1 Modeling Algorithms {#occt_user_guides__modeling_algos}
2 =========================
6 @section occt_modalg_1 Introduction
8 This manual explains how to use the Modeling Algorithms. It provides basic documentation on modeling algorithms. For advanced information on Modeling Algorithms, see our <a href="http://www.opencascade.com/content/tutorial-learning">E-learning & Training</a> offerings.
10 The Modeling Algorithms module brings together a wide range of topological algorithms used in modeling. Along with these tools, you will find the geometric algorithms, which they call.
12 @section occt_modalg_2 Geometric Tools
14 Open CASCADE Technology geometric tools provide algorithms to:
15 * Calculate the intersection of two 2D curves, surfaces, or a 3D curve and a surface;
16 * Project points onto 2D and 3D curves, points onto surfaces, and 3D curves onto surfaces;
17 * Construct lines and circles from constraints;
18 * Construct curves and surfaces from constraints;
19 * Construct curves and surfaces by interpolation.
21 @subsection occt_modalg_2_2 Intersections
23 The Intersections component is used to compute intersections between 2D or 3D geometrical objects:
24 * the intersections between two 2D curves;
25 * the self-intersections of a 2D curve;
26 * the intersection between a 3D curve and a surface;
27 * the intersection between two surfaces.
29 The *Geom2dAPI_InterCurveCurve* class allows the evaluation of the intersection points (*gp_Pnt2d*) between two geometric curves (*Geom2d_Curve*) and the evaluation of the points of self-intersection of a curve.
31 @image html /user_guides/modeling_algos/images/modeling_algos_image003.png "Intersection and self-intersection of curves"
32 @image latex /user_guides/modeling_algos/images/modeling_algos_image003.png "Intersection and self-intersection of curves"
34 In both cases, the algorithm requires a value for the tolerance (Standard_Real) for the confusion between two points. The default tolerance value used in all constructors is *1.0e-6.*
36 @image html /user_guides/modeling_algos/images/modeling_algos_image004.png "Intersection and tangent intersection"
37 @image latex /user_guides/modeling_algos/images/modeling_algos_image004.png "Intersection and tangent intersection"
39 The algorithm returns a point in the case of an intersection and a segment in the case of tangent intersection.
41 @subsubsection occt_modalg_2_2_1 Intersection of two curves
43 *Geom2dAPI_InterCurveCurve* class may be instantiated for intersection of curves *C1* and *C2*.
45 Geom2dAPI_InterCurveCurve Intersector(C1,C2,tolerance);
48 or for self-intersection of curve *C3*.
50 Geom2dAPI_InterCurveCurve Intersector(C3,tolerance);
54 Standard_Integer N = Intersector.NbPoints();
56 Calls the number of intersection points
58 To select the desired intersection point, pass an integer index value in argument.
60 gp_Pnt2d P = Intersector.Point(Index);
63 To call the number of intersection segments, use
65 Standard_Integer M = Intersector.NbSegments();
68 To select the desired intersection segment pass integer index values in argument.
70 Handle(Geom2d_Curve) Seg1, Seg2;
71 Intersector.Segment(Index,Seg1,Seg2);
72 // if intersection of 2 curves
73 Intersector.Segment(Index,Seg1);
74 // if self-intersection of a curve
77 If you need access to a wider range of functionalities the following method will return the algorithmic object for the calculation of intersections:
80 Geom2dInt_GInter& TheIntersector = Intersector.Intersector();
83 @subsubsection occt_modalg_2_2_2 Intersection of Curves and Surfaces
85 The *GeomAPI_IntCS* class is used to compute the intersection points between a curve and a surface.
87 This class is instantiated as follows:
89 GeomAPI_IntCS Intersector(C, S);
92 To call the number of intersection points, use:
94 Standard_Integer nb = Intersector.NbPoints();
99 gp_Pnt& P = Intersector.Point(Index);
102 Where *Index* is an integer between 1 and *nb*, calls the intersection points.
104 @subsubsection occt_modalg_2_2_3 Intersection of two Surfaces
105 The *GeomAPI_IntSS* class is used to compute the intersection of two surfaces from *Geom_Surface* with respect to a given tolerance.
107 This class is instantiated as follows:
109 GeomAPI_IntSS Intersector(S1, S2, Tolerance);
111 Once the *GeomAPI_IntSS* object has been created, it can be interpreted.
114 Standard_Integer nb = Intersector. NbLines();
116 Calls the number of intersection curves.
119 Handle(Geom_Curve) C = Intersector.Line(Index)
121 Where *Index* is an integer between 1 and *nb*, calls the intersection curves.
124 @subsection occt_modalg_2_3 Interpolations
126 The Interpolation Laws component provides definitions of functions: <i> y=f(x) </i>.
128 In particular, it provides definitions of:
130 * an <i> S </i> function, and
131 * an interpolation function for a range of values.
133 Such functions can be used to define, for example, the evolution law of a fillet along the edge of a shape.
135 The validity of the function built is never checked: the Law package does not know for what application or to what end the function will be used. In particular, if the function is used as the evolution law of a fillet, it is important that the function is always positive. The user must check this.
137 @subsubsection occt_modalg_2_3_1 Geom2dAPI_Interpolate
138 This class is used to interpolate a BSplineCurve passing through an array of points. If tangency is not requested at the point of interpolation, continuity will be *C2*. If tangency is requested at the point, continuity will be *C1*. If Periodicity is requested, the curve will be closed and the junction will be the first point given. The curve will then have a continuity of *C1* only.
139 This class may be instantiated as follows:
141 Geom2dAPI_Interpolate
142 (const Handle_TColgp_HArray1OfPnt2d& Points,
143 const Standard_Boolean PeriodicFlag,
144 const Standard_Real Tolerance);
146 Geom2dAPI_Interpolate Interp(Points, Standard_False,
147 Precision::Confusion());
151 It is possible to call the BSpline curve from the object defined above it.
153 Handle(Geom2d_BSplineCurve) C = Interp.Curve();
156 Note that the *Handle(Geom2d_BSplineCurve)* operator has been redefined by the method *Curve()*. Consequently, it is unnecessary to pass via the construction of an intermediate object of the *Geom2dAPI_Interpolate* type and the following syntax is correct.
159 Handle(Geom2d_BSplineCurve) C =
160 Geom2dAPI_Interpolate(Points,
162 Precision::Confusion());
165 @subsubsection occt_modalg_2_3_2 GeomAPI_Interpolate
167 This class may be instantiated as follows:
170 (const Handle_TColgp_HArray1OfPnt& Points,
171 const Standard_Boolean PeriodicFlag,
172 const Standard_Real Tolerance);
174 GeomAPI_Interpolate Interp(Points, Standard_False,
175 Precision::Confusion());
178 It is possible to call the BSpline curve from the object defined above it.
180 Handle(Geom_BSplineCurve) C = Interp.Curve();
182 Note that the *Handle(Geom_BSplineCurve)* operator has been redefined by the method *Curve()*. Thus, it is unnecessary to pass via the construction of an intermediate object of the *GeomAPI_Interpolate* type and the following syntax is correct.
184 Handle(Geom_BSplineCurve) C =
185 GeomAPI_Interpolate(Points,
189 Boundary conditions may be imposed with the method Load.
191 GeomAPI_Interpolate AnInterpolator
192 (Points, Standard_False, 1.0e-5);
193 AnInterpolator.Load (StartingTangent, EndingTangent);
196 @subsection occt_modalg_2_4 Lines and Circles from Constraints
198 @subsubsection occt_modalg_2_4_1 Types of constraints
200 The algorithms for construction of 2D circles or lines can be described with numeric or geometric constraints in relation to other curves.
202 These constraints can impose the following :
203 * the radius of a circle,
204 * the angle that a straight line makes with another straight line,
205 * the tangency of a straight line or circle in relation to a curve,
206 * the passage of a straight line or circle through a point,
207 * the circle with center in a point or curve.
209 For example, these algorithms enable to easily construct a circle of a given radius, centered on a straight line and tangential to another circle.
211 The implemented algorithms are more complex than those provided by the Direct Constructions component for building 2D circles or lines.
213 The expression of a tangency problem generally leads to several results, according to the relative positions of the solution and the circles or straight lines in relation to which the tangency constraints are expressed. For example, consider the following
214 case of a circle of a given radius (a small one) which is tangential to two secant circles C1 and C2:
216 @figure{/user_guides/modeling_algos/images/modeling_algos_image058.png,"Example of a Tangency Constraint"}
218 This diagram clearly shows that there are 8 possible solutions.
220 In order to limit the number of solutions, we can try to express the relative position
221 of the required solution in relation to the circles to which it is tangential. For
222 example, if we specify that the solution is inside the circle C1 and outside the
223 circle C2, only two solutions referenced 3 and 4 on the diagram respond to the problem
226 These definitions are very easy to interpret on a circle, where it is easy to identify
227 the interior and exterior sides. In fact, for any kind of curve the interior is defined
228 as the left-hand side of the curve in relation to its orientation.
230 This technique of qualification of a solution, in relation to the curves to which
231 it is tangential, can be used in all algorithms for constructing a circle or a straight
232 line by geometric constraints. Four qualifiers are used:
233 * **Enclosing** - the solution(s) must enclose the argument;
234 * **Enclosed** - the solution(s) must be enclosed by the argument;
235 * **Outside** - the solution(s) and the argument must be external to one another;
236 * **Unqualified** - the relative position is not qualified, i.e. all solutions apply.
238 It is possible to create expressions using the qualifiers, for example:
241 Solver(GccEnt::Outside(C1),
242 GccEnt::Enclosing(C2), Rad, Tolerance);
245 This expression finds all circles of radius *Rad*, which are tangent to both circle *C1* and *C2*, while *C1* is outside and *C2* is inside.
247 @subsubsection occt_modalg_2_4_2 Available types of lines and circles
249 The following analytic algorithms using value-handled entities for creation of 2D lines or circles with geometric constraints are available:
250 * circle tangent to three elements (lines, circles, curves, points),
251 * circle tangent to two elements and having a radius,
252 * circle tangent to two elements and centered on a third element,
253 * circle tangent to two elements and centered on a point,
254 * circle tangent to one element and centered on a second,
255 * bisector of two points,
256 * bisector of two lines,
257 * bisector of two circles,
258 * bisector of a line and a point,
259 * bisector of a circle and a point,
260 * bisector of a line and a circle,
261 * line tangent to two elements (points, circles, curves),
262 * line tangent to one element and parallel to a line,
263 * line tangent to one element and perpendicular to a line,
264 * line tangent to one element and forming angle with a line.
266 #### Exterior/Interior
267 It is not hard to define the interior and exterior of a circle. As is shown in the following diagram, the exterior is indicated by the sense of the binormal, that is to say the right side according to the sense of traversing the circle. The left side is therefore the interior (or "material").
269 @image html /user_guides/modeling_algos/images/modeling_algos_image006.png "Exterior/Interior of a Circle"
270 @image latex /user_guides/modeling_algos/images/modeling_algos_image006.png "Exterior/Interior of a Circle"
272 By extension, the interior of a line or any open curve is defined as the left side according to the passing direction, as shown in the following diagram:
274 @image html /user_guides/modeling_algos/images/modeling_algos_image007.png "Exterior/Interior of a Line and a Curve"
275 @image latex /user_guides/modeling_algos/images/modeling_algos_image007.png "Exterior/Interior of a Line and a Curve"
277 #### Orientation of a Line
278 It is sometimes necessary to define in advance the sense of travel along a line to be created. This sense will be from first to second argument.
280 The following figure shows a line, which is first tangent to circle C1 which is interior to the line, and then passes through point P1.
282 @image html /user_guides/modeling_algos/images/modeling_algos_image008.png "An Oriented Line"
283 @image latex /user_guides/modeling_algos/images/modeling_algos_image008.png "An Oriented Line"
286 #### Line tangent to two circles
287 The following four diagrams illustrate four cases of using qualifiers in the creation of a line. The fifth shows the solution if no qualifiers are given.
292 @image html /user_guides/modeling_algos/images/modeling_algos_image009.png "Both circles outside"
293 @image latex /user_guides/modeling_algos/images/modeling_algos_image009.png "Both circles outside"
296 Tangent and Exterior to C1.
297 Tangent and Exterior to C2.
303 Solver(GccEnt::Outside(C1),
310 @image html /user_guides/modeling_algos/images/modeling_algos_image010.png "Both circles enclosed"
311 @image latex /user_guides/modeling_algos/images/modeling_algos_image010.png "Both circles enclosed"
314 Tangent and Including C1.
315 Tangent and Including C2.
321 Solver(GccEnt::Enclosing(C1),
322 GccEnt::Enclosing(C2),
328 @image html /user_guides/modeling_algos/images/modeling_algos_image011.png "C1 enclosed, C2 outside"
329 @image latex /user_guides/modeling_algos/images/modeling_algos_image011.png "C1 enclosed, C2 outside"
332 Tangent and Including C1.
333 Tangent and Exterior to C2.
338 Solver(GccEnt::Enclosing(C1),
345 @image html /user_guides/modeling_algos/images/modeling_algos_image012.png "C1 outside, C2 enclosed"
346 @image latex /user_guides/modeling_algos/images/modeling_algos_image012.png "C1 outside, C2 enclosed"
348 Tangent and Exterior to C1.
349 Tangent and Including C2.
354 Solver(GccEnt::Outside(C1),
355 GccEnt::Enclosing(C2),
361 @image html /user_guides/modeling_algos/images/modeling_algos_image013.png "With no qualifiers specified"
362 @image latex /user_guides/modeling_algos/images/modeling_algos_image013.png "With no qualifiers specified"
365 Tangent and Undefined with respect to C1.
366 Tangent and Undefined with respect to C2.
371 Solver(GccEnt::Unqualified(C1),
372 GccEnt::Unqualified(C2),
376 #### Circle of given radius tangent to two circles
377 The following four diagrams show the four cases in using qualifiers in the creation of a circle.
380 @image html /user_guides/modeling_algos/images/modeling_algos_image014.png "Both solutions outside"
381 @image latex /user_guides/modeling_algos/images/modeling_algos_image014.png "Both solutions outside"
384 Tangent and Exterior to C1.
385 Tangent and Exterior to C2.
390 Solver(GccEnt::Outside(C1),
391 GccEnt::Outside(C2), Rad, Tolerance);
396 @image html /user_guides/modeling_algos/images/modeling_algos_image015.png "C2 encompasses C1"
397 @image latex /user_guides/modeling_algos/images/modeling_algos_image015.png "C2 encompasses C1"
400 Tangent and Exterior to C1.
401 Tangent and Included by C2.
406 Solver(GccEnt::Outside(C1),
407 GccEnt::Enclosed(C2), Rad, Tolerance);
411 @image html /user_guides/modeling_algos/images/modeling_algos_image016.png "Solutions enclose C2"
412 @image latex /user_guides/modeling_algos/images/modeling_algos_image016.png "Solutions enclose C2"
415 Tangent and Exterior to C1.
416 Tangent and Including C2.
421 Solver(GccEnt::Outside(C1),
422 GccEnt::Enclosing(C2), Rad, Tolerance);
426 @image html /user_guides/modeling_algos/images/modeling_algos_image017.png "Solutions enclose C1"
427 @image latex /user_guides/modeling_algos/images/modeling_algos_image017.png "Solutions enclose C1"
430 Tangent and Enclosing C1.
431 Tangent and Enclosing C2.
436 Solver(GccEnt::Enclosing(C1),
437 GccEnt::Enclosing(C2), Rad, Tolerance);
442 The following syntax will give all the circles of radius *Rad*, which are tangent to *C1* and *C2* without discrimination of relative position:
445 GccAna_Circ2d2TanRad Solver(GccEnt::Unqualified(C1),
446 GccEnt::Unqualified(C2),
451 @subsubsection occt_modalg_2_4_3 Types of algorithms
453 OCCT implements several categories of algorithms:
455 * **Analytic** algorithms, where solutions are obtained by the resolution of an equation, such algorithms are used when the geometries which are worked on (tangency arguments, position of the center, etc.) are points, lines or circles;
456 * **Geometric** algorithms, where the solution is generally obtained by calculating the intersection of parallel or bisecting curves built from geometric arguments;
457 * **Iterative** algorithms, where the solution is obtained by a process of iteration.
