image047.png}
1399 * The result of *Fuse* operation is not defined because the dimension of the face (2) is not equal to the dimension of the solid (3).
1401 * The result of *Common* operation is a compound containing split part of the argument *F1*. In this case the argument face *F1* has a common part with solid *S2*, so the corresponding part of the image of *F1* is included in the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1403 @figure{/user_guides/boolean_operations/images/boolean_image048.png}
1405 * The result of *Cut12* operation is a compound containing split part of the argument *F1*. In this case argument face *F1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1407 @figure{/user_guides/boolean_operations/images/boolean_image049.png}
1409 * The result of *Cut21* operation is is not defined because the dimension of the face (2) is less than the dimension of the solid (3).
1412 @subsubsection occt_algorithms_9_4_17 Case 17: A Face and a Solid that have overlapping edges.
1414 Let us consider face *F1* and solid *S2* that have overlapping edges:
1416 @figure{/user_guides/boolean_operations/images/boolean_image050.png}
1418 * The result of *Fuse* operation is not defined because the dimension of the face (2) is not equal to the dimension of the solid (3).
1420 * The result of *Common* operation is an empty compound because the dimension (1) of the common part between *F1* and *S2* (edge) is less than the lower dimension of the arguments (2).
1422 * The result of *Cut12* operation is a compound containing split part of the argument *F1*. In this case argument face *F1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1424 @figure{/user_guides/boolean_operations/images/boolean_image051.png}
1426 * The result of *Cut21* operation is is not defined because the dimension of the face (2) is less than the dimension of the solid (3).
1428 @subsubsection occt_algorithms_9_4_18 Case 18: A Face and a Solid that have overlapping vertices.
1430 Let us consider face *F1* and solid *S2* that have overlapping vertices:
1432 @figure{/user_guides/boolean_operations/images/boolean_image052.png}
1434 * The result of *Fuse* operation is not defined because the dimension of the face (2) is not equal to the dimension of the solid (3).
1436 * The result of *Common* operation is an empty compound because the dimension (1) of the common part between *F1* and *S2* (vertex) is less than the lower dimension of the arguments (2).
1438 * The result of *Cut12* operation is a compound containing split part of the argument *F1*. In this case argument face *F1* has a common part with solid *S2* so the corresponding part is not included into the result. The yellow contour is not a part of the result. It only shows the place of *S2*.
1440 @figure{/user_guides/boolean_operations/images/boolean_image053.png}
1442 * The result of *Cut21* operation is is not defined because the dimension of the face (2) is less than the dimension of the solid (3).
1444 @subsubsection occt_algorithms_9_4_19 Case 19: Two intersecting Solids.
1446 Let us consider two intersecting solids *S1* and *S2*:
1448 @figure{/user_guides/boolean_operations/images/boolean_image054.png}
1450 * The result of *Fuse* operation is a compound composed from the split parts of arguments *S11, S12* and *S22* <i>(Cut12, Common, Cut21)</i>. All inner webs are removed, so the result is one new solid *R*.
1452 @figure{/user_guides/boolean_operations/images/boolean_image055.png}
1454 * The result of *Common* operation is a compound containing split parts of arguments i.e. one new solid *S12*. In this case solid *S12* is common for the images of *S1* and *S2*. The common part between the solids (solid) has the same dimension (3) as the dimension of the arguments (3). The yellow contour is not a part of the result. It only shows the place of *S1*.
1456 @figure{/user_guides/boolean_operations/images/boolean_image056.png}
1458 * The result of *Cut12* operation is a compound containing split part of the argument *S1*, i.e. 1 new solid *S11*.
1460 @figure{/user_guides/boolean_operations/images/boolean_image057.png}
1462 * The result of *Cut21* operation is a compound containing split part of the argument *S2*, i.e. 1 new solid *S21*.
1464 @figure{/user_guides/boolean_operations/images/boolean_image058.png}
1466 @subsubsection occt_algorithms_9_4_20 Case 20: Two Solids that have overlapping faces.
1468 Let us consider two solids *S1* and *S2* that have a common part on face:
1470 @figure{/user_guides/boolean_operations/images/boolean_image059.png}
1472 * The result of *Fuse* operation is a compound composed from the split parts of arguments *S11, S12* and *S22* <i>(Cut12, Common, Cut21)</i>. All inner webs are removed, so the result is one new solid *R*.
1474 @figure{/user_guides/boolean_operations/images/boolean_image060.png}
1476 * The result of *Common* operation is an empty compound because the dimension (2) of the common part between *S1* and *S2* (face) is less than the lower dimension of the arguments (3).
1478 * The result of *Cut12* operation is a compound containing split part of the argument *S1*, i.e. 1 new solid *S11*.
1480 @figure{/user_guides/boolean_operations/images/boolean_image061.png}
1482 * The result of *Cut21* operation is a compound containing split part of the argument *S2*, i.e. 1 new solid *S21*.
1483 @figure{/user_guides/boolean_operations/images/boolean_image062.png}
1486 @subsubsection occt_algorithms_9_4_21 Case 21: Two Solids that have overlapping edges.
1488 Let us consider two solids *S1* and *S2* that have overlapping edges:
1490 @figure{/user_guides/boolean_operations/images/boolean_image063.png}
1492 * The result of *Fuse* operation is a compound composed from the split parts of arguments i.e. 2 new solids *S11* and *S21*. These solids have one shared edge *En1*.
1494 @figure{/user_guides/boolean_operations/images/boolean_image064.png}
1496 * The result of *Common* operation is an empty compound because the dimension (1) of the common part between *S1* and *S2* (edge) is less than the lower dimension of the arguments (3).
1498 * The result of *Cut12* operation is a compound containing split part of the argument *S1*. In this case
1499 argument *S1* has a common part with solid *S2* so the corresponding part is not included into the result.
1501 @figure{/user_guides/boolean_operations/images/boolean_image065.png}
1503 * The result of *Cut21* operation is a compound containing split part of the argument *S2*. In this case
1504 argument *S2* has a common part with solid *S1* so the corresponding part is not included into the result.
1505 @figure{/user_guides/boolean_operations/images/boolean_image066.png}
1507 @subsubsection occt_algorithms_9_4_22 Case 22: Two Solids that have overlapping vertices.
1509 Let us consider two solids *S1* and *S2* that have overlapping vertices:
1511 @figure{/user_guides/boolean_operations/images/boolean_image067.png}
1513 * The result of *Fuse* operation is a compound composed from the split parts of arguments i.e. 2 new solids *S11* and *S21*. These solids share *Vn1*.
1515 @figure{/user_guides/boolean_operations/images/boolean_image068.png}
1517 * The result of *Common* operation is an empty compound because the dimension (0) of the common part between *S1* and *S2* (vertex) is less than the lower dimension of the arguments (3).
