1 Modeling Algorithms {#user_guides__modeling_algos}
2 =========================
4 @section occt_modalg_1 Introduction
6 @subsection occt_modalg_1_1 The Modeling Algorithms Module
9 This manual explains how to use the Modeling Algorithms. It provides basic documentation on modeling algorithms. For advanced information on Modeling Algorithms, see our offerings on our web site at <a href="http://www.opencascade.org/support/training/">www.opencascade.org/support/training/</a>
11 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.
13 The algorithms available are divided into:
18 @subsection occt_modalg_1_2 The Topology API
20 The Topology API of Open CASCADE Technology (**OCCT**) includes the following six packages:
29 The classes in these six packages provide the user with a simple and powerful interface.
30 * A simple interface: a function call works ideally,
31 * A powerful interface: including error handling and access to extra information provided by the algorithms.
33 As an example, the class BRepBuilderAPI_MakeEdge can be used to create a linear edge from two points.
36 gp_Pnt P1(10,0,0), P2(20,0,0);
37 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(P1,P2);
40 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.
44 #include <TopoDS_Edge.hxx>
45 #include <BRepBuilderAPI_MakeEdge.hxx>
50 BRepBuilderAPI_MakeEdge ME(P1,P2);
53 // doing ME.Edge() or E = ME here
54 // would raise StdFail_NotDone
55 Standard_DomainError::Raise
56 (“ProcessPoints::Failed to createan edge”);
62 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.
64 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.
67 void MakeEdgeAndVertices(const gp_Pnt& P1,
70 TopoDS_Vertex& V1,
71 TopoDS_Vertex& V2)
73 BRepBuilderAPI_MakeEdge ME(P1,P2);
75 Standard_DomainError::Raise
76 (“MakeEdgeAndVerices::Failed to create an edge”);
83 The BRepBuilderAPI_MakeEdge class provides the two methods Vertex1 and Vertex2, which return the two vertices used to create the edge.
85 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 E = ME could have been written.
91 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.
93 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.
96 @subsubsection occt_modalg_1_2_1 Error Handling in the Topology API
98 A method can report an error in the two following situations:
99 * 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.
100 * 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).
102 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.
104 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.
106 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.
107 As the test involves a great deal of computation, performing it twice is also time-consuming.
109 Consequently, you might be tempted to adopt the *highly inadvisable *style of programming illustrated in the following example:
112 #include <Standard_ErrorHandler.hxx>
114 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(P1,P2);
115 // go on with the edge
118 // process the error.
122 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.
124 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.
127 BRepBuilderAPI_MakeEdge ME(P1,P2);
129 // doing ME.Edge() or E = ME here
130 // would raise StdFail_NotDone
131 Standard_DomainError::Raise
132 (“ProcessPoints::Failed to create an edge”);
137 @section occt_modalg_2 Geometric Tools
139 @subsection occt_modalg_2_1 Overview
141 Open CASCADE Technology geometric tools include:
143 * Computation of intersections
145 * Computation of curves and surfaces from constraints
146 * Computation of lines and circles from constraints
149 @subsection occt_modalg_2_2 Intersections
151 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.
153 
155 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.*
157 
159 The algorithm returns a point in the case of an intersection and a segment in the case of tangent intersection.
161 @subsubsection occt_modalg_2_2_1 Geom2dAPI_InterCurveCurve
163 This class may be instantiated either for intersection of curves C1 and C2.
165 Geom2dAPI_InterCurveCurve Intersector(C1,C2,tolerance);
168 or for self-intersection of curve C3.