459 For each kind of geometric construction of a constrained line or circle, OCCT provides two types of access:
461 * algorithms from the package <i> Geom2dGcc </i> automatically select the algorithm best suited to the problem, both in the general case and in all types of specific cases; the used arguments are *Geom2d* objects, while the computed solutions are <i> gp </i> objects;
462 * algorithms from the package <i> GccAna</i> resolve the problem analytically, and can only be used when the geometries to be worked on are lines or circles; both the used arguments and the computed solutions are <i> gp </i> objects.
464 The provided algorithms compute all solutions, which correspond to the stated geometric problem, unless the solution is found by an iterative algorithm.
466 Iterative algorithms compute only one solution, closest to an initial position. They can be used in the following cases:
467 * to build a circle, when an argument is more complex than a line or a circle, and where the radius is not known or difficult to determine: this is the case for a circle tangential to three geometric elements, or tangential to two geometric elements and centered on a curve;
468 * to build a line, when a tangency argument is more complex than a line or a circle.
470 Qualified curves (for tangency arguments) are provided either by:
471 * the <i> GccEnt</i> package, for direct use by <i> GccAna</i> algorithms, or
472 * the <i> Geom2dGcc </i> package, for general use by <i> Geom2dGcc </i> algorithms.
474 The <i> GccEnt</i> and <i> Geom2dGcc</i> packages also provide simple functions for building qualified curves in a very efficient way.
476 The <i> GccAna </i>package also provides algorithms for constructing bisecting loci between circles, lines or points. Bisecting loci between two geometric objects are such that each of their points is at the same distance from the two geometric objects. They
477 are typically curves, such as circles, lines or conics for <i> GccAna</i> algorithms.
478 Each elementary solution is given as an elementary bisecting locus object (line, circle, ellipse, hyperbola, parabola), described by the <i>GccInt</i> package.
480 Note: Curves used by <i>GccAna</i> algorithms to define the geometric problem to be solved, are 2D lines or circles from the <i> gp</i> package: they are not explicitly parameterized. However, these lines or circles retain an implicit parameterization, corresponding to that which they induce on equivalent Geom2d objects. This induced parameterization is the one used when returning parameter values on such curves, for instance with the functions <i> Tangency1, Tangency2, Tangency3, Intersection2</i> and <i> CenterOn3</i> provided by construction algorithms from the <i> GccAna </i> or <i> Geom2dGcc</i> packages.
482 @subsection occt_modalg_2_5 Curves and Surfaces from Constraints
484 The Curves and Surfaces from Constraints component groups together high level functions used in 2D and 3D geometry for:
485 * creation of faired and minimal variation 2D curves
486 * construction of ruled surfaces
487 * construction of pipe surfaces
488 * filling of surfaces
489 * construction of plate surfaces
490 * extension of a 3D curve or surface beyond its original bounds.
492 OPEN CASCADE company also provides a product known as <a href="http://www.opencascade.com/content/surfaces-scattered-points">Surfaces from Scattered Points</a>, which allows constructing surfaces from scattered points. This algorithm accepts or constructs an initial B-Spline surface and looks for its deformation (finite elements method) which would satisfy the constraints. Using optimized computation methods, this algorithm is able to construct a surface from more than 500 000 points.
494 SSP product is not supplied with Open CASCADE Technology, but can be purchased separately.
496 @subsubsection occt_modalg_2_5_1 Faired and Minimal Variation 2D Curves
498 Elastic beam curves have their origin in traditional methods of modeling applied
499 in boat-building, where a long thin piece of wood, a lathe, was forced to pass
500 between two sets of nails and in this way, take the form of a curve based on the
501 two points, the directions of the forces applied at those points, and the properties
502 of the wooden lathe itself.
504 Maintaining these constraints requires both longitudinal and transversal forces to
505 be applied to the beam in order to compensate for its internal elasticity. The longitudinal
506 forces can be a push or a pull and the beam may or may not be allowed to slide over
511 The class *FairCurve_Batten* allows producing faired curves defined on the basis of one or more constraints on each of the two reference points. These include point, angle of tangency and curvature settings.
512 The following constraint orders are available:
514 * 0 the curve must pass through a point
515 * 1 the curve must pass through a point and have a given tangent
516 * 2 the curve must pass through a point, have a given tangent and a given curvature.
518 Only 0 and 1 constraint orders are used.
519 The function Curve returns the result as a 2D BSpline curve.
521 #### Minimal Variation Curves
523 The class *FairCurve_MinimalVariation* allows producing curves with minimal variation in curvature at each reference point. The following constraint orders are available:
525 * 0 the curve must pass through a point
526 * 1 the curve must pass through a point and have a given tangent
527 * 2 the curve must pass through a point, have a given tangent and a given curvature.
529 Constraint orders of 0, 1 and 2 can be used. The algorithm minimizes tension, sagging and jerk energy.
531 The function *Curve* returns the result as a 2D BSpline curve.
533 If you want to give a specific length to a batten curve, use:
536 b.SetSlidingFactor(L / b.SlidingOfReference())
538 where *b* is the name of the batten curve object
540 Free sliding is generally more aesthetically pleasing than constrained sliding. However, the computation can fail with values such as angles greater than *p/2* because in this case the length is theoretically infinite.
542 In other cases, when sliding is imposed and the sliding factor is too large, the batten can collapse.
544 The constructor parameters, *Tolerance* and *NbIterations*, control how precise the computation is, and how long it will take.
546 @subsubsection occt_modalg_2_5_2 Ruled Surfaces
548 A ruled surface is built by ruling a line along the length of two curves.
550 #### Creation of Bezier surfaces
552 The class *GeomFill_BezierCurves* allows producing a Bezier surface from contiguous Bezier curves. Note that problems may occur with rational Bezier Curves.
554 #### Creation of BSpline surfaces
556 The class *GeomFill_BSplineCurves* allows producing a BSpline surface from contiguous BSpline curves. Note that problems may occur with rational BSplines.
558 @subsubsection occt_modalg_2_5_3 Pipe Surfaces
560 The class *GeomFill_Pipe* allows producing a pipe by sweeping a curve (the section) along another curve (the path). The result is a BSpline surface.
562 The following types of construction are available:
563 * pipes with a circular section of constant radius,
564 * pipes with a constant section,
565 * pipes with a section evolving between two given curves.
568 @subsubsection occt_modalg_2_5_4 Filling a contour
570 It is often convenient to create a surface from two or more curves which will form the boundaries that define the new surface.
571 This is done by the class *GeomFill_ConstrainedFilling*, which allows filling a contour defined by two, three or four curves as well as by tangency constraints. The resulting surface is a BSpline.
573 A case in point is the intersection of two fillets at a corner. If the radius of the fillet on one edge is different from that of the fillet on another, it becomes impossible to sew together all the edges of the resulting surfaces. This leaves a gap in the overall surface of the object which you are constructing.
575 @figure{/user_guides/modeling_algos/images/modeling_algos_image059.png,"Intersecting filleted edges with differing radiuses"}
577 These algorithms allow you to fill this gap from two, three or four curves. This can be done with or without constraints, and the resulting surface will be either a Bezier or a BSpline surface in one of a range of filling styles.
579 #### Creation of a Boundary
581 The class *GeomFill_SimpleBound* allows you defining a boundary for the surface to be constructed.
583 #### Creation of a Boundary with an adjoining surface
585 The class *GeomFill_BoundWithSurf* allows defining a boundary for the surface to be constructed. This boundary will already be joined to another surface.
589 The enumerations *FillingStyle* specify the styles used to build the surface. These include:
591 * *Stretch* - the style with the flattest patches
592 * *Coons* - a rounded style with less depth than *Curved*
593 * *Curved* - the style with the most rounded patches.
595 @image html /user_guides/modeling_algos/images/modeling_algos_image018.png "Intersecting filleted edges with different radii leave a gap, is filled by a surface"
596 @image latex /user_guides/modeling_algos/images/modeling_algos_image018.png "Intersecting filleted edges with different radii leave a gap, is filled by a surface"
598 @subsubsection occt_modalg_2_5_5 Plate surfaces
600 In CAD, it is often necessary to generate a surface which has no exact mathematical definition, but which is defined by respective constraints. These can be of a mathematical, a technical or an aesthetic order.
602 Essentially, a plate surface is constructed by deforming a surface so that it conforms to a given number of curve or point constraints. In the figure below, you can see four segments of the outline of the plane, and a point which have been used as the
603 curve constraints and the point constraint respectively. The resulting surface can be converted into a BSpline surface by using the function <i> MakeApprox </i>.
605 The surface is built using a variational spline algorithm. It uses the principle of deformation of a thin plate by localised mechanical forces. If not already given in the input, an initial surface is calculated. This corresponds to the plate prior
606 to deformation. Then, the algorithm is called to calculate the final surface. It looks for a solution satisfying constraints and minimizing energy input.
608 @figure{/user_guides/modeling_algos/images/modeling_algos_image061.png,"Surface generated from two curves and a point"}
610 The package *GeomPlate* provides the following services for creating surfaces respecting curve and point constraints:
612 #### Definition of a Framework
614 The class *BuildPlateSurface* allows creating a framework to build surfaces according to curve and point constraints as well as tolerance settings. The result is returned with the function *Surface*.
616 Note that you do not have to specify an initial surface at the time of construction. It can be added later or, if none is loaded, a surface will be computed automatically.
618 #### Definition of a Curve Constraint
620 The class *CurveConstraint* allows defining curves as constraints to the surface, which you want to build.
622 #### Definition of a Point Constraint
624 The class *PointConstraint* allows defining points as constraints to the surface, which you want to build.
626 #### Applying Geom_Surface to Plate Surfaces
628 The class *Surface* allows describing the characteristics of plate surface objects returned by **BuildPlateSurface::Surface** using the methods of *Geom_Surface*
630 #### Approximating a Plate surface to a BSpline
632 The class *MakeApprox* allows converting a *GeomPlate* surface into a *Geom_BSplineSurface*.
634 @figure{/user_guides/modeling_algos/images/modeling_algos_image060.png,"Surface generated from four curves and a point"}
636 Let us create a Plate surface and approximate it from a polyline as a curve constraint and a point constraint
639 Standard_Integer NbCurFront=4,
642 gp_Pnt P2(0.,10.,0.);
643 gp_Pnt P3(0.,10.,10.);
644 gp_Pnt P4(0.,0.,10.);
646 BRepBuilderAPI_MakePolygon W;
652 // Initialize a BuildPlateSurface
653 GeomPlate_BuildPlateSurface BPSurf(3,15,2);
654 // Create the curve constraints
655 BRepTools_WireExplorer anExp;
656 for(anExp.Init(W); anExp.More(); anExp.Next())
658 TopoDS_Edge E = anExp.Current();
659 Handle(BRepAdaptor_HCurve) C = new
660 BRepAdaptor_HCurve();
661 C-ChangeCurve().Initialize(E);
662 Handle(BRepFill_CurveConstraint) Cont= new
663 BRepFill_CurveConstraint(C,0);
667 Handle(GeomPlate_PointConstraint) PCont= new
668 GeomPlate_PointConstraint(P5,0);
670 // Compute the Plate surface
672 // Approximation of the Plate surface
673 Standard_Integer MaxSeg=9;
674 Standard_Integer MaxDegree=8;
675 Standard_Integer CritOrder=0;
676 Standard_Real dmax,Tol;
677 Handle(GeomPlate_Surface) PSurf = BPSurf.Surface();
678 dmax = Max(0.0001,10*BPSurf.G0Error());
681 Mapp(PSurf,Tol,MaxSeg,MaxDegree,dmax,CritOrder);
682 Handle (Geom_Surface) Surf (Mapp.Surface());
683 // create a face corresponding to the approximated Plate
685 Standard_Real Umin, Umax, Vmin, Vmax;
686 PSurf-Bounds( Umin, Umax, Vmin, Vmax);
687 BRepBuilderAPI_MakeFace MF(Surf,Umin, Umax, Vmin, Vmax);
690 @subsection occt_modalg_2_6 Projections
692 Projections provide for computing the following:
693 * the projections of a 2D point onto a 2D curve
694 * the projections of a 3D point onto a 3D curve or surface
695 * the projection of a 3D curve onto a surface.
696 * the planar curve transposition from the 3D to the 2D parametric space of an underlying plane and v. s.
697 * the positioning of a 2D gp object in the 3D geometric space.
699 @subsubsection occt_modalg_2_6_1 Projection of a 2D Point on a Curve
701 *Geom2dAPI_ProjectPointOnCurve* allows calculation of all normals projected from a point (*gp_Pnt2d*) onto a geometric curve (*Geom2d_Curve*). The calculation may be restricted to a given domain.
703 @image html /user_guides/modeling_algos/images/modeling_algos_image020.png "Normals from a point to a curve"
704 @image latex /user_guides/modeling_algos/images/modeling_algos_image020.png "Normals from a point to a curve"
706 The curve does not have to be a *Geom2d_TrimmedCurve*. The algorithm will function with any class inheriting *Geom2d_Curve*.
708 The class *Geom2dAPI_ProjectPointOnCurve* may be instantiated as in the following example:
712 Handle(Geom2d_BezierCurve) C =
713 new Geom2d_BezierCurve(args);
714 Geom2dAPI_ProjectPointOnCurve Projector (P, C);
717 To restrict the search for normals to a given domain <i>[U1,U2]</i>, use the following constructor:
719 Geom2dAPI_ProjectPointOnCurve Projector (P, C, U1, U2);
721 Having thus created the *Geom2dAPI_ProjectPointOnCurve* object, we can now interrogate it.
723 #### Calling the number of solution points
726 Standard_Integer NumSolutions = Projector.NbPoints();
729 #### Calling the location of a solution point
731 The solutions are indexed in a range from *1* to *Projector.NbPoints()*. The point, which corresponds to a given *Index* may be found:
733 gp_Pnt2d Pn = Projector.Point(Index);
736 #### Calling the parameter of a solution point
738 For a given point corresponding to a given *Index*:
741 Standard_Real U = Projector.Parameter(Index);
744 This can also be programmed as:
748 Projector.Parameter(Index,U);
751 #### Calling the distance between the start and end points
753 We can find the distance between the initial point and a point, which corresponds to the given *Index*:
756 Standard_Real D = Projector.Distance(Index);
759 #### Calling the nearest solution point
762 This class offers a method to return the closest solution point to the starting point. This solution is accessed as follows:
764 gp_Pnt2d P1 = Projector.NearestPoint();
767 #### Calling the parameter of the nearest solution point
770 Standard_Real U = Projector.LowerDistanceParameter();
773 #### Calling the minimum distance from the point to the curve
776 Standard_Real D = Projector.LowerDistance();
779 #### Redefined operators
781 Some operators have been redefined to find the closest solution.
783 *Standard_Real()* returns the minimum distance from the point to the curve.
786 Standard_Real D = Geom2dAPI_ProjectPointOnCurve (P,C);
789 *Standard_Integer()* returns the number of solutions.
793 Geom2dAPI_ProjectPointOnCurve (P,C);
796 *gp_Pnt2d()* returns the nearest solution point.
799 gp_Pnt2d P1 = Geom2dAPI_ProjectPointOnCurve (P,C);
802 Using these operators makes coding easier when you only need the nearest point. Thus:
804 Geom2dAPI_ProjectPointOnCurve Projector (P, C);
805 gp_Pnt2d P1 = Projector.NearestPoint();
807 can be written more concisely as:
809 gp_Pnt2d P1 = Geom2dAPI_ProjectPointOnCurve (P,C);
811 However, note that in this second case no intermediate *Geom2dAPI_ProjectPointOnCurve* object is created, and thus it is impossible to have access to other solution points.