1519 * The result of *Cut12* operation is a compound containing split part of the argument *S1*.
1521 @figure{/user_guides/boolean_operations/images/boolean_image069.png}
1523 * The result of *Cut21* operation is a compound containing split part of the argument *S2*.
1525 @figure{/user_guides/boolean_operations/images/boolean_image070.png}
1527 @subsubsection occt_algorithms_9_4_23 Case 23: A Shell and a Wire cut by a Solid.
1529 Let us consider Shell *Sh* and Wire *W* as the objects and Solid *S* as the tool:
1531 @figure{/user_guides/boolean_operations/images/boolean_image136.png}
1533 * The result of *Fuse* operation is not defined as the dimension of the arguments is not the same.
1535 * The result of *Common* operation is a compound containing the parts of the initial Shell and Wire common for the Solid. The new Shell and Wire are created from the objects.
1537 @figure{/user_guides/boolean_operations/images/boolean_image137.png}
1539 * The result of *Cut12* operation is a compound containing the parts of the initial Shell and Wire out of the Solid. The new Shell and Wire are created from the objects.
1541 @figure{/user_guides/boolean_operations/images/boolean_image138.png}
1543 * The result of *Cut21* operation is not defined as the objects have lower dimension than the tool.
1546 @subsection occt_algorithms_9_5 Class BOPAlgo_BOP
1548 BOA is implemented in the class *BOPAlgo_BOP*. The main fields of this class are described in the Table:
1552 | *myOperation* | The type of the Boolean operation (Common, Fuse, Cut) |
1553 | *myTools* | The tools |
1554 | *myDims[2]* | The values of the dimensions of the arguments |
1555 | *myRC* | The draft result (shape) |
1557 The main steps of the *BOPAlgo_BOP* are the same as of @ref occt_algorithms_7_4 "BOPAlgo_Builder" except for some aspects described in the next paragraphs.
1559 @subsection occt_algorithms_9_6 Building Draft Result
1561 The input data for this step is as follows:
1562 * *BOPAlgo_BOP* object after building result of type *Compound*;
1563 * *Type* of the Boolean operation.
1565 | No | Contents | Implementation |
1566 | :---- | :----- | :----- |
1567 | 1 | For the Boolean operation *Fuse* add to *myRC* all images of arguments. | *BOPAlgo_BOP::BuildRC()* |
1568 | 2 | For the Boolean operation *Common* or *Cut* add to *myRC* all images of argument *S1* that are *Common* for the Common operation and are *Not Common* for the Cut operation | *BOPAlgo_BOP::BuildRC()* |
1570 @subsection occt_algorithms_9_7 Building the Result
1572 The input data for this step is as follows:
1573 * *BOPAlgo_BOP* object the state after building draft result.
1575 | No | Contents | Implementation |
1576 | :---- | :---- | :------ |
1577 | 1 | For the Type of the Boolean operation Common, Cut with any dimension and operation Fuse with *myDim[0] < 3* | |
1578 | 1.1 | Find containers (WIRE, SHELL, COMPSOLID) in the arguments | *BOPAlgo_BOP:: BuildShape()* |
1579 | 1.2 | Make connexity blocks from splits of each container that are in *myRC* | *BOPTools_Tools::MakeConnexityBlocks()* |
1580 | 1.3 | Build the result from shapes made from the connexity blocks | *BOPAlgo_BOP:: BuildShape()* |
1581 | 1.4 | Add the remaining shapes from *myRC* to the result | *BOPAlgo_BOP:: BuildShape()* |
1582 | 2 | For the Type of the Boolean operation Fuse with *myDim[0] = 3* | |
1583 | 2.1 | Find internal faces <i>(FWi)</i> in *myRC* | *BOPAlgo_BOP::BuildSolid()* |
1584 | 2.2 | Collect all faces of *myRC* except for internal faces <i>(FWi) -> SFS</i> | *BOPAlgo_BOP::BuildSolid ()* |
1585 | 2.3 | Build solids <i>(SDi)</i> from *SFS*. | *BOPAlgo_BuilderSolid* |
1586 | 2.4 | Add the solids <i>(SDi)</i> to the result | |
1588 @section occt_algorithms_10a Section Algorithm
1590 @subsection occt_algorithms_10a_1 Arguments
1592 The arguments of BOA are shapes in terms of *TopoDS_Shape*. The main requirements for the arguments are described in the Algorithms.
1594 @subsection occt_algorithms_10a_2 Results and general rules
1595 * The result of Section operation is a compound. Each sub-shape of the compound has shared sub-shapes in accordance with interferences between the arguments.
1596 * The result of Section operation contains shapes that have dimension that is less then 2 i.e. vertices and edges.
1597 * The result of Section operation contains standalone vertices if these vertices do not belong to the edges of the result.
1598 * The result of Section operation contains vertices and edges of the arguments (or images of the arguments) that belong to at least two arguments (or two images of the arguments).
1599 * The result of Section operation contains Section vertices and edges obtained from Face/Face interferences.
1600 * The result of Section operation contains vertices that are the result of interferences between vertices and faces.
1601 * The result of Section operation contains edges that are the result of interferences between edges and faces (Common Blocks),