170 Geom2dAPI_InterCurveCurve Intersector(C3,tolerance);
174 Standard_Integer N = Intersector.NbPoints();
176 Calls the number of intersection points
178 To select the desired intersection point, pass an integer index value in argument.
180 gp_Pnt2d P = Intersector.Point(Index);
184 Standard_Integer M = Intersector.NbSegments();
187 Calls the number of intersection segments.
189 To select the desired intersection segment pass integer index values in argument.
191 Handle(Geom2d_Curve) Seg1, Seg2;
192 Intersector.Segment(Index,Seg1,Seg2);
193 // if intersection of 2 curves
194 Intersector.Segment(Index,Seg1);
195 // if self-intersection of a curve
198 If you need access to a wider range of functionalities the following method will return the algorithmic object for the calculation of intersections:
201 Geom2dInt_GInter& TheIntersector = Intersector.Intersector();
204 @subsubsection occt_modalg_2_2_2 Intersection of Curves and Surfaces
205 The *GeomAPI_IntCS *class is used to compute the intersection points between a curve and a surface.
207 This class is instantiated as follows:
209 GeomAPI_IntCS Intersector(C, S);
213 Standard_Integer nb = Intersector.NbPoints();
215 Calls the number of intersection points.
218 gp_Pnt& P = Intersector.Point(Index);
221 Where *Index *is an integer between *1 *and *nb*, calls the intersection points.
223 @subsubsection occt_modalg_2_2_3 Intersection of two Surfaces
224 The *GeomAPI_IntSS *class is used to compute the intersection of two surfaces from *Geom_Surface *with respect to a given tolerance.
226 This class is instantiated as follows:
228 GeomAPI_IntSS Intersector(S1, S2, Tolerance);
230 Once the *GeomAPI_IntSS *object has been created, it can be interpreted.
233 Standard_Integer nb = Intersector. NbLines();
235 Calls the number of intersection curves.
238 Handle(Geom_Curve) C = Intersector.Line(Index)
240 Where *Index *is an integer between *1 *and *nb*, calls the intersection curves.
242 @subsection occt_modalg_2_3 Interpolations
243 *Interpolation* provides functionalities for interpolating BSpline curves, whether in 2D, using *Geom2dAPI_Interpolate*, or 3D using *GeomAPI_Interpolate*.
246 @subsubsection occt_modalg_2_3_1 Geom2dAPI_Interpolate
247 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.
248 This class may be instantiated as follows:
250 Geom2dAPI_Interpolate
251 (const Handle_TColgp_HArray1OfPnt2d& Points,
252 const Standard_Boolean PeriodicFlag,
253 const Standard_Real Tolerance);
255 Geom2dAPI_Interpolate Interp(Points, Standard_False,
256 Precision::Confusion());
260 It is possible to call the BSpline curve from the object defined above it.
262 Handle(Geom2d_BSplineCurve) C = Interp.Curve();
265 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.
268 Handle(Geom2d_BSplineCurve) C =
269 Geom2dAPI_Interpolate(Points,
271 Precision::Confusion());
274 @subsubsection occt_modalg_2_3_2 GeomAPI_Interpolate
276 This class may be instantiated as follows:
279 (const Handle_TColgp_HArray1OfPnt& Points,
280 const Standard_Boolean PeriodicFlag,
281 const Standard_Real Tolerance);
283 GeomAPI_Interpolate Interp(Points, Standard_False,
284 Precision::Confusion());
287 It is possible to call the BSpline curve from the object defined above it.
289 Handle(Geom_BSplineCurve) C = Interp.Curve();
291 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.
293 Handle(Geom_BSplineCurve) C =
294 GeomAPI_Interpolate(Points,
298 Boundary conditions may be imposed with the method Load.
300 GeomAPI_Interpolate AnInterpolator
301 (Points, Standard_False, 1.0e-5);
302 AnInterpolator.Load (StartingTangent, EndingTangent);
305 @subsection occt_modalg_2_4 Lines and Circles from Constraints
307 There are two packages to create lines and circles from constraints: *Geom2dGcc *and *GccAna*. *Geom2dGcc* deals with reference-handled geometric objects from the *Geom2d *package while *GccAna* deals with value-handled geometric objects from the *gp* package.
309 The *Geom2dGcc* package solves geometric constructions of lines and circles expressed by constraints such as tangency or parallelism, that is, a constraint expressed in geometric terms. As a simple example the following figure shows a line which is constrained to pass through a point and be tangent to a circle.