814 #### Access to lower-level functionalities
816 If you want to use the wider range of functionalities available from the *Extrema* package, a call to the *Extrema()* method will return the algorithmic object for calculating extrema. For example:
819 Extrema_ExtPC2d& TheExtrema = Projector.Extrema();
822 @subsubsection occt_modalg_2_6_2 Projection of a 3D Point on a Curve
824 The class *GeomAPI_ProjectPointOnCurve* is instantiated as in the following example:
828 Handle(Geom_BezierCurve) C =
829 new Geom_BezierCurve(args);
830 GeomAPI_ProjectPointOnCurve Projector (P, C);
833 If you wish to restrict the search for normals to the given domain [U1,U2], use the following constructor:
836 GeomAPI_ProjectPointOnCurve Projector (P, C, U1, U2);
838 Having thus created the *GeomAPI_ProjectPointOnCurve* object, you can now interrogate it.
840 #### Calling the number of solution points
843 Standard_Integer NumSolutions = Projector.NbPoints();
846 #### Calling the location of a solution point
848 The solutions are indexed in a range from 1 to *Projector.NbPoints()*. The point, which corresponds to a given index, may be found:
850 gp_Pnt Pn = Projector.Point(Index);
853 #### Calling the parameter of a solution point
855 For a given point corresponding to a given index:
858 Standard_Real U = Projector.Parameter(Index);
861 This can also be programmed as:
864 Projector.Parameter(Index,U);
867 #### Calling the distance between the start and end point
869 The distance between the initial point and a point, which corresponds to a given index, may be found:
871 Standard_Real D = Projector.Distance(Index);
874 #### Calling the nearest solution point
876 This class offers a method to return the closest solution point to the starting point. This solution is accessed as follows:
878 gp_Pnt P1 = Projector.NearestPoint();
881 #### Calling the parameter of the nearest solution point
884 Standard_Real U = Projector.LowerDistanceParameter();
887 #### Calling the minimum distance from the point to the curve
890 Standard_Real D = Projector.LowerDistance();
893 #### Redefined operators
895 Some operators have been redefined to find the nearest solution.
897 *Standard_Real()* returns the minimum distance from the point to the curve.
900 Standard_Real D = GeomAPI_ProjectPointOnCurve (P,C);
903 *Standard_Integer()* returns the number of solutions.
905 Standard_Integer N = GeomAPI_ProjectPointOnCurve (P,C);
908 *gp_Pnt2d()* returns the nearest solution point.
911 gp_Pnt P1 = GeomAPI_ProjectPointOnCurve (P,C);
913 Using these operators makes coding easier when you only need the nearest point. In this way,
916 GeomAPI_ProjectPointOnCurve Projector (P, C);
917 gp_Pnt P1 = Projector.NearestPoint();
920 can be written more concisely as:
922 gp_Pnt P1 = GeomAPI_ProjectPointOnCurve (P,C);
924 In the second case, however, no intermediate *GeomAPI_ProjectPointOnCurve* object is created, and it is impossible to access other solutions points.
926 #### Access to lower-level functionalities
928 If you want to use the wider range of functionalities available from the *Extrema* package, a call to the *Extrema()* method will return the algorithmic object for calculating the extrema. For example:
931 Extrema_ExtPC& TheExtrema = Projector.Extrema();
934 @subsubsection occt_modalg_2_6_3 Projection of a Point on a Surface
936 The class *GeomAPI_ProjectPointOnSurf* allows calculation of all normals projected from a point from *gp_Pnt* onto a geometric surface from *Geom_Surface*.
938 @image html /user_guides/modeling_algos/images/modeling_algos_image021.png "Projection of normals from a point to a surface"
939 @image latex /user_guides/modeling_algos/images/modeling_algos_image021.png "Projection of normals from a point to a surface"
941 Note that the surface does not have to be of *Geom_RectangularTrimmedSurface* type.
942 The algorithm will function with any class inheriting *Geom_Surface*.
944 *GeomAPI_ProjectPointOnSurf* is instantiated as in the following example:
947 Handle (Geom_Surface) S = new Geom_BezierSurface(args);
948 GeomAPI_ProjectPointOnSurf Proj (P, S);
951 To restrict the search for normals within the given rectangular domain [U1, U2, V1, V2], use the constructor <i>GeomAPI_ProjectPointOnSurf Proj (P, S, U1, U2, V1, V2)</i>
953 The values of *U1, U2, V1* and *V2* lie at or within their maximum and minimum limits, i.e.:
955 Umin <= U1 < U2 <= Umax
956 Vmin <= V1 < V2 <= Vmax
958 Having thus created the *GeomAPI_ProjectPointOnSurf* object, you can interrogate it.
960 #### Calling the number of solution points
963 Standard_Integer NumSolutions = Proj.NbPoints();
966 #### Calling the location of a solution point
968 The solutions are indexed in a range from 1 to *Proj.NbPoints()*. The point corresponding to the given index may be found:
971 gp_Pnt Pn = Proj.Point(Index);
974 #### Calling the parameters of a solution point
976 For a given point corresponding to the given index:
980 Proj.Parameters(Index, U, V);
983 #### Calling the distance between the start and end point
986 The distance between the initial point and a point corresponding to the given index may be found:
988 Standard_Real D = Projector.Distance(Index);
991 #### Calling the nearest solution point
993 This class offers a method, which returns the closest solution point to the starting point. This solution is accessed as follows:
995 gp_Pnt P1 = Proj.NearestPoint();
998 #### Calling the parameters of the nearest solution point
1002 Proj.LowerDistanceParameters (U, V);
1005 #### Calling the minimum distance from a point to the surface
1008 Standard_Real D = Proj.LowerDistance();
1011 #### Redefined operators
1013 Some operators have been redefined to help you find the nearest solution.
1015 *Standard_Real()* returns the minimum distance from the point to the surface.
1018 Standard_Real D = GeomAPI_ProjectPointOnSurf (P,S);
1021 *Standard_Integer()* returns the number of solutions.
1024 Standard_Integer N = GeomAPI_ProjectPointOnSurf (P,S);
1027 *gp_Pnt2d()* returns the nearest solution point.
1030 gp_Pnt P1 = GeomAPI_ProjectPointOnSurf (P,S);
1033 Using these operators makes coding easier when you only need the nearest point. In this way,
1036 GeomAPI_ProjectPointOnSurface Proj (P, S);
1037 gp_Pnt P1 = Proj.NearestPoint();
1040 can be written more concisely as:
1043 gp_Pnt P1 = GeomAPI_ProjectPointOnSurface (P,S);
1046 In the second case, however, no intermediate *GeomAPI_ProjectPointOnSurf* object is created, and it is impossible to access other solution points.
1048 #### Access to lower-level functionalities
1050 If you want to use the wider range of functionalities available from the *Extrema* package, a call to the *Extrema()* method will return the algorithmic object for calculating the extrema as follows:
1053 Extrema_ExtPS& TheExtrema = Proj.Extrema();
1056 @subsubsection occt_modalg_2_12_8 Switching from 2d and 3d Curves
1058 The *To2d* and *To3d* methods are used to;
1060 * build a 2d curve from a 3d *Geom_Curve* lying on a *gp_Pln* plane
1061 * build a 3d curve from a *Geom2d_Curve* and a *gp_Pln* plane.
1063 These methods are called as follows:
1065 Handle(Geom2d_Curve) C2d = GeomAPI::To2d(C3d, Pln);
1066 Handle(Geom_Curve) C3d = GeomAPI::To3d(C2d, Pln);
1069 @section occt_modalg_3a The Topology API
1071 The Topology API of Open CASCADE Technology (**OCCT**) includes the following six packages:
1079 The classes provided by the API have the following features:
1080 * The constructors of classes provide different construction methods;
1081 * The class retains different tools used to build objects as fields;
1082 * The class provides a casting method to obtain the result automatically with a function-like call.
1084 Let us use the class *BRepBuilderAPI_MakeEdge* to create a linear edge from two points.
1087 gp_Pnt P1(10,0,0), P2(20,0,0);
1088 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(P1,P2);
1091 This is the simplest way to create edge E from two points P1, P2, but the developer can test for errors when he is not as confident of the data as in the previous example.
1094 #include <gp_Pnt.hxx>
1095 #include <TopoDS_Edge.hxx>
1096 #include <BRepBuilderAPI_MakeEdge.hxx>
1101 BRepBuilderAPI_MakeEdge ME(P1,P2);
1104 // doing ME.Edge() or E = ME here
1105 // would raise StdFail_NotDone
1106 Standard_DomainError::Raise
1107 (“ProcessPoints::Failed to createan edge”);
1113 In this example an intermediary object ME has been introduced. This can be tested for the completion of the function before accessing the result. More information on **error handling** in the topology programming interface can be found in the next section.
1115 *BRepBuilderAPI_MakeEdge* provides valuable information. For example, when creating an edge from two points, two vertices have to be created from the points. Sometimes you may be interested in getting these vertices quickly without exploring the new edge. Such information can be provided when using a class. The following example shows a function creating an edge and two vertices from two points.
1118 void MakeEdgeAndVertices(const gp_Pnt& P1,
1124 BRepBuilderAPI_MakeEdge ME(P1,P2);
1126 Standard_DomainError::Raise
1127 (“MakeEdgeAndVerices::Failed to create an edge”);
1134 The class *BRepBuilderAPI_MakeEdge* provides two methods *Vertex1* and *Vertex2*, which return two vertices used to create the edge.
1136 How can *BRepBuilderAPI_MakeEdge* be both a function and a class? It can do this because it uses the casting capabilities of C++. The *BRepBuilderAPI_MakeEdge* class has a method called Edge; in the previous example the line <i>E = ME</i> could have been written.
1142 This instruction tells the C++ compiler that there is an **implicit casting** of a *BRepBuilderAPI_MakeEdge* into a *TopoDS_Edge* using the *Edge* method. It means this method is automatically called when a *BRepBuilderAPI_MakeEdge* is found where a *TopoDS_Edge* is required.
1144 This feature allows you to provide classes, which have the simplicity of function calls when required and the power of classes when advanced processing is necessary. All the benefits of this approach are explained when describing the topology programming interface classes.
1147 @subsection occt_modalg_3a_1 Error Handling in the Topology API
1149 A method can report an error in the two following situations:
1150 * The data or arguments of the method are incorrect, i.e. they do not respect the restrictions specified by the methods in its specifications. Typical example: creating a linear edge from two identical points is likely to lead to a zero divide when computing the direction of the line.
1151 * Something unexpected happened. This situation covers every error not included in the first category. Including: interruption, programming errors in the method or in another method called by the first method, bad specifications of the arguments (i.e. a set of arguments that was not expected to fail).
1153 The second situation is supposed to become increasingly exceptional as a system is debugged and it is handled by the **exception mechanism**. Using exceptions avoids handling error statuses in the call to a method: a very cumbersome style of programming.
1155 In the first situation, an exception is also supposed to be raised because the calling method should have verified the arguments and if it did not do so, there is a bug. For example, if before calling *MakeEdge* you are not sure that the two points are non-identical, this situation must be tested.
1157 Making those validity checks on the arguments can be tedious to program and frustrating as you have probably correctly surmised that the method will perform the test twice. It does not trust you.
1158 As the test involves a great deal of computation, performing it twice is also time-consuming.
1160 Consequently, you might be tempted to adopt the highly inadvisable style of programming illustrated in the following example:
1163 #include <Standard_ErrorHandler.hxx>
1165 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(P1,P2);
1166 // go on with the edge
1169 // process the error.
1173 To help the user, the Topology API classes only raise the exception *StdFail_NotDone*. Any other exception means that something happened which was unforeseen in the design of this API.
1175 The *NotDone* exception is only raised when the user tries to access the result of the computation and the original data is corrupted. At the construction of the class instance, if the algorithm cannot be completed, the internal flag *NotDone* is set. This flag can be tested and in some situations a more complete description of the error can be queried. If the user ignores the *NotDone* status and tries to access the result, an exception is raised.
1178 BRepBuilderAPI_MakeEdge ME(P1,P2);
1180 // doing ME.Edge() or E = ME here
1181 // would raise StdFail_NotDone
1182 Standard_DomainError::Raise
1183 (“ProcessPoints::Failed to create an edge”);
1188 @section occt_modalg_3 Standard Topological Objects
1190 The following standard topological objects can be created:
1199 There are two root classes for their construction and modification:
1200 * The deferred class *BRepBuilderAPI_MakeShape* is the root of all *BRepBuilderAPI* classes, which build shapes. It inherits from the class *BRepBuilderAPI_Command* and provides a field to store the constructed shape.
1201 * The deferred class *BRepBuilderAPI_ModifyShape* is used as a root for the shape modifications. It inherits *BRepBuilderAPI_MakeShape* and implements the methods used to trace the history of all sub-shapes.
1203 @subsection occt_modalg_3_1 Vertex
1205 *BRepBuilderAPI_MakeVertex* creates a new vertex from a 3D point from gp.
1208 TopoDS_Vertex V = BRepBuilderAPI_MakeVertex(P);
1211 This class always creates a new vertex and has no other methods.
1213 @subsection occt_modalg_3_2 Edge
1215 @subsubsection occt_modalg_3_2_1 Basic edge construction method
1217 Use *BRepBuilderAPI_MakeEdge* to create from a curve and vertices. The basic method constructs an edge from a curve, two vertices, and two parameters.
1220 Handle(Geom_Curve) C = ...; // a curve
1221 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1222 Standard_Real p1 = ..., p2 = ..;// two parameters
1223 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(C,V1,V2,p1,p2);
1226 where C is the domain of the edge; V1 is the first vertex oriented FORWARD; V2 is the second vertex oriented REVERSED; p1 and p2 are the parameters for the vertices V1 and V2 on the curve. The default tolerance is associated with this edge.
1228 @image html /user_guides/modeling_algos/images/modeling_algos_image022.png "Basic Edge Construction"
1229 @image latex /user_guides/modeling_algos/images/modeling_algos_image022.png "Basic Edge Construction"
1231 The following rules apply to the arguments:
1234 * Must not be a Null Handle.
1235 * If the curve is a trimmed curve, the basis curve is used.
1238 * Can be null shapes. When V1 or V2 is Null the edge is open in the corresponding direction and the corresponding parameter p1 or p2 must be infinite (i.e p1 is RealFirst(), p2 is RealLast()).
1239 * Must be different vertices if they have different 3d locations and identical vertices if they have the same 3d location (identical vertices are used when the curve is closed).
1242 * Must be increasing and in the range of the curve, i.e.:
1245 C->FirstParameter() <= p1 < p2 <= C->LastParameter()
1248 * If the parameters are decreasing, the Vertices are switched, i.e. V2 becomes V1 and V1 becomes V2.
1249 * On a periodic curve the parameters p1 and p2 are adjusted by adding or subtracting the period to obtain p1 in the range of the curve and p2 in the range p1 < p2 <= p1+ Period. So on a parametric curve p2 can be greater than the second parameter, see the figure below.
1250 * Can be infinite but the corresponding vertex must be Null (see above).
1251 * The distance between the Vertex 3d location and the point evaluated on the curve with the parameter must be lower than the default precision.
1253 The figure below illustrates two special cases, a semi-infinite edge and an edge on a periodic curve.
1255 @image html /user_guides/modeling_algos/images/modeling_algos_image023.png "Infinite and Periodic Edges"
1256 @image latex /user_guides/modeling_algos/images/modeling_algos_image023.png "Infinite and Periodic Edges"
1258 @subsubsection occt_modalg_3_2_2 Supplementary edge construction methods
1260 There exist supplementary edge construction methods derived from the basic one.
1262 *BRepBuilderAPI_MakeEdge* class provides methods, which are all simplified calls of the previous one:
1264 * The parameters can be omitted. They are computed by projecting the vertices on the curve.
1265 * 3d points (Pnt from gp) can be given in place of vertices. Vertices are created from the points. Giving vertices is useful when creating connected vertices.
1266 * The vertices or points can be omitted if the parameters are given. The points are computed by evaluating the parameters on the curve.
1267 * The vertices or points and the parameters can be omitted. The first and the last parameters of the curve are used.