1603 @subsection occt_algorithms_10a_3 Examples
1605 @subsubsection occt_algorithms_10a_3_1 Case 1: Two Vertices
1607 Let us consider two interfering vertices: *V1* and *V2*.
1609 @figure{/user_guides/boolean_operations/images/boolean_image080.png}
1611 The result of *Section* operation is the compound that contains a new vertex *V*.
1613 @figure{/user_guides/boolean_operations/images/boolean_image081.png}
1615 @subsubsection occt_algorithms_10a_3_2 Case 1: Case 2: A Vertex and an Edge
1617 Let us consider vertex *V1* and the edge *E2*, that intersect in a 3D point:
1619 @figure{/user_guides/boolean_operations/images/boolean_image082.png}
1621 The result of *Section* operation is the compound that contains vertex *V1*.
1623 @figure{/user_guides/boolean_operations/images/boolean_image083.png}
1625 @subsubsection occt_algorithms_10a_3_3 Case 1: Case 2: A Vertex and a Face
1627 Let us consider vertex *V1* and face *F2*, that intersect in a 3D point:
1629 @figure{/user_guides/boolean_operations/images/boolean_image084.png}
1631 The result of *Section* operation is the compound that contains vertex *V1*.
1633 @figure{/user_guides/boolean_operations/images/boolean_image085.png}
1635 @subsubsection occt_algorithms_10a_3_4 Case 4: A Vertex and a Solid
1637 Let us consider vertex *V1* and solid *Z2*. The vertex *V1* is inside the solid *Z2*.
1639 @figure{/user_guides/boolean_operations/images/boolean_image086.png}
1641 The result of *Section* operation is an empty compound.
1643 @subsubsection occt_algorithms_10a_3_5 Case 5: Two edges intersecting at one point
1645 Let us consider edges *E1* and *E2*, that intersect in a 3D point:
1647 @figure{/user_guides/boolean_operations/images/boolean_image087.png}
1649 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1651 @figure{/user_guides/boolean_operations/images/boolean_image088.png}
1653 @subsubsection occt_algorithms_10a_3_6 Case 6: Two edges having a common block
1655 Let us consider edges *E1* and *E2*, that have a common block:
1657 @figure{/user_guides/boolean_operations/images/boolean_image089.png}
1659 The result of *Section* operation is the compound that contains a new edge *Enew*.
1661 @figure{/user_guides/boolean_operations/images/boolean_image090.png}
1663 @subsubsection occt_algorithms_10a_3_7 Case 7: An Edge and a Face intersecting at a point
1665 Let us consider edge *E1* and face *F2*, that intersect at a 3D point:
1667 @figure{/user_guides/boolean_operations/images/boolean_image091.png}
1669 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1671 @figure{/user_guides/boolean_operations/images/boolean_image092.png}
1673 @subsubsection occt_algorithms_10a_3_8 Case 8: A Face and an Edge that have a common block
1675 Let us consider edge *E1* and face *F2*, that have a common block:
1677 @figure{/user_guides/boolean_operations/images/boolean_image093.png}
1679 The result of *Section* operation is the compound that contains new edge *Enew*.
1681 @figure{/user_guides/boolean_operations/images/boolean_image094.png}
1684 @subsubsection occt_algorithms_10a_3_9 Case 9: An Edge and a Solid intersecting at a point
1686 Let us consider edge *E1* and solid *Z2*, that intersect at a point:
1688 @figure{/user_guides/boolean_operations/images/boolean_image095.png}
1690 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1692 @figure{/user_guides/boolean_operations/images/boolean_image096.png}
1694 @subsubsection occt_algorithms_10a_3_10 Case 10: An Edge and a Solid that have a common block
1696 Let us consider edge *E1* and solid *Z2*, that have a common block at a face:
1698 @figure{/user_guides/boolean_operations/images/boolean_image097.png}
1700 The result of *Section* operation is the compound that contains a new edge *Enew*.
1702 @figure{/user_guides/boolean_operations/images/boolean_image098.png}
1704 @subsubsection occt_algorithms_10a_3_11 Case 11: Two intersecting faces
1706 Let us consider two intersecting faces *F1* and *F2*:
1708 @figure{/user_guides/boolean_operations/images/boolean_image099.png}
1710 The result of *Section* operation is the compound that contains a new edge *Enew*.
1712 @figure{/user_guides/boolean_operations/images/boolean_image100.png}
1714 @subsubsection occt_algorithms_10a_3_12 Case 12: Two faces that have a common part
1716 Let us consider two faces *F1* and *F2* that have a common part:
1718 @figure{/user_guides/boolean_operations/images/boolean_image133.png}
1720 The result of *Section* operation is the compound that contains 4 new edges.
1722 @figure{/user_guides/boolean_operations/images/boolean_image134.png}
1724 @subsubsection occt_algorithms_10a_3_13 Case 13: Two faces that have overlapping edges
1726 Let us consider two faces *F1* and *F2* that have a overlapping edges:
1728 @figure{/user_guides/boolean_operations/images/boolean_image101.png}
1730 The result of *Section* operation is the compound that contains a new edge *Enew*.
1732 @figure{/user_guides/boolean_operations/images/boolean_image102.png}
1734 @subsubsection occt_algorithms_10a_3_14 Case 14: Two faces that have overlapping vertices
1736 Let us consider two faces *F1* and *F2* that have overlapping vertices:
1738 @figure{/user_guides/boolean_operations/images/boolean_image103.png}
1740 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1742 @figure{/user_guides/boolean_operations/images/boolean_image104.png}
1744 @subsubsection occt_algorithms_10a_3_15 Case 15: A Face and a Solid that have an intersection curve
1746 Let us consider face *F1* and solid *Z2* that have an intersection curve:
1748 @figure{/user_guides/boolean_operations/images/boolean_image105.png}
1750 The result of *Section* operation is the compound that contains new edges.
1752 @figure{/user_guides/boolean_operations/images/boolean_image106.png}
1754 @subsubsection occt_algorithms_10a_3_16 Case 16: A Face and a Solid that have overlapping faces.
1756 Let us consider face *F1* and solid *Z2* that have overlapping faces:
1758 @figure{/user_guides/boolean_operations/images/boolean_image107.png}
1760 The result of *Section* operation is the compound that contains new edges
1762 @figure{/user_guides/boolean_operations/images/boolean_image108.png}
1764 @subsubsection occt_algorithms_10a_3_17 Case 17: A Face and a Solid that have overlapping edges.
1766 Let us consider face *F1* and solid *Z2* that have a common part on edge:
1768 @figure{/user_guides/boolean_operations/images/boolean_image109.png}
1770 The result of *Section* operation is the compound that contains a new edge *Enew*.
1772 @figure{/user_guides/boolean_operations/images/boolean_image110.png}
1774 @subsubsection occt_algorithms_10a_3_18 Case 18: A Face and a Solid that have overlapping vertices.
1776 Let us consider face *F1* and solid *Z2* that have overlapping vertices:
1778 @figure{/user_guides/boolean_operations/images/boolean_image111.png}
1780 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1782 @figure{/user_guides/boolean_operations/images/boolean_image112.png}
1784 @subsubsection occt_algorithms_10a_3_19 Case 19: Two intersecting Solids
1786 Let us consider two intersecting solids *Z1* and *Z2*:
1787 @figure{/user_guides/boolean_operations/images/boolean_image113.png}
1789 The result of *Section* operation is the compound that contains new edges.
1790 @figure{/user_guides/boolean_operations/images/boolean_image114.png}
1792 @subsubsection occt_algorithms_10a_3_20 Case 20: Two Solids that have overlapping faces
1794 Let us consider two solids *Z1* and *Z2* that have a common part on face:
1795 @figure{/user_guides/boolean_operations/images/boolean_image115.png}
1797 The result of *Section* operation is the compound that contains new edges.
1798 @figure{/user_guides/boolean_operations/images/boolean_image116.png}
1800 @subsubsection occt_algorithms_10a_3_21 Case 21: Two Solids that have overlapping edges
1802 Let us consider two solids *Z1* and *Z2* that have overlapping edges:
1803 @figure{/user_guides/boolean_operations/images/boolean_image117.png}
1805 The result of *Section* operation is the compound that contains a new edge *Enew*.
1806 @figure{/user_guides/boolean_operations/images/boolean_image118.png}
1808 @subsubsection occt_algorithms_10a_3_22 Case 22: Two Solids that have overlapping vertices