311 
313 The *Geom2dGcc *package focuses on algorithms; it is useful for finding results, but it does not offer any management or modification functions, which could be applied to the constraints or their arguments. This package is designed to offer optimum performance, both in rapidity and precision. Trivial cases (for example, a circle centered on one point and passing through another) are not treated.
315 The *Geom2dGcc *package deals only with 2d objects from the *Geom2d *package. These objects are the points, lines and circles available.
317 All other lines such as Bezier curves and conic sections - with the exception of circles -are considered general curves and must be differentiable twice.
319 The *GccAna *package deals with points, lines, and circles from the *gp *package. Apart from constructors for lines and circles, it also allows the creation of conics from the bisection of other geometric objects.
321 @subsection occt_modalg_2_5 Provided algorithms
323 The following analytic algorithms using value-handled entities for creation of 2D lines or circles with geometric constraints are available:
325 * circle tangent to three elements (lines, circles, curves, points),
326 * circle tangent to two elements and having a radius,
327 * circle tangent to two elements and centered on a third element,
328 * circle tangent to two elements and centered on a point,
329 * circle tangent to one element and centered on a second,
330 * bisector of two points,
331 * bisector of two lines,
332 * bisector of two circles,
333 * bisector of a line and a point,
334 * bisector of a circle and a point,
335 * bisector of a line and a circle,
336 * line tangent to two elements (points, circles, curves),
337 * line tangent to one element and parallel to a line,
338 * line tangent to one element and perpendicular to a line,
339 * line tangent to one element and forming angle with a line.
341 @subsection occt_modalg_2_6 Types of algorithms
342 There are three categories of available algorithms, which complement each other:
347 An analytic algorithm will solve a system of equations, whereas a geometric algorithm works with notions of parallelism, tangency, intersection and so on.
349 Both methods can provide solutions. An iterative algorithm, however, seeks to refine an approximate solution.
351 @subsection occt_modalg_2_7 Performance factors
353 The appropriate algorithm is the one, which reaches a solution of the required accuracy in the least time. Only the solutions actually requested by the user should be calculated. A simple means to reduce the number of solutions is the notion of a "qualifier". There are four qualifiers, which are:
355 * Unqualified: the position of the solution is undefined with respect to this argument.
356 * Enclosing: the solution encompasses this argument.
357 * Enclosed: the solution is encompassed by this argument.
358 * Outside: the solution and argument are outside each other.
361 @subsection occt_modalg_2_8 Conventions
363 @subsubsection occt_modalg_2_8_1 Exterior/Interior
364 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").
366 
368 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:
370 
372 @subsubsection occt_modalg_2_8_2 Orientation of a Line
373 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.
375 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.
377 
379 @subsection occt_modalg_2_9 Examples
381 @subsubsection occt_modalg_2_9_1 Line tangent to two circles
382 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.
384 Note that the qualifier "Outside" is used to mean "Mutually exterior".
388 
391 Tangent and Exterior to C1.
392 Tangent and Exterior to C2.
398 Solver(GccEnt::Outside(C1),
405 
408 Tangent and Including C1.
409 Tangent and Including C2.
415 Solver(GccEnt::Enclosing(C1),
416 GccEnt::Enclosing(C2),
422 
425 Tangent and Including C1.
426 Tangent and Exterior to C2.
431 Solver(GccEnt::Enclosing(C1),
438 
440 Tangent and Exterior to C1.
441 Tangent and Including C2.
446 Solver(GccEnt::Outside(C1),
447 GccEnt::Enclosing(C2),
453 
456 Tangent and Undefined with respect to C1.
457 Tangent and Undefined with respect to C2.
462 Solver(GccEnt::Unqualified(C1),
463 GccEnt::Unqualified(C2),
467 @subsubsection occt_modalg_2_9_2 Circle of given radius tangent to two circles