1269 The five following methods are thus derived from the basic construction:
1272 Handle(Geom_Curve) C = ...; // a curve
1273 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1274 Standard_Real p1 = ..., p2 = ..;// two parameters
1275 gp_Pnt P1 = ..., P2 = ...;// two points
1277 // project the vertices on the curve
1278 E = BRepBuilderAPI_MakeEdge(C,V1,V2);
1279 // Make vertices from points
1280 E = BRepBuilderAPI_MakeEdge(C,P1,P2,p1,p2);
1281 // Make vertices from points and project them
1282 E = BRepBuilderAPI_MakeEdge(C,P1,P2);
1283 // Computes the points from the parameters
1284 E = BRepBuilderAPI_MakeEdge(C,p1,p2);
1285 // Make an edge from the whole curve
1286 E = BRepBuilderAPI_MakeEdge(C);
1290 Six methods (the five above and the basic method) are also provided for curves from the gp package in place of Curve from Geom. The methods create the corresponding Curve from Geom and are implemented for the following classes:
1292 *gp_Lin* creates a *Geom_Line*
1293 *gp_Circ* creates a *Geom_Circle*
1294 *gp_Elips* creates a *Geom_Ellipse*
1295 *gp_Hypr* creates a *Geom_Hyperbola*
1296 *gp_Parab* creates a *Geom_Parabola*
1298 There are also two methods to construct edges from two vertices or two points. These methods assume that the curve is a line; the vertices or points must have different locations.
1302 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1303 gp_Pnt P1 = ..., P2 = ...;// two points
1306 // linear edge from two vertices
1307 E = BRepBuilderAPI_MakeEdge(V1,V2);
1309 // linear edge from two points
1310 E = BRepBuilderAPI_MakeEdge(P1,P2);
1313 @subsubsection occt_modalg_3_2_3 Other information and error status
1315 The class *BRepBuilderAPI_MakeEdge* can provide extra information and return an error status.
1317 If *BRepBuilderAPI_MakeEdge* is used as a class, it can provide two vertices. This is useful when the vertices were not provided as arguments, for example when the edge was constructed from a curve and parameters. The two methods *Vertex1* and *Vertex2* return the vertices. Note that the returned vertices can be null if the edge is open in the corresponding direction.
1319 The *Error* method returns a term of the *BRepBuilderAPI_EdgeError* enumeration. It can be used to analyze the error when *IsDone* method returns False. The terms are:
1321 * **EdgeDone** - No error occurred, *IsDone* returns True.
1322 * **PointProjectionFailed** - No parameters were given, but the projection of the 3D points on the curve failed. This happens if the point distance to the curve is greater than the precision.
1323 * **ParameterOutOfRange** - The given parameters are not in the range *C->FirstParameter()*, *C->LastParameter()*
1324 * **DifferentPointsOnClosedCurve** - The two vertices or points have different locations but they are the extremities of a closed curve.
1325 * **PointWithInfiniteParameter** - A finite coordinate point was associated with an infinite parameter (see the Precision package for a definition of infinite values).
1326 * **DifferentsPointAndParameter** - The distance of the 3D point and the point evaluated on the curve with the parameter is greater than the precision.
1327 * **LineThroughIdenticPoints** - Two identical points were given to define a line (construction of an edge without curve), *gp::Resolution* is used to test confusion .
1329 The following example creates a rectangle centered on the origin of dimensions H, L with fillets of radius R. The edges and the vertices are stored in the arrays *theEdges* and *theVertices*. We use class *Array1OfShape* (i.e. not arrays of edges or vertices). See the image below.
1331 @image html /user_guides/modeling_algos/images/modeling_algos_image024.png "Creating a Wire"
1332 @image latex /user_guides/modeling_algos/images/modeling_algos_image024.png "Creating a Wire"
1335 #include <BRepBuilderAPI_MakeEdge.hxx>
1336 #include <TopoDS_Shape.hxx>
1337 #include <gp_Circ.hxx>
1339 #include <TopoDS_Wire.hxx>
1340 #include <TopTools_Array1OfShape.hxx>
1341 #include <BRepBuilderAPI_MakeWire.hxx>
1343 // Use MakeArc method to make an edge and two vertices
1344 void MakeArc(Standard_Real x,Standard_Real y,
1351 gp_Ax2 Origin = gp::XOY();
1352 gp_Vec Offset(x, y, 0.);
1353 Origin.Translate(Offset);
1354 BRepBuilderAPI_MakeEdge
1355 ME(gp_Circ(Origin,R), ang, ang+PI/2);
1361 TopoDS_Wire MakeFilletedRectangle(const Standard_Real H,
1362 const Standard_Real L,
1363 const Standard_Real R)
1365 TopTools_Array1OfShape theEdges(1,8);
1366 TopTools_Array1OfShape theVertices(1,8);
1368 // First create the circular edges and the vertices
1369 // using the MakeArc function described above.
1370 void MakeArc(Standard_Real, Standard_Real,
1371 Standard_Real, Standard_Real,
1372 TopoDS_Shape&, TopoDS_Shape&, TopoDS_Shape&);
1374 Standard_Real x = L/2 - R, y = H/2 - R;
1375 MakeArc(x,-y,R,3.*PI/2.,theEdges(2),theVertices(2),
1377 MakeArc(x,y,R,0.,theEdges(4),theVertices(4),
1379 MakeArc(-x,y,R,PI/2.,theEdges(6),theVertices(6),
1381 MakeArc(-x,-y,R,PI,theEdges(8),theVertices(8),
1383 // Create the linear edges
1384 for (Standard_Integer i = 1; i <= 7; i += 2)
1386 theEdges(i) = BRepBuilderAPI_MakeEdge
1387 (TopoDS::Vertex(theVertices(i)),TopoDS::Vertex
1388 (theVertices(i+1)));
1390 // Create the wire using the BRepBuilderAPI_MakeWire
1391 BRepBuilderAPI_MakeWire MW;
1392 for (i = 1; i <= 8; i++)
1394 MW.Add(TopoDS::Edge(theEdges(i)));
1400 @subsection occt_modalg_3_3 Edge 2D
1402 Use *BRepBuilderAPI_MakeEdge2d* class to make edges on a working plane from 2d curves. The working plane is a default value of the *BRepBuilderAPI* package (see the *Plane* methods).
1404 *BRepBuilderAPI_MakeEdge2d* class is strictly similar to BRepBuilderAPI_MakeEdge, but it uses 2D geometry from gp and Geom2d instead of 3D geometry.
1406 @subsection occt_modalg_3_4 Polygon
1408 *BRepBuilderAPI_MakePolygon* class is used to build polygonal wires from vertices or points. Points are automatically changed to vertices as in *BRepBuilderAPI_MakeEdge*.
1410 The basic usage of *BRepBuilderAPI_MakePolygon* is to create a wire by adding vertices or points using the Add method. At any moment, the current wire can be extracted. The close method can be used to close the current wire. In the following example, a closed wire is created from an array of points.
1413 #include <TopoDS_Wire.hxx>
1414 #include <BRepBuilderAPI_MakePolygon.hxx>
1415 #include <TColgp_Array1OfPnt.hxx>
1417 TopoDS_Wire ClosedPolygon(const TColgp_Array1OfPnt& Points)
1419 BRepBuilderAPI_MakePolygon MP;
1420 for(Standard_Integer i=Points.Lower();i=Points.Upper();i++)
1429 Short-cuts are provided for 2, 3, or 4 points or vertices. Those methods have a Boolean last argument to tell if the polygon is closed. The default value is False.
1433 Example of a closed triangle from three vertices:
1435 TopoDS_Wire W = BRepBuilderAPI_MakePolygon(V1,V2,V3,Standard_True);
1438 Example of an open polygon from four points:
1440 TopoDS_Wire W = BRepBuilderAPI_MakePolygon(P1,P2,P3,P4);
1443 *BRepBuilderAPI_MakePolygon* class maintains a current wire. The current wire can be extracted at any moment and the construction can proceed to a longer wire. After each point insertion, the class maintains the last created edge and vertex, which are returned by the methods *Edge, FirstVertex* and *LastVertex*.
1445 When the added point or vertex has the same location as the previous one it is not added to the current wire but the most recently created edge becomes Null. The *Added* method can be used to test this condition. The *MakePolygon* class never raises an error. If no vertex has been added, the *Wire* is *Null*. If two vertices are at the same location, no edge is created.
1447 @subsection occt_modalg_3_5 Face
1449 Use *BRepBuilderAPI_MakeFace* class to create a face from a surface and wires. An underlying surface is constructed from a surface and optional parametric values. Wires can be added to the surface. A planar surface can be constructed from a wire. An error status can be returned after face construction.
1451 @subsubsection occt_modalg_3_5_1 Basic face construction method
1453 A face can be constructed from a surface and four parameters to determine a limitation of the UV space. The parameters are optional, if they are omitted the natural bounds of the surface are used. Up to four edges and vertices are created with a wire. No edge is created when the parameter is infinite.
1456 Handle(Geom_Surface) S = ...; // a surface
1457 Standard_Real umin,umax,vmin,vmax; // parameters
1458 TopoDS_Face F = BRepBuilderAPI_MakeFace(S,umin,umax,vmin,vmax);
1461 @image html /user_guides/modeling_algos/images/modeling_algos_image025.png "Basic Face Construction"
1462 @image latex /user_guides/modeling_algos/images/modeling_algos_image025.png "Basic Face Construction"
1464 To make a face from the natural boundary of a surface, the parameters are not required:
1467 Handle(Geom_Surface) S = ...; // a surface
1468 TopoDS_Face F = BRepBuilderAPI_MakeFace(S);
1471 Constraints on the parameters are similar to the constraints in *BRepBuilderAPI_MakeEdge*.
1472 * *umin,umax (vmin,vmax)* must be in the range of the surface and must be increasing.
1473 * On a *U (V)* periodic surface *umin* and *umax (vmin,vmax)* are adjusted.
1474 * *umin, umax, vmin, vmax* can be infinite. There will be no edge in the corresponding direction.
1476 @subsubsection occt_modalg_3_5_2 Supplementary face construction methods
1478 The two basic constructions (from a surface and from a surface and parameters) are implemented for all *gp* package surfaces, which are transformed in the corresponding Surface from Geom.
1480 | gp package surface | | Geom package surface |
1481 | :------------------- | :----------- | :------------- |
1482 | *gp_Pln* | | *Geom_Plane* |
1483 | *gp_Cylinder* | | *Geom_CylindricalSurface* |
1484 | *gp_Cone* | creates a | *Geom_ConicalSurface* |
1485 | *gp_Sphere* | | *Geom_SphericalSurface* |
1486 | *gp_Torus* | | *Geom_ToroidalSurface* |
1488 Once a face has been created, a wire can be added using the *Add* method. For example, the following code creates a cylindrical surface and adds a wire.
1491 gp_Cylinder C = ..; // a cylinder
1492 TopoDS_Wire W = ...;// a wire
1493 BRepBuilderAPI_MakeFace MF(C);
1498 More than one wire can be added to a face, provided that they do not cross each other and they define only one area on the surface. (Note that this is not checked). The edges on a Face must have a parametric curve description.
1500 If there is no parametric curve for an edge of the wire on the Face it is computed by projection.
1502 For one wire, a simple syntax is provided to construct the face from the surface and the wire. The above lines could be written:
1505 TopoDS_Face F = BRepBuilderAPI_MakeFace(C,W);
1508 A planar face can be created from only a wire, provided this wire defines a plane. For example, to create a planar face from a set of points you can use *BRepBuilderAPI_MakePolygon* and *BRepBuilderAPI_MakeFace*.
1511 #include <TopoDS_Face.hxx>
1512 #include <TColgp_Array1OfPnt.hxx>
1513 #include <BRepBuilderAPI_MakePolygon.hxx>
1514 #include <BRepBuilderAPI_MakeFace.hxx>
1516 TopoDS_Face PolygonalFace(const TColgp_Array1OfPnt& thePnts)
1518 BRepBuilderAPI_MakePolygon MP;
1519 for(Standard_Integer i=thePnts.Lower();
1520 i<=thePnts.Upper(); i++)
1525 TopoDS_Face F = BRepBuilderAPI_MakeFace(MP.Wire());
1530 The last use of *MakeFace* is to copy an existing face to add new wires. For example, the following code adds a new wire to a face:
1533 TopoDS_Face F = ...; // a face
1534 TopoDS_Wire W = ...; // a wire
1535 F = BRepBuilderAPI_MakeFace(F,W);
1538 To add more than one wire an instance of the *BRepBuilderAPI_MakeFace* class can be created with the face and the first wire and the new wires inserted with the *Add* method.
1540 @subsubsection occt_modalg_3_5_3 Error status
1542 The *Error* method returns an error status, which is a term from the *BRepBuilderAPI_FaceError* enumeration.
1544 * *FaceDone* - no error occurred.
1545 * *NoFace* - no initialization of the algorithm; an empty constructor was used.
1546 * *NotPlanar* - no surface was given and the wire was not planar.
1547 * *CurveProjectionFailed* - no curve was found in the parametric space of the surface for an edge.
1548 * *ParametersOutOfRange* - the parameters *umin, umax, vmin, vmax* are out of the surface.
1550 @subsection occt_modalg_3_6 Wire
1551 The wire is a composite shape built not from a geometry, but by the assembly of edges. *BRepBuilderAPI_MakeWire* class can build a wire from one or more edges or connect new edges to an existing wire.
1553 Up to four edges can be used directly, for example:
1556 TopoDS_Wire W = BRepBuilderAPI_MakeWire(E1,E2,E3,E4);
1559 For a higher or unknown number of edges the Add method must be used; for example, to build a wire from an array of shapes (to be edges).
1562 TopTools_Array1OfShapes theEdges;
1563 BRepBuilderAPI_MakeWire MW;
1564 for (Standard_Integer i = theEdge.Lower();
1565 i <= theEdges.Upper(); i++)
1566 MW.Add(TopoDS::Edge(theEdges(i));
1570 The class can be constructed with a wire. A wire can also be added. In this case, all the edges of the wires are added. For example to merge two wires:
1573 #include <TopoDS_Wire.hxx>
1574 #include <BRepBuilderAPI_MakeWire.hxx>
1576 TopoDS_Wire MergeWires (const TopoDS_Wire& W1,
1577 const TopoDS_Wire& W2)
1579 BRepBuilderAPI_MakeWire MW(W1);
1585 *BRepBuilderAPI_MakeWire* class connects the edges to the wire. When a new edge is added if one of its vertices is shared with the wire it is considered as connected to the wire. If there is no shared vertex, the algorithm searches for a vertex of the edge and a vertex of the wire, which are at the same location (the tolerances of the vertices are used to test if they have the same location). If such a pair of vertices is found, the edge is copied with the vertex of the wire in place of the original vertex. All the vertices of the edge can be exchanged for vertices from the wire. If no connection is found the wire is considered to be disconnected. This is an error.
1587 BRepBuilderAPI_MakeWire class can return the last edge added to the wire (Edge method). This edge can be different from the original edge if it was copied.
1589 The Error method returns a term of the *BRepBuilderAPI_WireError* enumeration:
1590 *WireDone* - no error occurred.
1591 *EmptyWire* - no initialization of the algorithm, an empty constructor was used.
1592 *DisconnectedWire* - the last added edge was not connected to the wire.
1593 *NonManifoldWire* - the wire with some singularity.
1595 @subsection occt_modalg_3_7 Shell
1596 The shell is a composite shape built not from a geometry, but by the assembly of faces.
1597 Use *BRepBuilderAPI_MakeShell* class to build a Shell from a set of Faces. What may be important is that each face should have the required continuity. That is why an initial surface is broken up into faces.
1599 @subsection occt_modalg_3_8 Solid
1600 The solid is a composite shape built not from a geometry, but by the assembly of shells. Use *BRepBuilderAPI_MakeSolid* class to build a Solid from a set of Shells. Its use is similar to the use of the MakeWire class: shells are added to the solid in the same way that edges are added to the wire in MakeWire.
1603 @section occt_modalg_3b Object Modification
1605 @subsection occt_modalg_3b_1 Transformation
1606 *BRepBuilderAPI_Transform* class can be used to apply a transformation to a shape (see class *gp_Trsf*). The methods have a boolean argument to copy or share the original shape, as long as the transformation allows (it is only possible for direct isometric transformations). By default, the original shape is shared.