1810 Let us consider two solids *Z1* and *Z2* that have overlapping vertices:
1811 @figure{/user_guides/boolean_operations/images/boolean_image119.png}
1813 The result of *Section* operation is the compound that contains a new vertex *Vnew*.
1814 @figure{/user_guides/boolean_operations/images/boolean_image120.png}
1816 @subsection occt_algorithms_10a_4 Class BOPAlgo_Section
1818 SA is implemented in the class *BOPAlgo_Section*. The class has no specific fields.
1819 The main steps of the *BOPAlgo_Section* are the same as of *BOPAlgo_Builder* except for the following steps:
1821 * Build Images for Wires;
1822 * Build Result of Type Wire;
1823 * Build Images for Faces;
1824 * Build Result of Type Face;
1825 * Build Images for Shells;
1826 * Build Result of Type Shell;
1827 * Build Images for Solids;
1828 * Build Result of Type Solid;
1829 * Build Images for Type CompSolid;
1830 * Build Result of Type CompSolid;
1831 * Build Images for Compounds;
1832 Some aspects of building the result are described in the next paragraph
1834 @subsection occt_algorithms_10a_5 Building the Result
1836 | No | Contents | Implementation |
1837 | :---- | :---- | :------ |
1838 | 1 | Build the result of the operation using all information contained in *FaceInfo*, Common Block, Shared entities of the arguments, etc. | *BOPAlgo_Section:: BuildSection()* |
1842 @section occt_algorithms_10 Algorithm Limitations
1844 The chapter describes the problems that are considered as Algorithm limitations. In most cases an Algorithm failure is caused by a combination of various factors, such as self-interfered arguments, inappropriate or ungrounded values of the argument tolerances, adverse mutual position of the arguments, tangency, etc.
1846 A lot of failures of GFA algorithm can be caused by bugs in low-level algorithms: Intersection Algorithm, Projection Algorithm, Approximation Algorithm, Classification Algorithm, etc.
1847 * The Intersection, Projection and Approximation Algorithms are mostly used at the Intersection step. Their bugs directly cause wrong section results (i.e. incorrect section edges, section points, missing section edges or micro edges). It is not possible to obtain a correct final result of the GFA if a section result is wrong.
1848 * The Projection Algorithm is used at the Intersection step. The purpose of Projection Algorithm is to compute 2D-curves on surfaces. Wrong results here lead to incorrect or missing faces in the final GFA result.
1849 * The Classification Algorithm is used at the Building step. The bugs in the Classification Algorithm lead to errors in selecting shape parts (edges, faces, solids) and ultimately to a wrong final GFA result.
1851 The description below illustrates some known GFA limitations. It does not enumerate exhaustively all problems that can arise in practice. Please, address cases of Algorithm failure to the OCCT Maintenance Service.
1854 @subsection occt_algorithms_10_1 Arguments
1856 @subsubsection occt_algorithms_10_1_1 Common requirements
1858 Each argument should be valid (in terms of *BRepCheck_Analyzer*), or conversely, if the argument is considered as non-valid (in terms of *BRepCheck_Analyzer*), it cannot be used as an argument of the algorithm.
1860 The class *BRepCheck_Analyzer* is used to check the overall validity of a shape. In OCCT a Shape (or its sub-shapes) is considered valid if it meets certain criteria. If the shape is found as invalid, it can be fixed by tools from *ShapeAnalysis, ShapeUpgrade* and *ShapeFix* packages.
1862 However, it is important to note that class *BRepCheck_Analyzer* is just a tool that can have its own problems; this means that due to a specific factor(s) this tool can sometimes provide a wrong result.
1864 Let us consider the following example:
1866 The Analyzer checks distances between couples of 3D check-points <i>(Pi, PSi)</i> of edge *E* on face *F*. Point *Pi* is obtained from the 3D-curve (at the parameter *ti*) of the edge. *PSi* is obtained from 2D-curve (at the parameter *ti*) of the edge on surface *S* of face *F*. To be valid the distance should be less than *Tol(E)* for all couples of check-points. The number of these check-points is a pre-defined value (e.g. 23).
1868 Let us consider the case when edge *E* is recognized valid (in terms of *BRepCheck_Analyzer*).
1870 Further, after some operation, edge *E* is split into two edges *E1* and *E2*. Each split edge has the same 3D-curve and 2D-curve as the original edge *E*.
1872 Let us check *E1* (or E2). The Analyzer again checks the distances between the couples of check-points points <i>(Pi, PSi)</i>. The number of these check-points is the same constant value (23), but there is no guarantee that the distances will be less than *Tol(E)*, because the points chosen for *E1* are not the same as for *E*.
1874 Thus, if *E1* is recognized by the Analyzer as non-valid, edge *E* should also be non-valid. However *E* has been recognized as valid. Thus the Analyzer gives a wrong result for *E*.
1876 The fact that the argument is a valid shape (in terms of *BRepCheck_Analyzer*) is a necessary but insufficient requirement to produce a valid result of the Algorithms.
1878 @subsubsection occt_algorithms_10_1_3 Pure self-interference
1880 The argument should not be self-interfered, i.e. all sub-shapes of the argument that have geometrical coincidence through any topological entities (vertices, edges, faces) should share these entities.
1882 #### Example 1: Compound of two edges
1883 The compound of two edges *E1* and *E2* is a self-interfered shape and cannot be used as the argument of the Algorithms.
1885 @figure{/user_guides/boolean_operations/images/operations_image036.svg, "Compound of two edges"}
1887 #### Example 2: Self-interfered Edge
1888 The edge *E* is a self-interfered shape and cannot be used as an argument of the Algorithms.
1890 @figure{/user_guides/boolean_operations/images/operations_image037.svg, "Self-interfered Edge"}
1892 #### Example 3: Self-interfered Face
1893 The face *F* is a self-interfered shape and cannot be used as an argument of the Algorithms.
1895 @figure{/user_guides/boolean_operations/images/operations_image038.svg, "Self-interfered Face"}
1897 #### Example 4: Face of Revolution
1898 The face *F* has been obtained by revolution of edge *E* around line *L*.
1900 @figure{/user_guides/boolean_operations/images/operations_image039a.png, "Face of Revolution: Arguments"}
1901 @figure{/user_guides/boolean_operations/images/operations_image039b.png, "Face of Revolution: Result"}
1903 In spite of the fact that face *F* is valid (in terms of *BRepCheck_Analyzer*) it is a self-interfered shape and cannot be used as the argument of the Algorithms.