468 The following four diagrams show the four cases in using qualifiers in the creation of a circle.
471 
474 Tangent and Exterior to C1.
475 Tangent and Exterior to C2.
480 Solver(GccEnt::Outside(C1),
481 GccEnt::Outside(C2), Rad, Tolerance);
486 
489 Tangent and Exterior to C1.
490 Tangent and Included by C2.
495 Solver(GccEnt::Outside(C1),
496 GccEnt::Enclosed(C2), Rad, Tolerance);
500 
503 Tangent and Exterior to C1.
504 Tangent and Including C2.
509 Solver(GccEnt::Outside(C1),
510 GccEnt::Enclosing(C2), Rad, Tolerance);
514 
517 Tangent and Enclosing C1.
518 Tangent and Enclosing C2.
523 Solver(GccEnt::Enclosing(C1),
524 GccEnt::Enclosing(C2), Rad, Tolerance);
528 The following syntax will give all the circles of radius *Rad, *which are tangent to *C1 *and *C2 *without discrimination of relative position:
531 GccAna_Circ2d2TanRad Solver(GccEnt::Unqualified(C1),
532 GccEnt::Unqualified(C2),
536 @subsection occt_modalg_2_10 Algorithms
538 The objects created by this toolkit are non-persistent.
540 @subsubsection occt_modalg_2_10_1 Qualifiers
541 The *GccEnt* package contains the following package methods:
547 This enables creation of expressions, for example:
550 Solver(GccEnt::Outside(C1),
551 GccEnt::Enclosing(C2), Rad, Tolerance);
554 The objective in this case is to find all circles of radius *Rad*, which are tangent to both circle *C1* and *C2*, C1 being outside and C2 being inside.
556 @subsubsection occt_modalg_2_10_2 General Remarks about Algorithms
558 We consider the following to be the case:
559 * If a circle passes through a point then the circle is tangential to it.
560 * A distinction is made between the trivial case of the center at a point and the complex case of the center on a line.
562 @subsubsection occt_modalg_2_10_3 Analytic Algorithms
563 GccAna package implements analytic algorithms. It deals only with points, lines, and circles from gp package. Here is a list of the services offered:
569 Tangent ( point | circle ) & Parallel ( line )
570 Tangent ( point | circle ) & Perpendicular ( line | circle )
571 Tangent ( point | circle ) & Oblique ( line )
572 Tangent ( 2 { point | circle } )
573 Bisector( line | line )
580 Bisector ( point | point )
581 Bisector ( line | point )
582 Bisector ( circle | point )
583 Bisector ( line | line )
584 Bisector ( circle | line )
585 Bisector ( circle | circle )
591 Tangent ( point | line | circle ) & Center ( point )
592 Tangent ( 3 { point | line | circle } )
593 Tangent ( 2 { point | line | circle } ) & Radius ( real )
594 Tangent ( 2 { point | line | circle } ) & Center ( line | circle )
595 Tangent ( point | line | circle ) & Center ( line | circle ) & Radius ( real )
598 For each algorithm, the tolerance (and angular tolerance if appropriate) is given as an argument. Calculation is done with the highest precision available from the hardware.
600 @subsubsection occt_modalg_2_10_4 Geometric Algorithms
602 *Geom2dGcc *package offers algorithms, which produce 2d lines or circles with geometric constraints. For arguments, it takes curves for which an approximate solution is not requested. A tolerance value on the result is given as a starting parameter. The following services are provided:
608 Tangent ( curve ) & Center ( point )
609 Tangent ( curve , point | line | circle | curve ) & Radius ( real )
610 Tangent ( 2 {point | line | circle} ) & Center ( curve )
611 Tangent ( curve ) & Center ( line | circle | curve ) & Radius ( real )
612 Tangent ( point | line | circle ) & Center ( curve ) & Radius ( real )
615 All calculations will be done to the highest precision available from the hardware.
617 @subsubsection occt_modalg_2_10_5 Iterative Algorithms
618 Geom2dGcc package offers iterative algorithms find a solution by refining an approximate solution. It produces 2d lines or circles with geometric constraints. For all geometric arguments except points, an approximate solution may be given as a starting parameter. The tolerance or angular tolerance value is given as an argument. The following services are provided:
623 Tangent ( curve ) & Oblique ( line )
624 Tangent ( curve , { point | circle | curve } )
631 Tangent ( curve , 2 { point | circle | curve } )
632 Tangent ( curve , { point | circle | curve } )
633 & Center ( line | circle | curve )
636 @subsection occt_modalg_2_1 Curves and Surfaces from Constraints
638 @subsubsection occt_modalg_2_1_1 Fair Curve
640 *FairCurve* package provides a set of classes to create faired 2D curves or 2D curves with minimal variation in curvature.