1608 The following example deals with the rotation of shapes.
1612 TopoDS_Shape myShape1 = ...;
1613 // The original shape 1
1614 TopoDS_Shape myShape2 = ...;
1615 // The original shape2
1617 T.SetRotation(gp_Ax1(gp_Pnt(0.,0.,0.),gp_Vec(0.,0.,1.)),
1619 BRepBuilderAPI_Transformation theTrsf(T);
1620 theTrsf.Perform(myShape1);
1621 TopoDS_Shape myNewShape1 = theTrsf.Shape()
1622 theTrsf.Perform(myShape2,Standard_True);
1623 // Here duplication is forced
1624 TopoDS_Shape myNewShape2 = theTrsf.Shape()
1627 @subsection occt_modalg_3b_2 Duplication
1629 Use the *BRepBuilderAPI_Copy* class to duplicate a shape. A new shape is thus created.
1630 In the following example, a solid is copied:
1633 TopoDS Solid MySolid;
1634 ....// Creates a solid
1636 TopoDS_Solid myCopy = BRepBuilderAPI_Copy(mySolid);
1640 @section occt_modalg_4 Primitives
1642 The <i> BRepPrimAPI</i> package provides an API (Application Programming Interface) for construction of primitives such as:
1648 It is possible to create partial solids, such as a sphere limited by longitude. In real models, primitives can be used for easy creation of specific sub-parts.
1650 * Construction by sweeping along a profile:
1652 * Rotational (through an angle of rotation).
1654 Sweeps are objects obtained by sweeping a profile along a path. The profile can be any topology and the path is usually a curve or a wire. The profile generates objects according to the following rules:
1655 * Vertices generate Edges
1656 * Edges generate Faces.
1657 * Wires generate Shells.
1658 * Faces generate Solids.
1659 * Shells generate Composite Solids.
1661 It is not allowed to sweep Solids and Composite Solids. Swept constructions along complex profiles such as BSpline curves also available in the <i> BRepOffsetAPI </i> package. This API provides simple, high level calls for the most common operations.
1663 @subsection occt_modalg_4_1 Making Primitives
1664 @subsubsection occt_modalg_4_1_1 Box
1666 The class *BRepPrimAPI_MakeBox* allows building a parallelepiped box. The result is either a **Shell** or a **Solid**. There are four ways to build a box:
1668 * From three dimensions *dx, dy* and *dz*. The box is parallel to the axes and extends for <i>[0,dx] [0,dy] [0,dz] </i>.
1669 * From a point and three dimensions. The same as above but the point is the new origin.
1670 * From two points, the box is parallel to the axes and extends on the intervals defined by the coordinates of the two points.
1671 * From a system of axes *gp_Ax2* and three dimensions. Same as the first way but the box is parallel to the given system of axes.
1673 An error is raised if the box is flat in any dimension using the default precision. The following code shows how to create a box:
1675 TopoDS_Solid theBox = BRepPrimAPI_MakeBox(10.,20.,30.);
1678 The four methods to build a box are shown in the figure:
1680 @image html /user_guides/modeling_algos/images/modeling_algos_image026.png "Making Boxes"
1681 @image latex /user_guides/modeling_algos/images/modeling_algos_image026.png "Making Boxes"
1683 @subsubsection occt_modalg_4_1_2 Wedge
1684 *BRepPrimAPI_MakeWedge* class allows building a wedge, which is a slanted box, i.e. a box with angles. The wedge is constructed in much the same way as a box i.e. from three dimensions dx,dy,dz plus arguments or from an axis system, three dimensions, and arguments.
1686 The following figure shows two ways to build wedges. One is to add a dimension *ltx*, which is the length in *x* of the face at *dy*. The second is to add *xmin, xmax, zmin* and *zmax* to describe the face at *dy*.
1688 The first method is a particular case of the second with *xmin = 0, xmax = ltx, zmin = 0, zmax = dz*.
1689 To make a centered pyramid you can use *xmin = xmax = dx / 2, zmin = zmax = dz / 2*.
1691 @image html /user_guides/modeling_algos/images/modeling_algos_image027.png "Making Wedges"
1692 @image latex /user_guides/modeling_algos/images/modeling_algos_image027.png "Making Wedges"
1694 @subsubsection occt_modalg_4_1_3 Rotation object
1695 *BRepPrimAPI_MakeOneAxis* is a deferred class used as a root class for all classes constructing rotational primitives. Rotational primitives are created by rotating a curve around an axis. They cover the cylinder, the cone, the sphere, the torus, and the revolution, which provides all other curves.
1697 The particular constructions of these primitives are described, but they all have some common arguments, which are:
1699 * A system of coordinates, where the Z axis is the rotation axis..
1700 * An angle in the range [0,2*PI].
1701 * A vmin, vmax parameter range on the curve.
1703 The result of the OneAxis construction is a Solid, a Shell, or a Face. The face is the face covering the rotational surface. Remember that you will not use the OneAxis directly but one of the derived classes, which provide improved constructions. The following figure illustrates the OneAxis arguments.
1705 @image html /user_guides/modeling_algos/images/modeling_algos_image028.png "MakeOneAxis arguments"
1706 @image latex /user_guides/modeling_algos/images/modeling_algos_image028.png "MakeOneAxis arguments"
1708 @subsubsection occt_modalg_4_1_4 Cylinder
1709 *BRepPrimAPI_MakeCylinder* class allows creating cylindrical primitives. A cylinder is created either in the default coordinate system or in a given coordinate system *gp_Ax2*. There are two constructions:
1711 * Radius and height, to build a full cylinder.
1712 * Radius, height and angle to build a portion of a cylinder.
1714 The following code builds the cylindrical face of the figure, which is a quarter of cylinder along the *Y* axis with the origin at *X,Y,Z* the length of *DY* and radius *R*.
1718 Standard_Real X = 20, Y = 10, Z = 15, R = 10, DY = 30;
1719 // Make the system of coordinates
1720 gp_Ax2 axes = gp::ZOX();
1721 axes.Translate(gp_Vec(X,Y,Z));
1723 BRepPrimAPI_MakeCylinder(axes,R,DY,PI/2.);
1725 @image html /user_guides/modeling_algos/images/modeling_algos_image029.png "Cylinder"
1726 @image latex /user_guides/modeling_algos/images/modeling_algos_image029.png "Cylinder"
1728 @subsubsection occt_modalg_4_1_5 Cone
1729 *BRepPrimAPI_MakeCone* class allows creating conical primitives. Like a cylinder, a cone is created either in the default coordinate system or in a given coordinate system (gp_Ax2). There are two constructions:
1731 * Two radii and height, to build a full cone. One of the radii can be null to make a sharp cone.
1732 * Radii, height and angle to build a truncated cone.
1734 The following code builds the solid cone of the figure, which is located in the default system with radii *R1* and *R2* and height *H*.
1737 Standard_Real R1 = 30, R2 = 10, H = 15;
1738 TopoDS_Solid S = BRepPrimAPI_MakeCone(R1,R2,H);
1741 @image html /user_guides/modeling_algos/images/modeling_algos_image030.png "Cone"
1742 @image latex /user_guides/modeling_algos/images/modeling_algos_image030.png "Cone"
1744 @subsubsection occt_modalg_4_1_6 Sphere
1745 *BRepPrimAPI_MakeSphere* class allows creating spherical primitives. Like a cylinder, a sphere is created either in the default coordinate system or in a given coordinate system *gp_Ax2*. There are four constructions:
1747 * From a radius - builds a full sphere.
1748 * From a radius and an angle - builds a lune (digon).
1749 * From a radius and two angles - builds a wraparound spherical segment between two latitudes. The angles *a1* and *a2* must follow the relation: <i>PI/2 <= a1 < a2 <= PI/2 </i>.
1750 * From a radius and three angles - a combination of two previous methods builds a portion of spherical segment.
1752 The following code builds four spheres from a radius and three angles.
1755 Standard_Real R = 30, ang =
1756 PI/2, a1 = -PI/2.3, a2 = PI/4;
1757 TopoDS_Solid S1 = BRepPrimAPI_MakeSphere(R);
1758 TopoDS_Solid S2 = BRepPrimAPI_MakeSphere(R,ang);
1759 TopoDS_Solid S3 = BRepPrimAPI_MakeSphere(R,a1,a2);
1760 TopoDS_Solid S4 = BRepPrimAPI_MakeSphere(R,a1,a2,ang);
1763 Note that we could equally well choose to create Shells instead of Solids.
1765 @image html /user_guides/modeling_algos/images/modeling_algos_image031.png "Examples of Spheres"
1766 @image latex /user_guides/modeling_algos/images/modeling_algos_image031.png "Examples of Spheres"
1769 @subsubsection occt_modalg_4_1_7 Torus
1770 *BRepPrimAPI_MakeTorus* class allows creating toroidal primitives. Like the other primitives, a torus is created either in the default coordinate system or in a given coordinate system *gp_Ax2*. There are four constructions similar to the sphere constructions:
1772 * Two radii - builds a full torus.
1773 * Two radii and an angle - builds an angular torus segment.
1774 * Two radii and two angles - builds a wraparound torus segment between two radial planes. The angles a1, a2 must follow the relation 0 < a2 - a1 < 2*PI.
1775 * Two radii and three angles - a combination of two previous methods builds a portion of torus segment.
1777 @image html /user_guides/modeling_algos/images/modeling_algos_image032.png "Examples of Tori"
1778 @image latex /user_guides/modeling_algos/images/modeling_algos_image032.png "Examples of Tori"
1780 The following code builds four toroidal shells from two radii and three angles.
1783 Standard_Real R1 = 30, R2 = 10, ang = PI, a1 = 0,
1785 TopoDS_Shell S1 = BRepPrimAPI_MakeTorus(R1,R2);
1786 TopoDS_Shell S2 = BRepPrimAPI_MakeTorus(R1,R2,ang);
1787 TopoDS_Shell S3 = BRepPrimAPI_MakeTorus(R1,R2,a1,a2);
1789 BRepPrimAPI_MakeTorus(R1,R2,a1,a2,ang);
1792 Note that we could equally well choose to create Solids instead of Shells.
1794 @subsubsection occt_modalg_4_1_8 Revolution
1795 *BRepPrimAPI_MakeRevolution* class allows building a uniaxial primitive from a curve. As other uniaxial primitives it can be created in the default coordinate system or in a given coordinate system.
1797 The curve can be any *Geom_Curve*, provided it is planar and lies in the same plane as the Z-axis of local coordinate system. There are four modes of construction:
1799 * From a curve, use the full curve and make a full rotation.
1800 * From a curve and an angle of rotation.
1801 * From a curve and two parameters to trim the curve. The two parameters must be growing and within the curve range.
1802 * From a curve, two parameters, and an angle. The two parameters must be growing and within the curve range.
1805 @subsection occt_modalg_4_2 Sweeping: Prism, Revolution and Pipe
1806 @subsubsection occt_modalg_4_2_1 Sweeping
1808 Sweeps are the objects you obtain by sweeping a **profile** along a **path**. The profile can be of any topology. The path is usually a curve or a wire. The profile generates objects according to the following rules:
1810 * Vertices generate Edges
1811 * Edges generate Faces.
1812 * Wires generate Shells.
1813 * Faces generate Solids.
1814 * Shells generate Composite Solids
1816 It is forbidden to sweep Solids and Composite Solids. A Compound generates a Compound with the sweep of all its elements.
1818 @image html /user_guides/modeling_algos/images/modeling_algos_image033.png "Generating a sweep"
1819 @image latex /user_guides/modeling_algos/images/modeling_algos_image033.png "Generating a sweep"
1821 *BRepPrimAPI_MakeSweep class* is a deferred class used as a root of the the following sweep classes:
1822 * *BRepPrimAPI_MakePrism* - produces a linear sweep
1823 * *BRepPrimAPI_MakeRevol* - produces a rotational sweep
1824 * *BRepPrimAPI_MakePipe* - produces a general sweep.
1827 @subsubsection occt_modalg_4_2_2 Prism
1828 *BRepPrimAPI_MakePrism* class allows creating a linear **prism** from a shape and a vector or a direction.
1829 * A vector allows creating a finite prism;
1830 * A direction allows creating an infinite or semi-infinite prism. The semi-infinite or infinite prism is toggled by a Boolean argument. All constructors have a boolean argument to copy the original shape or share it (by default).
1832 The following code creates a finite, an infinite and a semi-infinite solid using a face, a direction and a length.
1835 TopoDS_Face F = ..; // The swept face
1836 gp_Dir direc(0,0,1);
1837 Standard_Real l = 10;
1838 // create a vector from the direction and the length
1841 TopoDS_Solid P1 = BRepPrimAPI_MakePrism(F,v);
1843 TopoDS_Solid P2 = BRepPrimAPI_MakePrism(F,direc);
1845 TopoDS_Solid P3 = BRepPrimAPI_MakePrism(F,direc,Standard_False);
1849 @image html /user_guides/modeling_algos/images/modeling_algos_image034.png "Finite, infinite, and semi-infinite prisms"
1850 @image latex /user_guides/modeling_algos/images/modeling_algos_image034.png "Finite, infinite, and semi-infinite prisms"
1852 @subsubsection occt_modalg_4_2_3 Rotational Sweep
1853 *BRepPrimAPI_MakeRevol* class allows creating a rotational sweep from a shape, an axis (gp_Ax1), and an angle. The angle has a default value of 2*PI which means a closed revolution.
1855 *BRepPrimAPI_MakeRevol* constructors have a last argument to copy or share the original shape. The following code creates a a full and a partial rotation using a face, an axis and an angle.
1858 TopoDS_Face F = ...; // the profile
1859 gp_Ax1 axis(gp_Pnt(0,0,0),gp_Dir(0,0,1));
1860 Standard_Real ang = PI/3;
1861 TopoDS_Solid R1 = BRepPrimAPI_MakeRevol(F,axis);
1863 TopoDS_Solid R2 = BRepPrimAPI_MakeRevol(F,axis,ang);
1866 @image html /user_guides/modeling_algos/images/modeling_algos_image035.png "Full and partial rotation"
1867 @image latex /user_guides/modeling_algos/images/modeling_algos_image035.png "Full and partial rotation"
1869 @section occt_modalg_5 Boolean Operations
1871 Boolean operations are used to create new shapes from the combinations of two shapes.
1873 | Operation | Result |
1875 | Fuse | all points in S1 or S2 |
1876 | Common | all points in S1 and S2 |
1877 | Cut S1 by S2| all points in S1 and not in S2 |
1879 @image html /user_guides/modeling_algos/images/modeling_algos_image036.png "Boolean Operations"
1880 @image latex /user_guides/modeling_algos/images/modeling_algos_image036.png "Boolean Operations"
1882 From the viewpoint of Topology these are topological operations followed by blending (putting fillets onto edges created after the topological operation).
1884 Topological operations are the most convenient way to create real industrial parts. As most industrial parts consist of several simple elements such as gear wheels, arms, holes, ribs, tubes and pipes. It is usually easy to create those elements separately and then to combine them by Boolean operations in the whole final part.
1886 See @ref occt_user_guides__boolean_operations "Boolean Operations" for detailed documentation.
1888 @subsection occt_modalg_5_1 Input and Result Arguments
1890 Boolean Operations have the following types of the arguments and produce the following results:
1891 * For arguments having the same shape type (e.g. SOLID / SOLID) the type of the resulting shape will be a COMPOUND, containing shapes of this type;
1892 * For arguments having different shape types (e.g. SHELL / SOLID) the type of the resulting shape will be a COMPOUND, containing shapes of the type that is the same as that of the low type of the argument. Example: For SHELL/SOLID the result is a COMPOUND of SHELLs.
1893 * For arguments with different shape types some of Boolean Operations can not be done using the default implementation, because of a non-manifold type of the result. Example: the FUSE operation for SHELL and SOLID can not be done, but the CUT operation can be done, where SHELL is the object and SOLID is the tool.
1894 * It is possible to perform Boolean Operations on arguments of the COMPOUND shape type. In this case each compound must not be heterogeneous, i.e. it must contain equidimensional shapes (EDGEs or/and WIREs, FACEs or/and SHELLs, SOLIDs). SOLIDs inside the COMPOUND must not contact (intersect or touch) each other. The same condition should be respected for SHELLs or FACEs, WIREs or EDGEs.