1905 @subsubsection occt_algorithms_10_1_4 Self-interferences due to tolerances
1906 #### Example 1: Non-closed Edge
1908 Let us consider edge *E* based on a non-closed circle. @figure{/user_guides/boolean_operations/images/operations_image040.png, "Edge based on a non-closed circle"}
1910 The distance between the vertices of *E* is *D=0.69799*. The values of the tolerances *Tol(V1)=Tol(V2)=0.5*.
1911 @figure{/user_guides/boolean_operations/images/operations_image041.png, "Distance and Tolerances"}
1913 In spite of the fact that the edge *E* is valid in terms of *BRepCheck_Analyzer*, it is a self-interfered shape because its vertices are interfered. Thus, edge *E* cannot be used as an argument of the Algorithms.
1915 #### Example 2: Solid containing an interfered vertex
1917 Let us consider solid *S* containing vertex V. @figure{/user_guides/boolean_operations/images/operations_image042.png, "Solid containing an interfered vertex"}
1919 The value of tolerance Tol(V)= 50.000075982061.
1921 @figure{/user_guides/boolean_operations/images/operations_image043.png, "Tolerance"}
1923 In spite of the fact that solid *S* is valid in terms of *BRepCheck_Analyzer* it is a self-interfered shape because vertex *V* is interfered with a lot of sub-shapes from *S* without any topological connection with them. Thus solid *S* cannot be used as an argument of the Algorithms.
1925 @subsubsection occt_algorithms_10_1_5 Parametric representation
1926 The parameterization of some surfaces (cylinder, cone, surface of revolution) can be the cause of limitation.
1928 #### Example 1: Cylindrical surface
1929 The parameterization range for cylindrical surface is:
1931 @figure{/user_guides/boolean_operations/images/boolean_image135.png}
1933 The range of *U* coordinate is always restricted while the range of *V* coordinate is non-restricted.
1935 Let us consider a cylinder-based *Face 1* with radii *R=3* and *H=6*.
1937 @figure{/user_guides/boolean_operations/images/operations_image044.png, "Face 1"}
1939 @figure{/user_guides/boolean_operations/images/operations_image045.png, "P-Curves for Face 1"}
1941 Let us also consider a cylinder-based *Face 2* with radii *R=3000* and *H=6000* (resulting from scaling Face 1 with scale factor *ScF=1000*).
1943 @figure{/user_guides/boolean_operations/images/operations_image046.png, "Face 2"}
1945 @figure{/user_guides/boolean_operations/images/operations_image047.png, "P-Curves for Face 2"}
1947 Please, pay attention to the Zoom value of the Figures.
1949 It is obvious that starting with some value of *ScF*, e.g. *ScF>1000000*, all sloped p-Curves on *Face 2* will be almost vertical. At least, there will be no difference between the values of angles computed by standard C Run-Time Library functions, such as *double acos(double x)*. The loss of accuracy in computation of angles can cause failure of some BP sub-algorithms, such as building faces from a set of edges or building solids from a set of faces.
1952 @subsubsection occt_algorithms_10_1_6 Using tolerances of vertices to fix gaps
1954 It is possible to create shapes that use sub-shapes of lower order to avoid gaps in the tolerance-based data model.
1956 Let us consider the following example:
1958 @figure{/user_guides/boolean_operations/images/operations_image048.png, "Example"}
1960 * Face *F* has two edges *E1* and *E2* and two vertices, the base plane is <i>{0,0,0, 0,0,1}</i>;
1961 * Edge *E1* is based on line <i>{0,0,0, 1,0,0}, Tol(E1) = 1.e-7; </i>
1962 * Edge *E2* is based on line <i>{0,1,0, 1,0,0}, Tol(E2) = 1.e-7;</i>
1963 * Vertex *V1*, point <i>{0,0.5,0}, Tol(V1) = 1;</i>
1964 * Vertex *V2*, point <i>{10,0.5,0}, Tol(V2) = 1;</i>
1965 * Face *F* is valid (in terms of *BRepCheck_Analyzer*).
1967 The values of tolerances *Tol(V1)* and *Tol(V2)* are big enough to fix the gaps between the ends of the edges, but the vertices *V1* and *V2* do not contain any information about the trajectories connecting the corresponding ends of the edges. Thus, the trajectories are undefined. This will cause failure of some sub-algorithms of BP. For example, the sub-algorithms for building faces from a set of edges use the information about all edges connected in a vertex. The situation when a vertex has several pairs of edges such as above will not be solved in a right way.
1970 @subsection occt_algorithms_11_1 Intersection problems
1971 @subsubsection occt_algorithms_11_1_1 Pure intersections and common zones
1973 #### Example: Intersecting Edges
1975 Let us consider the intersection between two edges:
1976 * *E1* is based on a line: <i>{0,-10,0, 1,0,0}, Tol(E1)=2.</i>
1977 * *E2* is based on a circle: <i>{0,0,0, 0,0,1}, R=10, Tol(E2)=2.</i>
1979 @figure{/user_guides/boolean_operations/images/operations_image049.png, "Intersecting Edges"}
1981 The result of pure intersection between *E1* and *E2* is vertex *Vx {0,-10,0}*.
1983 The result of intersection taking into account tolerances is the common zone *CZ* (part of 3D-space where the distance between the curves is less than or equals to the sum of edge tolerances.
1985 The Intersection Part of Algorithms uses the result of pure intersection *Vx* instead of *CZ* for the following reasons:
1986 * The Algorithms do not produce Common Blocks between edges based on underlying curves of explicitly different type (e.g. Line / Circle). If the curves have different types, the rule of thumb is that the produced result is of type **vertex**. This rule does not work for non-analytic curves (Bezier, B-Spline) and their combinations with analytic curves.
1987 * The algorithm of intersection between two surfaces *IntPatch_Intersection* does not compute *CZ* of the intersection between curves and points. So even if *CZ* were computed by Edge/Edge intersection algorithm, its result could not be treated by Face/Face intersection algorithm.
1989 @subsubsection occt_algorithms_11_2_2 Tolerances and inaccuracies
1991 The following limitations result from modeling errors or inaccuracies.
1993 #### Example: Intersection of planar faces
1995 Let us consider two planar rectangular faces *F1* and *F2*.
1997 The intersection curve between the planes is curve *C12*. The curve produces a new intersection edge *EC12*. The edge goes through vertices *V1* and *V2* thanks to big tolerance values of vertices *Tol(V1)* and *Tol(V2)*. So, two straight edges *E12* and *EC12* go through two vertices, which is impossible in this case.
1999 @figure{/user_guides/boolean_operations/images/operations_image050.svg, "Intersecting Faces"}
2002 The problem cannot be solved in general, because the length of *E12* can be infinite and the values of *Tol(V1)* and *Tol(V2)* theoretically can be infinite too.
2004 In a particular case the problem can be solved in several ways:
2005 * Reduce, if possible, the values of *Tol(V1)* and *Tol(V2)* (refinement of *F1*).
2006 * Analyze the value of *Tol(EC12)* and increase *Tol(EC12)* to get a common part between the edges *EC12* and *E12*. Then the common part will be rejected as there is an already existing edge *E12* for face *F1*.