642 Creation of Batten Curves
643 -------------------------
644 The class 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.
645 The following constraint orders are available:
647 * 0 the curve must pass through a point
648 * 1 the curve must pass through a point and have a given tangent
649 * 2 the curve must pass through a point, have a given tangent and a given curvature.
651 Only 0 and 1 constraint orders are used.
652 The function Curve returns the result as a 2D BSpline curve.
654 Creation of Minimal Variation Curves
655 ------------------------------------
656 The class MinimalVariation allow producing curves with minimal variation in curvature at each reference point. The following constraint orders are available:
658 * 0 the curve must pass through a point
659 * 1 the curve must pass through a point and have a given tangent
660 * 2 the curve must pass through a point, have a given tangent and a given curvature.
662 Constraint orders of 0, 1 and 2 can be used. The algorithm minimizes tension, sagging and jerk energy.
664 The function *Curve* returns the result as a 2D BSpline curve.
666 Specifying the length of the curve
667 ----------------------------------
668 If you want to give a specific length to a batten curve, use:
671 b.SetSlidingFactor(L / b.SlidingOfReference())
673 where *b* is the name of the batten curve object
677 Free sliding is generally more aesthetically pleasing than constrained sliding.
678 However, the computation can fail with values such as angles greater than p/2, because in this case, the length is theoretically infinite.
680 In other cases, when sliding is imposed and the sliding factor is too large, the batten can collapse.
684 The constructor parameters, *Tolerance* and *NbIterations*, control how precise the computation is, and how long it will take.
686 @subsubsection occt_modalg_2_11_2 Surfaces from Boundary Curves
688 The *GeomFill* package provides the following services for creating surfaces from boundary curves:
690 Creation of Bezier surfaces
691 ---------------------------
692 The class *BezierCurves* allows producing a Bezier surface from contiguous Bezier curves. Note that problems may occur with rational Bezier Curves.
694 Creation of BSpline surfaces
695 ----------------------------
696 The class *BSplineCurves* allows producing a BSpline surface from contiguous BSpline curves. Note that problems may occur with rational BSplines.
700 The class *Pipe* allows you producing a pipe by sweeping a curve (the section) along another curve (the path). The result is a BSpline surface.
704 The class *GeomFill_ConstrainedFilling* allows filling a contour defined by two, three or four curves as well as by tangency constraints. The resulting surface is a BSpline.
706 Creation of a Boundary
707 ----------------------
708 The class *GeomFill_SimpleBound* allows you defining a boundary for the surface to be constructed.
710 Creation of a Boundary with an adjoining surface
711 ------------------------------------------------
712 The class *GeomFill_BoundWithSurf* allows defining a boundary for the surface to be constructed. This boundary will already be joined to another surface.
716 The enumerations *FillingStyle* specify the styles used to build the surface. These include:
718 * *Stretch* - the style with the flattest patches
719 * *Coons* - a rounded style with less depth than *Curved*
720 * *Curved* - the style with the most rounded patches.
722 ![](/user_guides/modeling_algos/images/modeling_algos_image018.jpg "Intersecting filleted edges with different radii leave a gap, is filled by a surface)
725 @subsubsection occt_modalg_2_11_3 Surfaces from curve and point constraints
726 The *GeomPlate* package provides the following services for creating surfaces respecting curve and point constraints:
728 Definition of a Framework
729 -------------------------
730 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*.
732 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.