1895 * Boolean Operations for COMPSOLID type of shape are not supported.
1897 @subsection occt_modalg_5_2 Implementation
1899 *BRepAlgoAPI_BooleanOperation* class is the deferred root class for Boolean operations.
1903 *BRepAlgoAPI_Fuse* performs the Fuse operation.
1906 TopoDS_Shape A = ..., B = ...;
1907 TopoDS_Shape S = BRepAlgoAPI_Fuse(A,B);
1912 *BRepAlgoAPI_Common* performs the Common operation.
1915 TopoDS_Shape A = ..., B = ...;
1916 TopoDS_Shape S = BRepAlgoAPI_Common(A,B);
1920 *BRepAlgoAPI_Cut* performs the Cut operation.
1923 TopoDS_Shape A = ..., B = ...;
1924 TopoDS_Shape S = BRepAlgoAPI_Cut(A,B);
1929 *BRepAlgoAPI_Section* performs the section, described as a *TopoDS_Compound* made of *TopoDS_Edge*.
1931 @image html /user_guides/modeling_algos/images/modeling_algos_image037.png "Section operation"
1932 @image latex /user_guides/modeling_algos/images/modeling_algos_image037.png "Section operation"
1935 TopoDS_Shape A = ..., TopoDS_ShapeB = ...;
1936 TopoDS_Shape S = BRepAlgoAPI_Section(A,B);
1939 @section occt_modalg_6 Fillets and Chamfers
1941 This library provides algorithms to make fillets and chamfers on shape edges.
1942 The following cases are addressed:
1944 * Corners and apexes with different radii;
1945 * Corners and apexes with different concavity.
1947 If there is a concavity, both surfaces that need to be extended and those, which do not, are processed.
1949 @subsection occt_modalg_6_1 Fillets
1950 @subsection occt_modalg_6_1_1 Fillet on shape
1952 A fillet is a smooth face replacing a sharp edge.
1954 *BRepFilletAPI_MakeFillet* class allows filleting a shape.
1956 To produce a fillet, it is necessary to define the filleted shape at the construction of the class and add fillet descriptions using the *Add* method.
1958 A fillet description contains an edge and a radius. The edge must be shared by two faces. The fillet is automatically extended to all edges in a smooth continuity with the original edge. It is not an error to add a fillet twice, the last description holds.
1960 @image html /user_guides/modeling_algos/images/modeling_algos_image038.png "Filleting two edges using radii r1 and r2."
1961 @image latex /user_guides/modeling_algos/images/modeling_algos_image038.png "Filleting two edges using radii r1 and r2."
1963 In the following example a filleted box with dimensions a,b,c and radius r is created.
1969 #include <TopoDS_Shape.hxx>
1970 #include <TopoDS.hxx>
1971 #include <BRepPrimAPI_MakeBox.hxx>
1972 #include <TopoDS_Solid.hxx>
1973 #include <BRepFilletAPI_MakeFillet.hxx>
1974 #include <TopExp_Explorer.hxx>
1976 TopoDS_Shape FilletedBox(const Standard_Real a,
1977 const Standard_Real b,
1978 const Standard_Real c,
1979 const Standard_Real r)
1981 TopoDS_Solid Box = BRepPrimAPI_MakeBox(a,b,c);
1982 BRepFilletAPI_MakeFillet MF(Box);
1984 // add all the edges to fillet
1985 TopExp_Explorer ex(Box,TopAbs_EDGE);
1988 MF.Add(r,TopoDS::Edge(ex.Current()));
1995 @image html /user_guides/modeling_algos/images/modeling_algos_image039.png "Fillet with constant radius"
1996 @image latex /user_guides/modeling_algos/images/modeling_algos_image039.png "Fillet with constant radius"
1998 #### Changing radius
2002 void CSampleTopologicalOperationsDoc::OnEvolvedblend1()
2004 TopoDS_Shape theBox = BRepPrimAPI_MakeBox(200,200,200);
2006 BRepFilletAPI_MakeFillet Rake(theBox);
2007 ChFi3d_FilletShape FSh = ChFi3d_Rational;
2008 Rake.SetFilletShape(FSh);
2010 TColgp_Array1OfPnt2d ParAndRad(1, 6);
2011 ParAndRad(1).SetCoord(0., 10.);
2012 ParAndRad(1).SetCoord(50., 20.);
2013 ParAndRad(1).SetCoord(70., 20.);
2014 ParAndRad(1).SetCoord(130., 60.);
2015 ParAndRad(1).SetCoord(160., 30.);
2016 ParAndRad(1).SetCoord(200., 20.);
2018 TopExp_Explorer ex(theBox,TopAbs_EDGE);
2019 Rake.Add(ParAndRad, TopoDS::Edge(ex.Current()));
2020 TopoDS_Shape evolvedBox = Rake.Shape();
2024 @image html /user_guides/modeling_algos/images/modeling_algos_image040.png "Fillet with changing radius"
2025 @image latex /user_guides/modeling_algos/images/modeling_algos_image040.png "Fillet with changing radius"
2027 @subsection occt_modalg_6_1_2 Chamfer
2029 A chamfer is a rectilinear edge replacing a sharp vertex of the face.
2031 The use of *BRepFilletAPI_MakeChamfer* class is similar to the use of *BRepFilletAPI_MakeFillet*, except for the following:
2032 * The surfaces created are ruled and not smooth.
2033 * The *Add* syntax for selecting edges requires one or two distances, one edge and one face (contiguous to the edge).
2037 Add(d1, d2, E, F) with d1 on the face F.
2040 @image html /user_guides/modeling_algos/images/modeling_algos_image041.png "Chamfer"
2041 @image latex /user_guides/modeling_algos/images/modeling_algos_image041.png "Chamfer"
2043 @subsection occt_modalg_6_1_3 Fillet on a planar face
2045 *BRepFilletAPI_MakeFillet2d* class allows constructing fillets and chamfers on planar faces.
2046 To create a fillet on planar face: define it, indicate, which vertex is to be deleted, and give the fillet radius with *AddFillet* method.
2048 A chamfer can be calculated with *AddChamfer* method. It can be described by
2049 * two edges and two distances
2050 * one edge, one vertex, one distance and one angle.
2051 Fillets and chamfers are calculated when addition is complete.
2053 If face F2 is created by 2D fillet and chamfer builder from face F1, the builder can be rebuilt (the builder recovers the status it had before deletion). To do so, use the following syntax:
2055 BRepFilletAPI_MakeFillet2d builder;
2056 builder.Init(F1,F2);
2063 #include “BRepPrimAPI_MakeBox.hxx”
2064 #include “TopoDS_Shape.hxx”
2065 #include “TopExp_Explorer.hxx”
2066 #include “BRepFilletAPI_MakeFillet2d.hxx”
2067 #include “TopoDS.hxx”
2068 #include “TopoDS_Solid.hxx”
2070 TopoDS_Shape FilletFace(const Standard_Real a,
2071 const Standard_Real b,
2072 const Standard_Real c,
2073 const Standard_Real r)
2076 TopoDS_Solid Box = BRepPrimAPI_MakeBox (a,b,c);
2077 TopExp_Explorer ex1(Box,TopAbs_FACE);
2079 const TopoDS_Face& F = TopoDS::Face(ex1.Current());
2080 BRepFilletAPI_MakeFillet2d MF(F);
2081 TopExp_Explorer ex2(F, TopAbs_VERTEX);
2084 MF.AddFillet(TopoDS::Vertex(ex2.Current()),r);
2092 @section occt_modalg_7 Offsets, Drafts, Pipes and Evolved shapes
2094 These classes provide the following services:
2096 * Creation of offset shapes and their variants such as:
2100 * Creation of tapered shapes using draft angles;
2101 * Creation of sweeps.
2103 @subsection occt_modalg_7_1 Shelling
2105 Shelling is used to offset given faces of a solid by a specific value. It rounds or intersects adjacent faces along its edges depending on the convexity of the edge.
2107 The constructor *BRepOffsetAPI_MakeThickSolid* shelling operator takes the solid, the list of faces to remove and an offset value as input.
2110 TopoDS_Solid SolidInitial = ...;
2112 Standard_Real Of = ...;
2113 TopTools_ListOfShape LCF;
2114 TopoDS_Shape Result;
2115 Standard_Real Tol = Precision::Confusion();
2117 for (Standard_Integer i = 1 ;i <= n; i++) {
2118 TopoDS_Face SF = ...; // a face from SolidInitial
2122 Result = BRepOffsetAPI_MakeThickSolid (SolidInitial,
2128 @image html /user_guides/modeling_algos/images/modeling_algos_image042.png "Shelling"
2129 @image latex /user_guides/modeling_algos/images/modeling_algos_image042.png "Shelling"
2132 @subsection occt_modalg_7_2 Draft Angle
2134 *BRepOffsetAPI_DraftAngle* class allows modifying a shape by applying draft angles to its planar, cylindrical and conical faces.
2137 The class is created or initialized from a shape, then faces to be modified are added; for each face, three arguments are used:
2138 * Direction: the direction with which the draft angle is measured
2139 * Angle: value of the angle
2140 * Neutral plane: intersection between the face and the neutral plane is invariant.
2142 The following code places a draft angle on several faces of a shape; the same direction, angle and neutral plane are used for each face:
2145 TopoDS_Shape myShape = ...
2146 // The original shape
2147 TopTools_ListOfShape ListOfFace;
2148 // Creation of the list of faces to be modified
2151 gp_Dir Direc(0.,0.,1.);
2153 Standard_Real Angle = 5.*PI/180.;
2155 gp_Pln Neutral(gp_Pnt(0.,0.,5.), Direc);
2156 // Neutral plane Z=5
2157 BRepOffsetAPI_DraftAngle theDraft(myShape);
2158 TopTools_ListIteratorOfListOfShape itl;
2159 for (itl.Initialize(ListOfFace); itl.More(); itl.Next()) {
2160 theDraft.Add(TopoDS::Face(itl.Value()),Direc,Angle,Neutral);
2161 if (!theDraft.AddDone()) {
2162 // An error has occurred. The faulty face is given by // ProblematicShape
2166 if (!theDraft.AddDone()) {
2167 // An error has occurred
2168 TopoDS_Face guilty = theDraft.ProblematicShape();
2172 if (!theDraft.IsDone()) {
2173 // Problem encountered during reconstruction
2177 TopoDS_Shape myResult = theDraft.Shape();
2182 @image html /user_guides/modeling_algos/images/modeling_algos_image043.png "DraftAngle"
2183 @image latex /user_guides/modeling_algos/images/modeling_algos_image043.png "DraftAngle"
2185 @subsection occt_modalg_7_3 Pipe Constructor
2187 *BRepOffsetAPI_MakePipe* class allows creating a pipe from a Spine, which is a Wire and a Profile which is a Shape. This implementation is limited to spines with smooth transitions, sharp transitions are precessed by *BRepOffsetAPI_MakePipeShell*. To be more precise the continuity must be G1, which means that the tangent must have the same direction, though not necessarily the same magnitude, at neighboring edges.
2189 The angle between the spine and the profile is preserved throughout the pipe.
2192 TopoDS_Wire Spine = ...;
2193 TopoDS_Shape Profile = ...;
2194 TopoDS_Shape Pipe = BRepOffsetAPI_MakePipe(Spine,Profile);
2197 @image html /user_guides/modeling_algos/images/modeling_algos_image044.png "Example of a Pipe"
2198 @image latex /user_guides/modeling_algos/images/modeling_algos_image044.png "Example of a Pipe"
2200 @subsection occt_modalg_7_4 Evolved Solid
2202 *BRepOffsetAPI_MakeEvolved* class allows creating an evolved solid from a Spine (planar face or wire) and a profile (wire).
2204 The evolved solid is an unlooped sweep generated by the spine and the profile.
2206 The evolved solid is created by sweeping the profile’s reference axes on the spine. The origin of the axes moves to the spine, the X axis and the local tangent coincide and the Z axis is normal to the face.
2208 The reference axes of the profile can be defined following two distinct modes:
2210 * The reference axes of the profile are the origin axes.
2211 * The references axes of the profile are calculated as follows:
2212 + the origin is given by the point on the spine which is the closest to the profile
2213 + the X axis is given by the tangent to the spine at the point defined above
2214 + the Z axis is the normal to the plane which contains the spine.
2217 TopoDS_Face Spine = ...;
2218 TopoDS_Wire Profile = ...;
2220 BRepOffsetAPI_MakeEvolved(Spine,Profile);
2223 @section occt_modalg_8 Sewing
2225 @subsection occt_modalg_8_1 Introduction
2227 Sewing allows creation of connected topology (shells and wires) from a set of separate topological elements (faces and edges). For example, Sewing can be used to create of shell from a compound of separate faces.
2229 @image html /user_guides/modeling_algos/images/modeling_algos_image045.png "Shapes with partially shared edges"
2230 @image latex /user_guides/modeling_algos/images/modeling_algos_image045.png "Shapes with partially shared edges"
2232 It is important to distinguish between sewing and other procedures, which modify the geometry, such as filling holes or gaps, gluing, bending curves and surfaces, etc.
2234 Sewing does not change geometrical representation of the shapes. Sewing applies to topological elements (faces, edges) which are not connected but can be connected because they are geometrically coincident : it adds the information about topological connectivity. Already connected elements are left untouched in case of manifold sewing.
2236 Let us define several terms:
2237 * **Floating edges** do not belong to any face;
2238 * **Free boundaries** belong to one face only;
2239 * **Shared edges** belong to several faces, (i.e. two faces in a manifold topology).
2240 * **Sewn faces** should have edges shared with each other.
2241 * **Sewn edges** should have vertices shared with each other.
2243 @subsection occt_modalg_8_2 Sewing Algorithm
2245 The sewing algorithm is one of the basic algorithms used for shape processing, therefore its quality is very important.
2247 Sewing algorithm is implemented in the class *BRepBuilder_Sewing*. This class provides the following methods:
2248 * loading initial data for global or local sewing;
2249 * setting customization parameters, such as special operation modes, tolerances and output results;
2250 * applying analysis methods that can be used to obtain connectivity data required by external algorithms;
2251 * sewing of the loaded shapes.
2253 Sewing supports working mode with big value tolerance. It is not necessary to repeat sewing step by step while smoothly increasing tolerance.
2255 It is also possible to sew edges to wire and to sew locally separate faces and edges from a shape.
2257 The Sewing algorithm can be subdivided into several independent stages, some of which can be turned on or off using Boolean or other flags.
2259 In brief, the algorithm should find a set of merge candidates for each free boundary, filter them according to certain criteria, and finally merge the found candidates and build the resulting sewn shape.
2261 Each stage of the algorithm or the whole algorithm can be adjusted with the following parameters:
2262 * **Working tolerance** defines the maximal distance between topological elements which can be sewn. It is not ultimate that such elements will be actually sewn as many other criteria are applied to make the final decision.
2263 * **Minimal tolerance** defines the size of the smallest element (edge) in the resulting shape. It is declared that no edges with size less than this value are created after sewing. If encountered, such topology becomes degenerated.
2264 * **Non-manifold mode** enables sewing of non-manifold topology.
2268 To connect a set of *n* contiguous but independent faces, do the following:
2271 BRepBuilderAPI_Sewing Sew;
2277 TopoDS_Shape result= Sew.SewedShape();
2280 If all faces have been sewn correctly, the result is a shell. Otherwise, it is a compound. After a successful sewing operation all faces have a coherent orientation.
2282 @subsection occt_modalg_8_3 Tolerance Management
2284 To produce a closed shell, Sewing allows specifying the value of working tolerance, exceeding the size of small faces belonging to the shape.
2286 However, if we produce an open shell, it is possible to get incorrect sewing results if the value of working tolerance is too large (i.e. it exceeds the size of faces lying on an open boundary).
2288 The following recommendations can be proposed for tuning-up the sewing process:
2289 - Use as small working tolerance as possible. This will reduce the sewing time and, consequently, the number of incorrectly sewn edges for shells with free boundaries.