2008 It is easy to see that if *C12* is slightly above the tolerance spheres of *V1* and *V2* the problem does not appear.
2010 #### Example: Intersection of two edges
2012 Let us consider two edges *E1* and *E2*, which have common vertices *V1* and *V2*. The edges *E1* and *E2* have 3D-curves *C1* and *C2. Tol(E1)=1.e<sup>-7</sup>, Tol(E2)=1.e<sup>-7</sup>.*
2014 *C1* practically coincides in 3D with *C2*. The value of deflection is *Dmax* (e.g. *Dmax=1.e<sup>-6</sup>*).
2016 @figure{/user_guides/boolean_operations/images/operations_image051.svg, "Intersecting Edges"}
2018 The evident and prospective result should be the Common Block between *E1* and *E2*. However, the result of intersection differs.
2020 @figure{/user_guides/boolean_operations/images/operations_image052.svg, "Result of Intersection"}
2022 The result contains three new vertices *Vx1, Vx2* and *Vx3*, 8 new edges <i>(V1, Vx1, Vx2, Vx3, V2)</i> and no Common Blocks. This is correct due to the source data: *Tol(E1)=1.e<sup>-7</sup>, Tol(E2)=1.e<sup>-7</sup>* and <i>Dmax=1.e<sup>-6</sup></i>.
2024 In this particular case the problem can be solved by several ways:
2025 * Increase, if possible, the values *Tol(E1)* and *Tol(E2)* to get coincidence in 3D between *E1* and *E2* in terms of tolerance.
2026 * Replace *E1* by a more accurate model.
2028 The example can be extended from 1D (edges) to 2D (faces).
2030 @figure{/user_guides/boolean_operations/images/operations_image053.svg, "Intersecting Faces"}
2032 The comments and recommendations are the same as for 1D case above.
2035 @subsubsection occt_algorithms_11_2_3 Acquired Self-interferences
2036 #### Example 1: Vertex and edge
2038 Let us consider vertex *V1* and edge *E2*.
2040 @figure{/user_guides/boolean_operations/images/operations_image054.svg, "Vertex and Edge"}
2042 Vertex *V1* interferes with vertices *V12* and *V22*.
2043 So vertex *V21* should interfere with vertex *V22*, which is impossible because vertices *V21* and *V22* are the vertices of edge *E2*, thus *V21* is not equal to *V22*.
2045 The problem cannot be solved in general, because the length can be as small as possible to provide validity of *E2* (in the extreme case: *Length (E2) = Tol(V21) + Tol(V22) + e,* where *e-> 0*).
2047 In a particular case the problem can be solved by refinement of arguments, i.e. by decreasing the values of *Tol(V21)*, *Tol(V22)* and *Tol(V1)*.
2049 #### Example 2: Vertex and wire
2051 Let us consider vertex *V2* and wire consisting of edges *E11* and *E12*.
2053 @figure{/user_guides/boolean_operations/images/operations_image055.svg, "Vertex and Wire"}
2055 The arguments themselves are not self-intersected.
2056 Vertex *V2* interferes with edges *E11* and *E12*. Thus, edge *E11* should interfere with edge *E22*, but it is impossible because edges *E11* and *E12* cannot interfere by the condition.
2058 The cases when a non-self-interfered argument (or its sub-shapes) become interfered due to the intersections with other arguments (or their sub-shapes) are considered as limitations for the Algorithms.
2060 @section occt_algorithms_11a Advanced Options
2062 The previous chapters describe so called Basic Operations. Most of tasks can be solved using Basic Operations. Nonetheless, there are cases that can not be solved straightforwardly by Basic Operations. The tasks are considered as limitations of Basic Operations.
2064 The chapter is devoted to Advanced Options. In some cases the usage of Advanced Options allows overcoming the limitations, improving the quality of the result of operations, robustness and performance of the operators themselves.
2066 @subsection occt_algorithms_11a_1 Fuzzy Boolean Operation
2068 Fuzzy Boolean operation is the option of Basic Operations (GFA, BOA, PA and SA), in which additional user-specified tolerance is used. This option allows operators to handle robustly cases of touching and near-coincident, misalignment entities of the arguments.
2070 The Fuzzy option is useful on the shapes with gaps or embeddings between the entities of these shapes which are not covered by the tolerance values of these entities. Such shapes can be the result of modeling mistakes, or translating process, or import from other systems with loss of precision, or errors in some algorithms.
2072 Most likely, the Basic Operations will give unsatisfactory results on such models. The result may contain unexpected and unwanted small entities, faulty entities (in terms of *BRepCheck_Analyzer*), or there can be no result at all.
2074 With the Fuzzy option it is possible to get the expected result - it is just necessary to define the appropriate value of fuzzy tolerance for the operation. To define that value it is necessary to measure the value of the gap (or the value of embedding depth) between the entities of the models, slightly increase it (to make the shifted entities coincident in terms of their tolerance plus the additional one) and pass it to the algorithm.
2076 Fuzzy option is included in interface of Intersection Part (class *BOPAlgo_PaveFiller*) and application programming interface (class *BRepAlgoAPI_BooleanOperation*)
2078 @subsection occt_algorithms_11a_2 Examples
2079 The following examples demonstrate the advantages of usage Fuzzy option operations over the Basic Operations in typical situations.
2081 @subsubsection occt_algorithms_11a_1_1 Case 1
2083 In this example the cylinder (shown in yellow and transparent) is subtracted from the box (shown in red). The cylinder is shifted by 5e<sup>-5</sup> relatively to the box along its axis (the distance between rear faces of the box and cylinder is 5e<sup>-5</sup>).
2085 @figure{/user_guides/boolean_operations/images/boolean_image121.png}
2087 The following results are obtained using Basic Operations and the Fuzzy ones with the fuzzy value 5e<sup>-5</sup>:
2089 @figure{/user_guides/boolean_operations/images/boolean_image122.png, "Result of CUT operation obtained with Basic Operations"}
2091 @figure{/user_guides/boolean_operations/images/boolean_image123.png, "Result of CUT operation obtained with Fuzzy Option"}
2093 In this example Fuzzy option allows eliminating a very thin part of the result shape produced by Basic algorithm due to misalignment of rear faces of the box and the cylinder.
2095 @subsubsection occt_algorithms_11a_1_2 Case 2
2097 In this example two boxes are fused. One of them has dimensions 10*10*10, and the other is 10*10.000001*10.000001 and adjacent to the first one. There is no gap in this case as the surfaces of the neighboring faces coincide, but one box is slightly greater than the other.