2290 - Use as large minimal tolerance as possible. This will reduce the number of small geometry in the shape, both original and appearing after cutting.
2291 - If it is expected to obtain a shell with holes (free boundaries) as a result of sewing, the working tolerance should be set to a value not greater than the size of the smallest element (edge) or smallest distance between elements of such free boundary. Otherwise the free boundary may be sewn only partially.
2292 - It should be mentioned that the Sewing algorithm is unable to understand which small (less than working tolerance) free boundary should be kept and which should be sewn.
2294 @subsection occt_modalg_8_4 Manifold and Non-manifold Sewing
2296 To create one or several shells from a set of faces, sewing merges edges, which belong to different faces or one closed face.
2298 Face sewing supports manifold and non manifold modes. Manifold mode can produce only a manifold shell. Sewing should be used in the non manifold mode to create non manifold shells.
2300 Manifold sewing of faces merges only two nearest edges belonging to different faces or one closed face with each other. Non manifold sewing of faces merges all edges at a distance less than the specified tolerance.
2302 For a complex topology it is advisable to apply first the manifold sewing and then the non manifold sewing a minimum possible working tolerance. However, this is not necessary for a easy topology.
2304 Giving a large tolerance value to non manifold sewing will cause a lot of incorrectness since all nearby geometry will be sewn.
2306 @subsection occt_modalg_8_5 Local Sewing
2308 If a shape still has some non-sewn faces or edges after sewing, it is possible to use local sewing with a greater tolerance.
2310 Local sewing is especially good for open shells. It allows sewing an unwanted hole in one part of the shape and keeping a required hole, which is smaller than the working tolerance specified for the local sewing in the other part of the shape. Local sewing is much faster than sewing on the whole shape.
2312 All preexisting connections of the whole shape are kept after local sewing.
2314 For example, if you want to sew two open shells having coincided free edges using local sewing, it is necessary to create a compound from two shells then load the full compound using method *BRepBuilderAPI_Sewing::Load()*. After that it is necessary to add local sub-shapes, which should be sewn using method *BRepBuilderAPI_Sewing::Add()*. The result of sewing can be obtained using method *BRepBuilderAPI_Sewing::SewedShape()*.
2320 //initial sewn shapes
2321 TopoDS_Shape aS1, aS2; // these shapes are expected to be well sewn shells
2324 aB.MakeCompound(aComp);
2327 ................................
2328 aSewing.Load(aComp);
2330 //sub shapes which should be locally sewed
2336 TopoDS_Shape aRes = aSewing.SewedShape();
2340 @section occt_modalg_9 Features
2342 This library contained in *BRepFeat* package is necessary for creation and manipulation of form and mechanical features that go beyond the classical boundary representation of shapes. In that sense, *BRepFeat* is an extension of *BRepBuilderAPI* package.
2344 @subsection occt_modalg_9_1 Form Features
2346 The form features are depressions or protrusions including the following types:
2354 Depending on whether you wish to make a depression or a protrusion,
2355 you can choose either to remove matter (Boolean cut: Fuse equal to 0) or to add it (Boolean fusion: Fuse equal to 1).
2357 The semantics of form feature creation is based on the construction of shapes:
2359 * for a certain length in a certain direction;
2360 * up to the limiting face;
2361 * from the limiting face at a height;
2362 * above and/or below a plane.
2364 The shape defining the construction of a feature can be either a supporting edge or a concerned area of a face.
2366 In case of supporting edge, this contour can be attached to a face of the basis shape by binding. When the contour is bound to this face, the information that the contour will slide on the face becomes available
2367 to the relevant class methods. In case of the concerned area of a face, you can, for example, cut it out and move it at a different height, which defines the limiting face of a protrusion or depression.
2369 Topological definition with local operations of this sort makes calculations simpler
2370 and faster than a global operation. The latter would entail a second phase
2371 of removing unwanted matter to get the same result.
2373 The *Form* from *BRepFeat* package is a deferred class used as a root for form features. It inherits *MakeShape* from *BRepBuilderAPI* and provides implementation of methods keep track of all sub-shapes.
2375 @subsubsection occt_modalg_9_1_1 Prism
2377 The class *BRepFeat_MakePrism* is used to build a prism interacting with a shape. It is created or initialized from
2378 * a shape (the basic shape),
2379 * the base of the prism,
2380 * a face (the face of sketch on which the base has been defined and used to determine whether the base has been defined on the basic shape or not),
2382 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2383 * another Boolean indicating if the self-intersections have to be found (not used in every case).
2385 There are six Perform methods:
2386 | Method | Description |
2387 | :---------------------- | :------------------------------------- |
2388 | *Perform(Height)* | The resulting prism is of the given length. |
2389 | *Perform(Until)* | The prism is defined between the position of the base and the given face. |
2390 | *Perform(From, Until)* | The prism is defined between the two faces From and Until. |
2391 | *PerformUntilEnd()* | The prism is semi-infinite, limited by the actual position of the base. |
2392 | *PerformFromEnd(Until)* | The prism is semi-infinite, limited by the face Until. |
2393 | *PerformThruAll()* | The prism is infinite. In the case of a depression, the result is similar to a cut with an infinite prism. In the case of a protrusion, infinite parts are not kept in the result. |
2395 **Note** that *Add* method can be used before *Perform* methods to indicate that a face generated by an edge slides onto a face of the base shape.
2397 In the following sequence, a protrusion is performed, i.e. a face of the shape is changed into a prism.
2400 TopoDS_Shape Sbase = ...; // an initial shape
2401 TopoDS_Face Fbase = ....; // a base of prism
2403 gp_Dir Extrusion (.,.,.);
2405 // An empty face is given as the sketch face
2407 BRepFeat_MakePrism thePrism(Sbase, Fbase, TopoDS_Face(), Extrusion, Standard_True, Standard_True);
2409 thePrism, Perform(100.);
2410 if (thePrism.IsDone()) {
2411 TopoDS_Shape theResult = thePrism;
2416 @image html /user_guides/modeling_algos/images/modeling_algos_image047.png "Fusion with MakePrism"
2417 @image latex /user_guides/modeling_algos/images/modeling_algos_image047.png "Fusion with MakePrism"
2419 @image html /user_guides/modeling_algos/images/modeling_algos_image048.png "Creating a prism between two faces with Perform(From, Until)"
2420 @image latex /user_guides/modeling_algos/images/modeling_algos_image048.png "Creating a prism between two faces with Perform(From, Until)"
2422 @subsubsection occt_modalg_9_1_2 Draft Prism
2424 The class *BRepFeat_MakeDPrism* is used to build draft prism topologies interacting with a basis shape. These can be depressions or protrusions. A class object is created or initialized from:
2425 * a shape (basic shape),
2426 * the base of the prism,
2427 * a face (face of sketch on which the base has been defined and used to determine whether the base has been defined on the basic shape or not),
2429 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2430 * another Boolean indicating if self-intersections have to be found (not used in every case).
2432 Evidently the input data for MakeDPrism are the same as for MakePrism except for a new parameter Angle and a missing parameter Direction: the direction of the prism generation is determined automatically as the normal to the base of the prism.
2433 The semantics of draft prism feature creation is based on the construction of shapes:
2435 * up to a limiting face
2436 * from a limiting face to a height.
2438 The shape defining construction of the draft prism feature can be either the supporting edge or the concerned area of a face.
2440 In case of the supporting edge, this contour can be attached to a face of the basis shape by binding. When the contour is bound to this face, the information that the contour will slide on the face becomes available to the relevant class methods.
2441 In case of the concerned area of a face, it is possible to cut it out and move it to a different height, which will define the limiting face of a protrusion or depression direction .
2443 The *Perform* methods are the same as for *MakePrism*.
2446 TopoDS_Shape S = BRepPrimAPI_MakeBox(400.,250.,300.);
2448 Ex.Init(S,TopAbs_FACE);
2454 TopoDS_Face F = TopoDS::Face(Ex.Current());
2455 Handle(Geom_Surface) surf = BRep_Tool::Surface(F);
2457 c(gp_Ax2d(gp_Pnt2d(200.,130.),gp_Dir2d(1.,0.)),50.);
2458 BRepBuilderAPI_MakeWire MW;
2459 Handle(Geom2d_Curve) aline = new Geom2d_Circle(c);
2460 MW.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,PI));
2461 MW.Add(BRepBuilderAPI_MakeEdge(aline,surf,PI,2.*PI));
2462 BRepBuilderAPI_MakeFace MKF;
2463 MKF.Init(surf,Standard_False);
2465 TopoDS_Face FP = MKF.Face();
2466 BRepLib::BuildCurves3d(FP);
2467 BRepFeat_MakeDPrism MKDP (S,FP,F,10*PI180,Standard_True,
2470 TopoDS_Shape res1 = MKDP.Shape();
2473 @image html /user_guides/modeling_algos/images/modeling_algos_image049.png "A tapered prism"
2474 @image latex /user_guides/modeling_algos/images/modeling_algos_image049.png "A tapered prism"
2476 @subsubsection occt_modalg_9_1_3 Revolution
2478 The class *BRepFeat_MakeRevol* is used to build a revolution interacting with a shape. It is created or initialized from:
2479 * a shape (the basic shape,)
2480 * the base of the revolution,
2481 * a face (the face of sketch on which the base has been defined and used to determine whether the base has been defined on the basic shape or not),
2482 * an axis of revolution,
2483 * a boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2484 * another boolean indicating whether the self-intersections have to be found (not used in every case).
2486 There are four Perform methods:
2487 | Method | Description |
2488 | :--------------- | :------------ |
2489 | *Perform(Angle)* | The resulting revolution is of the given magnitude. |
2490 | *Perform(Until)* | The revolution is defined between the actual position of the base and the given face. |
2491 | *Perform(From, Until)* | The revolution is defined between the two faces, From and Until. |
2492 | *PerformThruAll()* | The result is similar to Perform(2*PI). |
2494 **Note** that *Add* method can be used before *Perform* methods to indicate that a face generated by an edge slides onto a face of the base shape.
2497 In the following sequence, a face is revolved and the revolution is limited by a face of the base shape.
2500 TopoDS_Shape Sbase = ...; // an initial shape
2501 TopoDS_Face Frevol = ....; // a base of prism
2502 TopoDS_Face FUntil = ....; // face limiting the revol
2504 gp_Dir RevolDir (.,.,.);
2505 gp_Ax1 RevolAx(gp_Pnt(.,.,.), RevolDir);
2507 // An empty face is given as the sketch face
2509 BRepFeat_MakeRevol theRevol(Sbase, Frevol, TopoDS_Face(), RevolAx, Standard_True, Standard_True);
2511 theRevol.Perform(FUntil);
2512 if (theRevol.IsDone()) {
2513 TopoDS_Shape theResult = theRevol;
2518 @subsubsection occt_modalg_9_1_4 Pipe
2520 The class *BRepFeat_MakePipe* constructs compound shapes with pipe features: depressions or protrusions. A class object is created or initialized from:
2521 * a shape (basic shape),
2522 * a base face (profile of the pipe)
2523 * a face (face of sketch on which the base has been defined and used to determine whether the base has been defined on the basic shape or not),
2525 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2526 * another Boolean indicating if self-intersections have to be found (not used in every case).
2528 There are three Perform methods:
2529 | Method | Description |
2530 | :-------- | :---------- |
2531 | *Perform()* | The pipe is defined along the entire path (spine wire) |
2532 | *Perform(Until)* | The pipe is defined along the path until a given face |
2533 | *Perform(From, Until)* | The pipe is defined between the two faces From and Until |
2535 Let us have a look at the example:
2538 TopoDS_Shape S = BRepPrimAPI_MakeBox(400.,250.,300.);
2540 Ex.Init(S,TopAbs_FACE);
2543 TopoDS_Face F1 = TopoDS::Face(Ex.Current());
2544 Handle(Geom_Surface) surf = BRep_Tool::Surface(F1);
2545 BRepBuilderAPI_MakeWire MW1;
2547 p1 = gp_Pnt2d(100.,100.);
2548 p2 = gp_Pnt2d(200.,100.);
2549 Handle(Geom2d_Line) aline = GCE2d_MakeLine(p1,p2).Value();
2551 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2553 p2 = gp_Pnt2d(150.,200.);
2554 aline = GCE2d_MakeLine(p1,p2).Value();
2556 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2558 p2 = gp_Pnt2d(100.,100.);
2559 aline = GCE2d_MakeLine(p1,p2).Value();
2561 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2562 BRepBuilderAPI_MakeFace MKF1;
2563 MKF1.Init(surf,Standard_False);
2564 MKF1.Add(MW1.Wire());
2565 TopoDS_Face FP = MKF1.Face();
2566 BRepLib::BuildCurves3d(FP);
2567 TColgp_Array1OfPnt CurvePoles(1,3);
2568 gp_Pnt pt = gp_Pnt(150.,0.,150.);
2570 pt = gp_Pnt(200.,100.,150.);
2572 pt = gp_Pnt(150.,200.,150.);
2574 Handle(Geom_BezierCurve) curve = new Geom_BezierCurve
2576 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(curve);
2577 TopoDS_Wire W = BRepBuilderAPI_MakeWire(E);
2578 BRepFeat_MakePipe MKPipe (S,FP,F1,W,Standard_False,
2581 TopoDS_Shape res1 = MKPipe.Shape();
2584 @image html /user_guides/modeling_algos/images/modeling_algos_image050.png "Pipe depression"
2585 @image latex /user_guides/modeling_algos/images/modeling_algos_image050.png "Pipe depression"
2587 @subsection occt_modalg_9_2 Mechanical Features
2589 Mechanical features include ribs, protrusions and grooves (or slots), depressions along planar (linear) surfaces or revolution surfaces.
2591 The semantics of mechanical features is built around giving thickness to a contour. This thickness can either be symmetrical - on one side of the contour - or dissymmetrical - on both sides. As in the semantics of form features, the thickness is defined by construction of shapes in specific contexts.
2593 The development contexts differ, however, in the case of mechanical features.
2594 Here they include extrusion:
2595 * to a limiting face of the basis shape;
2596 * to or from a limiting plane;
2599 A class object is created or initialized from
2600 * a shape (basic shape);
2601 * a wire (base of rib or groove);
2602 * a plane (plane of the wire);
2603 * direction1 (a vector along which thickness will be built up);
2604 * direction2 (vector opposite to the previous one along which thickness will be built up, may be null);
2605 * a Boolean indicating the type of operation (fusion=rib or cut=groove) on the basic shape;
2606 * another Boolean indicating if self-intersections have to be found (not used in every case).
2608 @subsubsection occt_modalg_9_2_1 Linear Form
2610 Linear form is implemented in *MakeLinearForm* class, which creates a rib or a groove along a planar surface. There is one *Perform()* method, which performs a prism from the wire along the *direction1* and *direction2* interacting with base shape *Sbase*. The height of the prism is *Magnitude(Direction1)+Magnitude(direction2)*.
2613 BRepBuilderAPI_MakeWire mkw;
2614 gp_Pnt p1 = gp_Pnt(0.,0.,0.);
2615 gp_Pnt p2 = gp_Pnt(200.,0.,0.);
2616 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2618 p2 = gp_Pnt(200.,0.,50.);
2619 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2621 p2 = gp_Pnt(50.,0.,50.);
2622 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2624 p2 = gp_Pnt(50.,0.,200.);
2625 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2627 p2 = gp_Pnt(0.,0.,200.);
2628 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2630 mkw.Add(BRepBuilderAPI_MakeEdge(p2,gp_Pnt(0.,0.,0.)));
2631 TopoDS_Shape S = BRepBuilderAPI_MakePrism(BRepBuilderAPI_MakeFace
2632 (mkw.Wire()),gp_Vec(gp_Pnt(0.,0.,0.),gp_P
2634 TopoDS_Wire W = BRepBuilderAPI_MakeWire(BRepBuilderAPI_MakeEdge(gp_Pnt
2636 gp_Pnt(100.,45.,50.)));
2637 Handle(Geom_Plane) aplane =
2638 new Geom_Plane(gp_Pnt(0.,45.,0.), gp_Vec(0.,1.,0.));
2639 BRepFeat_MakeLinearForm aform(S, W, aplane, gp_Dir
2640 (0.,5.,0.), gp_Dir(0.,-3.,0.), 1, Standard_True);
2642 TopoDS_Shape res = aform.Shape();
2645 @image html /user_guides/modeling_algos/images/modeling_algos_image051.png "Creating a rib"
2646 @image latex /user_guides/modeling_algos/images/modeling_algos_image051.png "Creating a rib"
2648 @subsubsection occt_modalg_9_2_3 Gluer
2650 The class *BRepFeat_Gluer* allows gluing two solids along faces. The contact faces of the glued shape must not have parts outside the contact faces of the basic shape. Upon completion the algorithm gives the glued shape with cut out parts of faces inside the shape.