2099 @figure{/user_guides/boolean_operations/images/boolean_image124.png}
2101 The following results are obtained using Basic Operations and the Fuzzy ones with the fuzzy value 1e<sup>-6</sup>:
2103 @figure{/user_guides/boolean_operations/images/boolean_image125.png, "Result of CUT operation obtained with Basic Operations"}
2105 @figure{/user_guides/boolean_operations/images/boolean_image126.png, "Result of CUT operation obtained with Fuzzy Option"}
2107 In this example Fuzzy option allows eliminating an extremely narrow face in the result produced by Basic operation.
2109 @subsubsection occt_algorithms_11a_1_3 Case 3
2111 In this example the small planar face (shown in orange) is subtracted from the big one (shown in yellow). There is a gap 1e<sup>-5</sup> between the edges of these faces.
2113 @figure{/user_guides/boolean_operations/images/boolean_image127.png}
2115 The following results are obtained using Basic Operations and the Fuzzy ones with the fuzzy value 1e<sup>-5</sup>:
2117 @figure{/user_guides/boolean_operations/images/boolean_image128.png, "Result of CUT operation obtained with Basic Operations"}
2119 @figure{/user_guides/boolean_operations/images/boolean_image129.png, "Result of CUT operation obtained with Fuzzy Option"}
2121 In this example Fuzzy options eliminated a pin-like protrusion resulting from the gap between edges of the argument faces.
2123 @subsubsection occt_algorithms_11a_1_4 Case 4
2125 In this example the small edge is subtracted from the big one. The edges are overlapping not precisely, with max deviation between them equal to 5.28004e<sup>-5</sup>. We will use 6e<sup>-5</sup> value for Fuzzy option.
2127 @figure{/user_guides/boolean_operations/images/boolean_image130.png}
2129 The following results are obtained using Basic Operations and the Fuzzy ones with the fuzzy value 6e<sup>-5</sup>:
2131 @figure{/user_guides/boolean_operations/images/boolean_image131.png, "Result of CUT operation obtained with Basic Operations"}
2133 @figure{/user_guides/boolean_operations/images/boolean_image132.png, "Result of CUT operation obtained with Fuzzy Option"}
2135 This example stresses not only the validity, but also the performance issue. The usage of Fuzzy option with the appropriate value allows processing the case much faster than with the pure Basic operation. The performance gain for the case is 45 (Processor: Intel(R) Core(TM) i5-3450 CPU @ 3.10 GHz).
2137 @section occt_algorithms_11b Usage
2139 The chapter contains some examples of the OCCT Boolean Component usage. The usage is possible on two levels: C++ and Tcl.
2141 @subsection occt_algorithms_11b_1 Package BRepAlgoAPI
2143 The package *BRepAlgoAPI* provides the Application Programming Interface of the Boolean Component.
2145 The package consists of the following classes:
2146 * *BRepAlgoAPI_Algo* – the root class that provides the interface for algorithms.
2147 * *BRepAlgoAPI_BuilderAlgo* - the class API level of General Fuse algorithm.
2148 * *BRepAlgoAPI_BooleanOperation* – the root class for the classes *BRepAlgoAPI_Fuse*. *BRepAlgoAPI_Common*, *BRepAlgoAPI_Cut* and *BRepAlgoAPI_Section*.
2149 * *BRepAlgoAPI_Fuse* – the class provides Boolean fusion operation.
2150 * *BRepAlgoAPI_Common* - the class provides Boolean common operation.
2151 * *BRepAlgoAPI_Cut* - the class provides Boolean cut operation.
2152 * *BRepAlgoAPI_Section* - the class provides Boolean section operation.
2154 @figure{/user_guides/boolean_operations/images/operations_image065.svg, "Diagram of BRepAlgoAPI package"}
2156 The detailed description of the classes can be found in corresponding .cdl files. The examples are below in this chapter.
2158 @subsection occt_algorithms_11b_2 Package BOPTest
2159 The package *BOPTest* provides the usage of the Boolean Component on Tcl level. The method *BOPTest::APICommands* contains corresponding Tcl commands:
2161 * *bapibuild* – for General Fuse Operator;
2162 * *bapibop* – for Boolean Operator and Section Operator.
2164 The examples of how to use the commands are below in this chapter.
2166 @subsubsection occt_algorithms_11b_2_1 Case 1 General Fuse operation
2168 The following example illustrates how to use General Fuse operator:
2173 #include <TopoDS_Shape.hxx>
2174 #include <TopTools_ListOfShape.hxx>
2175 #include <BRepAlgoAPI_BuilderAlgo.hxx>
2177 Standard_Boolean bRunParallel;
2178 Standard_Integer iErr;
2179 Standard_Real aFuzzyValue;
2180 BRepAlgoAPI_BuilderAlgo aBuilder;
2182 // prepare the arguments
2183 TopTools_ListOfShape& aLS=…;
2185 bRunParallel=Standard_True;
2188 // set the arguments
2189 aBuilder.SetArguments(aLS);
2190 // set parallel processing mode
2191 // if bRunParallel= Standard_True : the parallel processing is switched on
2192 // if bRunParallel= Standard_False : the parallel processing is switched off
2193 aBuilder.SetRunParallel(bRunParallel);
2196 // if aFuzzyValue=0.: the Fuzzy option is off
2197 // if aFuzzyValue>0.: the Fuzzy option is on
2198 aBuilder.SetFuzzyValue(aFuzzyValue);
2200 // run the algorithm
2202 iErr=aBuilder.ErrorStatus();
2204 // an error treatment
2208 // result of the operation aR
2209 const TopoDS_Shape& aR=aBuilder.Shape();
2217 # prepare the arguments
2219 box b2 3 4 5 10 10 10
2220 box b3 5 6 7 10 10 10
2222 # clear inner contents
2223 bclearobjects; bcleartools;
2226 baddobjects b1 b2 b3
2227 # set parallel processing mode
2228 # 1: the parallel processing is switched on
2229 # 0: the parallel processing is switched off
2232 # 0. : the Fuzzy option is off
2233 # >0. : the Fuzzy option is on
2237 # r is the result of the operation
2241 @subsubsection occt_algorithms_11b_2_2 Case 2. Common operation
2243 The following example illustrates how to use Common operation:
2248 #include <TopoDS_Shape.hxx>
2249 #include <TopTools_ListOfShape.hxx>
2250 #include < BRepAlgoAPI_Common.hxx>
2252 Standard_Boolean bRunParallel;
2253 Standard_Integer iErr;
2254 Standard_Real aFuzzyValue;
2255 BRepAlgoAPI_Common aBuilder;
2257 // perpare the arguments
2258 TopTools_ListOfShape& aLS=…;
2259 TopTools_ListOfShape& aLT=…;
2261 bRunParallel=Standard_True;
2264 // set the arguments
2265 aBuilder.SetArguments(aLS);
2266 aBuilder.SetTools(aLT);
2268 // set parallel processing mode
2269 // if bRunParallel= Standard_True : the parallel processing is switched on
2270 // if bRunParallel= Standard_False : the parallel processing is switched off
2271 aBuilder.SetRunParallel(bRunParallel);
2274 // if aFuzzyValue=0.: the Fuzzy option is off
2275 // if aFuzzyValue>0.: the Fuzzy option is on
2276 aBuilder.SetFuzzyValue(aFuzzyValue);
2278 // run the algorithm
2280 iErr=aBuilder.ErrorStatus();
2282 // an error treatment
2286 // result of the operation aR
2287 const TopoDS_Shape& aR=aBuilder.Shape();
2295 # prepare the arguments
2297 box b2 7 0 4 10 10 10
2298 box b3 14 0 0 10 10 10
2300 # clear inner contents
2301 bclearobjects; bcleartools;
2307 # set parallel processing mode
2308 # 1: the parallel processing is switched on
2309 # 0: the parallel processing is switched off
2313 # 0. : the Fuzzy option is off
2314 # >0. : the Fuzzy option is on
2318 # r is the result of the operation
2319 # 0 means Common operation
2323 @subsubsection occt_algorithms_11b_2_3 Case 3. Fuse operation
2325 The following example illustrates how to use Fuse operation:
2330 #include <TopoDS_Shape.hxx>
2331 #include <TopTools_ListOfShape.hxx>
2332 #include < BRepAlgoAPI_Fuse.hxx>
2334 Standard_Boolean bRunParallel;
2335 Standard_Integer iErr;
2336 Standard_Real aFuzzyValue;
2337 BRepAlgoAPI_Fuse aBuilder;
2339 // perpare the arguments
2340 TopTools_ListOfShape& aLS=…;
2341 TopTools_ListOfShape& aLT=…;
2343 bRunParallel=Standard_True;
2346 // set the arguments
2347 aBuilder.SetArguments(aLS);
2348 aBuilder.SetTools(aLT);
2350 // set parallel processing mode
2351 // if bRunParallel= Standard_True : the parallel processing is switched on
2352 // if bRunParallel= Standard_False : the parallel processing is switched off
2353 aBuilder.SetRunParallel(bRunParallel);
2356 // if aFuzzyValue=0.: the Fuzzy option is off
2357 // if aFuzzyValue>0.: the Fuzzy option is on
2358 aBuilder.SetFuzzyValue(aFuzzyValue);
2360 // run the algorithm
2362 iErr=aBuilder.ErrorStatus();
2364 // an error treatment
2368 // result of the operation aR
2369 const TopoDS_Shape& aR=aBuilder.Shape();
2377 # prepare the arguments
2379 box b2 7 0 4 10 10 10
2380 box b3 14 0 0 10 10 10
2382 # clear inner contents
2383 bclearobjects; bcleartools;
2389 # set parallel processing mode
2390 # 1: the parallel processing is switched on
2391 # 0: the parallel processing is switched off
2395 # 0. : the Fuzzy option is off
2396 # >0. : the Fuzzy option is on
2400 # r is the result of the operation
2401 # 1 means Fuse operation
2405 @subsubsection occt_algorithms_11b_2_4 Case 4. Cut operation
2407 The following example illustrates how to use Cut operation:
2412 #include <TopoDS_Shape.hxx>
2413 #include <TopTools_ListOfShape.hxx>
2414 #include < BRepAlgoAPI_Cut.hxx>
2416 Standard_Boolean bRunParallel;
2417 Standard_Integer iErr;
2418 Standard_Real aFuzzyValue;
2419 BRepAlgoAPI_Cut aBuilder;
2421 // perpare the arguments
2422 TopTools_ListOfShape& aLS=…;
2423 TopTools_ListOfShape& aLT=…;
2425 bRunParallel=Standard_True;
2428 // set the arguments
2429 aBuilder.SetArguments(aLS);
2430 aBuilder.SetTools(aLT);
2432 // set parallel processing mode
2433 // if bRunParallel= Standard_True : the parallel processing is switched on
2434 // if bRunParallel= Standard_False : the parallel processing is switched off
2435 aBuilder.SetRunParallel(bRunParallel);
2438 // if aFuzzyValue=0.: the Fuzzy option is off
2439 // if aFuzzyValue>0.: the Fuzzy option is on
2440 aBuilder.SetFuzzyValue(aFuzzyValue);
2442 // run the algorithm
2444 iErr=aBuilder.ErrorStatus();
2446 // an error treatment
2450 // result of the operation aR
2451 const TopoDS_Shape& aR=aBuilder.Shape();
2459 # prepare the arguments
2461 box b2 7 0 4 10 10 10
2462 box b3 14 0 0 10 10 10
2464 # clear inner contents
2465 bclearobjects; bcleartools;
2471 # set parallel processing mode
2472 # 1: the parallel processing is switched on
2473 # 0: the parallel processing is switched off
2477 # 0. : the Fuzzy option is off
2478 # >0. : the Fuzzy option is on
2482 # r is the result of the operation
2483 # 2 means Cut operation
2488 @subsubsection occt_algorithms_11b_2_5 Case 5. Section operation
2490 The following example illustrates how to use Section operation:
2495 #include <TopoDS_Shape.hxx>
2496 #include <TopTools_ListOfShape.hxx>
2497 #include < BRepAlgoAPI_Section.hxx>
2499 Standard_Boolean bRunParallel;
2500 Standard_Integer iErr;
2501 Standard_Real aFuzzyValue;
2502 BRepAlgoAPI_Section aBuilder;
2504 // perpare the arguments
2505 TopTools_ListOfShape& aLS=…;
2506 TopTools_ListOfShape& aLT=…;
2508 bRunParallel=Standard_True;
2511 // set the arguments
2512 aBuilder.SetArguments(aLS);
2513 aBuilder.SetTools(aLT);
2515 // set parallel processing mode
2516 // if bRunParallel= Standard_True : the parallel processing is switched on
2517 // if bRunParallel= Standard_False : the parallel processing is switched off
2518 aBuilder.SetRunParallel(bRunParallel);
2521 // if aFuzzyValue=0.: the Fuzzy option is off
2522 // if aFuzzyValue>0.: the Fuzzy option is on
2523 aBuilder.SetFuzzyValue(aFuzzyValue);
2525 // run the algorithm
2527 iErr=aBuilder.ErrorStatus();
2529 // an error treatment
2533 // result of the operation aR
2534 const TopoDS_Shape& aR=aBuilder.Shape();
2542 # prepare the arguments
2544 box b2 3 4 5 10 10 10
2545 box b3 5 6 7 10 10 10
2547 # clear inner contents
2548 bclearobjects; bcleartools;
2554 # set parallel processing mode
2555 # 1: the parallel processing is switched on
2556 # 0: the parallel processing is switched off
2560 # 0. : the Fuzzy option is off
2561 # >0. : the Fuzzy option is on
2565 # r is the result of the operation
2566 # 4 means Section operation