2652 The class is created or initialized from two shapes: the “glued” shape and the basic shape (on which the other shape is glued).
2653 Two *Bind* methods are used to bind a face of the glued shape to a face of the basic shape and an edge of the glued shape to an edge of the basic shape.
2655 **Note** that every face and edge has to be bounded, if two edges of two glued faces are coincident they must be explicitly bounded.
2658 TopoDS_Shape Sbase = ...; // the basic shape
2659 TopoDS_Shape Sglued = ...; // the glued shape
2661 TopTools_ListOfShape Lfbase;
2662 TopTools_ListOfShape Lfglued;
2663 // Determination of the glued faces
2666 BRepFeat_Gluer theGlue(Sglue, Sbase);
2667 TopTools_ListIteratorOfListOfShape itlb(Lfbase);
2668 TopTools_ListIteratorOfListOfShape itlg(Lfglued);
2669 for (; itlb.More(); itlb.Next(), itlg(Next()) {
2670 const TopoDS_Face& f1 = TopoDS::Face(itlg.Value());
2671 const TopoDS_Face& f2 = TopoDS::Face(itlb.Value());
2672 theGlue.Bind(f1,f2);
2673 // for example, use the class FindEdges from LocOpe to
2674 // determine coincident edges
2675 LocOpe_FindEdge fined(f1,f2);
2676 for (fined.InitIterator(); fined.More(); fined.Next()) {
2677 theGlue.Bind(fined.EdgeFrom(),fined.EdgeTo());
2681 if (theGlue.IsDone() {
2682 TopoDS_Shape theResult = theGlue;
2687 @subsubsection occt_modalg_9_2_4 Split Shape
2689 The class *BRepFeat_SplitShape* is used to split faces of a shape into wires or edges. The shape containing the new entities is rebuilt, sharing the unmodified ones.
2691 The class is created or initialized from a shape (the basic shape).
2692 Three Add methods are available:
2693 * *Add(Wire, Face)* - adds a new wire on a face of the basic shape.
2694 * *Add(Edge, Face)* - adds a new edge on a face of the basic shape.
2695 * *Add(EdgeNew, EdgeOld)* - adds a new edge on an existing one (the old edge must contain the new edge).
2697 **Note** The added wires and edges must define closed wires on faces or wires located between two existing edges. Existing edges must not be intersected.
2700 TopoDS_Shape Sbase = ...; // basic shape
2701 TopoDS_Face Fsplit = ...; // face of Sbase
2702 TopoDS_Wire Wsplit = ...; // new wire contained in Fsplit
2703 BRepFeat_SplitShape Spls(Sbase);
2704 Spls.Add(Wsplit, Fsplit);
2705 TopoDS_Shape theResult = Spls;
2710 @section occt_modalg_10 Hidden Line Removal
2712 To provide the precision required in industrial design, drawings need to offer the possibility of removing lines, which are hidden in a given projection.
2714 For this the Hidden Line Removal component provides two algorithms: *HLRBRep_Algo* and *HLRBRep_PolyAlgo*.
2716 These algorithms are based on the principle of comparing each edge of the shape to be visualized with each of its faces, and calculating the visible and the hidden parts of each edge. Note that these are not the algorithms used in generating shading, which calculate the visible and hidden parts of each face in a shape to be visualized by comparing each face in the shape with every other face in the same shape.
2717 These algorithms operate on a shape and remove or indicate edges hidden by faces. For a given projection, they calculate a set of lines characteristic of the object being represented. They are also used in conjunction with extraction utilities, which reconstruct a new, simplified shape from a selection of the results of the calculation. This new shape is made up of edges, which represent the shape visualized in the projection.
2719 *HLRBRep_Algo* allows working with the shape itself, whereas *HLRBRep_PolyAlgo* works with a polyhedral simplification of the shape. When you use *HLRBRep_Algo*, you obtain an exact result, whereas, when you use *HLRBRep_PolyAlgo*, you reduce the computation time, but obtain polygonal segments.
2721 No smoothing algorithm is provided. Consequently, a polyhedron will be treated as such and the algorithms will give the results in form of line segments conforming to the mathematical definition of the polyhedron. This is always the case with *HLRBRep_PolyAlgo*.
2723 *HLRBRep_Algo* and *HLRBRep_PolyAlgo* can deal with any kind of object, for example, assemblies of volumes, surfaces, and lines, as long as there are no unfinished objects or points within it.
2725 However, there some restrictions in HLR use:
2726 * Points are not processed;
2727 * Z-clipping planes are not used;
2728 * Infinite faces or lines are not processed.
2731 @image html /user_guides/modeling_algos/images/modeling_algos_image052.png "Sharp, smooth and sewn edges in a simple screw shape"
2732 @image latex /user_guides/modeling_algos/images/modeling_algos_image052.png "Sharp, smooth and sewn edges in a simple screw shape"
2734 @image html /user_guides/modeling_algos/images/modeling_algos_image053.png "Outline edges and isoparameters in the same shape"
2735 @image latex /user_guides/modeling_algos/images/modeling_algos_image053.png "Outline edges and isoparameters in the same shape"
2737 @image html /user_guides/modeling_algos/images/modeling_algos_image054.png "A simple screw shape seen with shading"
2738 @image latex /user_guides/modeling_algos/images/modeling_algos_image054.png "A simple screw shape seen with shading"
2740 @image html /user_guides/modeling_algos/images/modeling_algos_image055.png "An extraction showing hidden sharp edges"
2741 @image latex /user_guides/modeling_algos/images/modeling_algos_image055.png "An extraction showing hidden sharp edges"
2744 The following services are related to Hidden Lines Removal :
2748 To pass a *TopoDS_Shape* to an *HLRBRep_Algo* object, use *HLRBRep_Algo::Add*. With an *HLRBRep_PolyAlgo* object, use *HLRBRep_PolyAlgo::Load*. If you wish to add several shapes, use Add or Load as often as necessary.
2750 ### Setting view parameters
2752 *HLRBRep_Algo::Projector* and *HLRBRep_PolyAlgo::Projector* set a projector object which defines the parameters of the view. This object is an *HLRAlgo_Projector*.
2754 ### Computing the projections
2756 *HLRBRep_PolyAlgo::Update* launches the calculation of outlines of the shape visualized by the *HLRBRep_PolyAlgo* framework.
2758 In the case of *HLRBRep_Algo*, use *HLRBRep_Algo::Update*. With this algorithm, you must also call the method *HLRBRep_Algo::Hide* to calculate visible and hidden lines of the shape to be visualized. With an *HLRBRep_PolyAlgo* object, visible and hidden lines are computed by *HLRBRep_PolyHLRToShape*.
2760 ### Extracting edges
2762 The classes *HLRBRep_HLRToShape* and *HLRBRep_PolyHLRToShape* present a range of extraction filters for an *HLRBRep_Algo object* and an *HLRBRep_PolyAlgo* object, respectively. They highlight the type of edge from the results calculated by the algorithm on a shape. With both extraction classes, you can highlight the following types of output:
2763 * visible/hidden sharp edges;
2764 * visible/hidden smooth edges;
2765 * visible/hidden sewn edges;
2766 * visible/hidden outline edges.
2768 To perform extraction on an *HLRBRep_PolyHLRToShape* object, use *HLRBRep_PolyHLRToShape::Update* function.
2770 For an *HLRBRep_HLRToShape* object built from an *HLRBRepAlgo* object you can also highlight:
2771 * visible isoparameters and
2772 * hidden isoparameters.
2774 @subsection occt_modalg_10_1 Examples
2779 // Build The algorithm object
2780 myAlgo = new HLRBRep_Algo();
2782 // Add Shapes into the algorithm
2783 TopTools_ListIteratorOfListOfShape anIterator(myListOfShape);
2784 for (;anIterator.More();anIterator.Next())
2785 myAlgo-Add(anIterator.Value(),myNbIsos);
2787 // Set The Projector (myProjector is a
2789 myAlgo-Projector(myProjector);
2794 // Set The Edge Status
2797 // Build the extraction object :
2798 HLRBRep_HLRToShape aHLRToShape(myAlgo);
2800 // extract the results :
2801 TopoDS_Shape VCompound = aHLRToShape.VCompound();
2802 TopoDS_Shape Rg1LineVCompound =
2803 aHLRToShape.Rg1LineVCompound();
2804 TopoDS_Shape RgNLineVCompound =
2805 aHLRToShape.RgNLineVCompound();
2806 TopoDS_Shape OutLineVCompound =
2807 aHLRToShape.OutLineVCompound();
2808 TopoDS_Shape IsoLineVCompound =
2809 aHLRToShape.IsoLineVCompound();
2810 TopoDS_Shape HCompound = aHLRToShape.HCompound();
2811 TopoDS_Shape Rg1LineHCompound =
2812 aHLRToShape.Rg1LineHCompound();
2813 TopoDS_Shape RgNLineHCompound =
2814 aHLRToShape.RgNLineHCompound();
2815 TopoDS_Shape OutLineHCompound =
2816 aHLRToShape.OutLineHCompound();
2817 TopoDS_Shape IsoLineHCompound =
2818 aHLRToShape.IsoLineHCompound();
2821 ### HLRBRep_PolyAlgo
2826 // Build The algorithm object
2827 myPolyAlgo = new HLRBRep_PolyAlgo();
2829 // Add Shapes into the algorithm
2830 TopTools_ListIteratorOfListOfShape
2831 anIterator(myListOfShape);
2832 for (;anIterator.More();anIterator.Next())
2833 myPolyAlgo-Load(anIterator.Value());
2835 // Set The Projector (myProjector is a
2837 myPolyAlgo->Projector(myProjector);
2840 myPolyAlgo->Update();
2842 // Build the extraction object :
2843 HLRBRep_PolyHLRToShape aPolyHLRToShape;
2844 aPolyHLRToShape.Update(myPolyAlgo);
2846 // extract the results :
2847 TopoDS_Shape VCompound =
2848 aPolyHLRToShape.VCompound();
2849 TopoDS_Shape Rg1LineVCompound =
2850 aPolyHLRToShape.Rg1LineVCompound();
2851 TopoDS_Shape RgNLineVCompound =
2852 aPolyHLRToShape.RgNLineVCompound();
2853 TopoDS_Shape OutLineVCompound =
2854 aPolyHLRToShape.OutLineVCompound();
2855 TopoDS_Shape HCompound =
2856 aPolyHLRToShape.HCompound();
2857 TopoDS_Shape Rg1LineHCompound =
2858 aPolyHLRToShape.Rg1LineHCompound();
2859 TopoDS_Shape RgNLineHCompound =
2860 aPolyHLRToShape.RgNLineHCompound();
2861 TopoDS_Shape OutLineHCompound =
2862 aPolyHLRToShape.OutLineHCompound();
2865 @section occt_modalg_11 Meshing
2867 @subsection occt_modalg_11_1 Mesh presentations
2869 In addition to support of exact geometrical representation of 3D objects Open CASCADE Technology provides functionality to work with tessellated representations of objects in form of meshes.
2871 Open CASCADE Technology mesh functionality provides:
2872 - data structures to store surface mesh data associated to shapes, and some basic algorithms to handle these data
2873 - data structures and algorithms to build surface triangular mesh from *BRep* objects (shapes).
2874 - tools to extend 3D visualization capabilities of Open CASCADE Technology with displaying meshes along with associated pre- and post-processor data.
2876 Open CASCADE Technology includes two mesh converters:
2877 - VRML converter translates Open CASCADE shapes to VRML 1.0 files (Virtual Reality Modeling Language). Open CASCADE shapes may be translated in two representations: shaded or wireframe. A shaded representation present shapes as sets of triangles computed by a mesh algorithm while a wireframe representation present shapes as sets of curves.
2878 - STL converter translates Open CASCADE shapes to STL files. STL (STtereoLithography) format is widely used for rapid prototyping.
2880 Open CASCADE SAS also offers Advanced Mesh Products:
2881 - <a href="http://www.opencascade.com/content/mesh-framework">Open CASCADE Mesh Framework (OMF)</a>
2882 - <a href="http://www.opencascade.com/content/express-mesh">Express Mesh</a>
2884 Besides, we can efficiently help you in the fields of surface and volume meshing algorithms, mesh optimization algorithms etc. If you require a qualified advice about meshing algorithms, do not hesitate to benefit from the expertise of our team in that domain.
2886 The projects dealing with numerical simulation can benefit from using SALOME - an Open Source Framework for CAE with CAD data interfaces, generic Pre- and Post- F.E. processors and API for integrating F.E. solvers.
2888 Learn more about SALOME platform on http://www.salome-platform.org
2890 @subsection occt_modalg_11_2 Meshing algorithm
2892 The algorithm of shape triangulation is provided by the functionality of *BRepMesh_IncrementalMesh* class, which adds a triangulation of the shape to its topological data structure. This triangulation is used to visualize the shape in shaded mode.
2895 const Standard_Real aRadius = 10.0;
2896 const Standard_Real aHeight = 25.0;
2897 BRepBuilderAPI_MakeCylinder aCylinder(aRadius, aHeight);
2898 TopoDS_Shape aShape = aCylinder.Shape();
2900 const Standard_Real aLinearDeflection = 0.01;
2901 const Standard_Real anAngularDeflection = 0.5;
2903 BRepMesh_IncrementalMesh aMesh(aShape, aLinearDeflection, Standard_False, anAngularDeflection);
2906 The default meshing algorithm *BRepMesh_IncrementalMesh* has two major options to define triangulation – linear and angular deflections.
2908 At the first step all edges from a face are discretized according to the specified parameters.
2910 At the second step, the faces are tessellated. Linear deflection limits the distance between a curve and its tessellation, whereas angular deflection limits the angle between subsequent segments in a polyline.
2912 @figure{/user_guides/modeling_algos/images/modeling_algos_image056.png, "Deflection parameters of BRepMesh_IncrementalMesh algorithm"}
2914 Linear deflection limits the distance between triangles and the face interior.
2916 @figure{/user_guides/modeling_algos/images/modeling_algos_image057.png, "Linear deflection"}
2918 Note that if a given value of linear deflection is less than shape tolerance then the algorithm will skip this value and will take into account the shape tolerance.
2920 The application should provide deflection parameters to compute a satisfactory mesh. Angular deflection is relatively simple and allows using a default value (12-20 degrees). Linear deflection has an absolute meaning and the application should provide the correct value for its models. Giving small values may result in a too huge mesh (consuming a lot of memory, which results in a long computation time and slow rendering) while big values result in an ugly mesh.
2922 For an application working in dimensions known in advance it can be reasonable to use the absolute linear deflection for all models. This provides meshes according to metrics and precision used in the application (for example, it it is known that the model will be stored in meters, 0.004 m is enough for most tasks).
2924 However, an application that imports models created in other applications may not use the same deflection for all models. Note that actually this is an abnormal situation and this application is probably just a viewer for CAD models with dimensions varying by an order of magnitude. This problem can be solved by introducing the concept of a relative linear deflection with some LOD (level of detail). The level of detail is a scale factor for absolute deflection, which is applied to model dimensions.
2926 Meshing covers a shape with a triangular mesh. Other than hidden line removal, you can use meshing to transfer the shape to another tool: a manufacturing tool, a shading algorithm, a finite element algorithm, or a collision algorithm.
2928 You can obtain information on the shape by first exploring it. To access triangulation of a face in the shape later, use *BRepTool::Triangulation*. To access a polygon, which is the approximation of an edge of the face, use *BRepTool::PolygonOnTriangulation*.