734 Definition of a Curve Constraint
735 --------------------------------
736 The class *CurveConstraint* allows defining curves as constraints to the surface, which you want to build.
738 Definition of a Point Constraint
739 --------------------------------
740 The class *PointConstraint* allows defining points as constraints to the surface, which you want to build.
742 Applying Geom_Surface to Plate Surfaces
743 --------------------------------------
744 The class *Surface* allows describing the characteristics of plate surface objects returned by **BuildPlateSurface::Surface** using the methods of *Geom_Surface*
746 Approximating a Plate surface to a BSpline
747 ------------------------------------------
748 The class *MakeApprox* allows converting a *GeomPlate* surface into a *Geom_BSplineSurface*.
750 
754 Create a Plate surface and approximate it from a polyline as a curve constraint and a point constraint
757 Standard_Integer NbCurFront=4,
760 gp_Pnt P2(0.,10.,0.);
761 gp_Pnt P3(0.,10.,10.);
762 gp_Pnt P4(0.,0.,10.);
764 BRepBuilderAPI_MakePolygon W;
770 // Initialize a BuildPlateSurface
771 GeomPlate_BuildPlateSurface BPSurf(3,15,2);
772 // Create the curve constraints
773 BRepTools_WireExplorer anExp;
774 for(anExp.Init(W); anExp.More(); anExp.Next())
776 TopoDS_Edge E = anExp.Current();
777 Handle(BRepAdaptor_HCurve) C = new
778 BRepAdaptor_HCurve();
779 C-ChangeCurve().Initialize(E);
780 Handle(BRepFill_CurveConstraint) Cont= new
781 BRepFill_CurveConstraint(C,0);
785 Handle(GeomPlate_PointConstraint) PCont= new
786 GeomPlate_PointConstraint(P5,0);
788 // Compute the Plate surface
790 // Approximation of the Plate surface
791 Standard_Integer MaxSeg=9;
792 Standard_Integer MaxDegree=8;
793 Standard_Integer CritOrder=0;
794 Standard_Real dmax,Tol;
795 Handle(GeomPlate_Surface) PSurf = BPSurf.Surface();
796 dmax = Max(0.0001,10*BPSurf.G0Error());
799 Mapp(PSurf,Tol,MaxSeg,MaxDegree,dmax,CritOrder);
800 Handle (Geom_Surface) Surf (Mapp.Surface());
801 // create a face corresponding to the approximated Plate
803 Standard_Real Umin, Umax, Vmin, Vmax;
804 PSurf-Bounds( Umin, Umax, Vmin, Vmax);
805 BRepBuilderAPI_MakeFace MF(Surf,Umin, Umax, Vmin, Vmax);
808 @subsection occt_modalg_2_12 Projections
809 This package provides functionality for projecting points onto 2D and 3D curves and surfaces.
811 @subsubsection occt_modalg_2_12_1 Projection of a Point onto a Curve
812 *Geom2dAPI_ProjectPointOnCurve* allows calculation of all the normals projected from a point (*gp_Pnt2d*) onto a geometric curve (*Geom2d_Curve*). The calculation may be restricted to a given domain.
815 
819 The curve does not have to be a *Geom2d_TrimmedCurve*. The algorithm will function with any
820 class inheriting Geom2d_Curve.
822 @subsubsection occt_modalg_2_12_2 Geom2dAPI_ProjectPointOnCurve
823 This class may be instantiated as in the following example:
827 Handle(Geom2d_BezierCurve) C =
828 new Geom2d_BezierCurve(args);
829 Geom2dAPI_ProjectPointOnCurve Projector (P, C);
832 To restrict the search for normals to a given domain *[U1,U2]*, use the following constructor:
834 Geom2dAPI_ProjectPointOnCurve Projector (P, C, U1, U2);
836 Having thus created the *Geom2dAPI_ProjectPointOnCurve* object, we can now interrogate it.
838 Calling the number of solution points
839 -------------------------------------
841 Standard_Integer NumSolutions = Projector.NbPoints();
844 Calling the location of a solution point
845 ----------------------------------------
846 The solutions are indexed in a range from *1* to *Projector.NbPoints()*. The point, which corresponds to a given *Index* may be found:
848 gp_Pnt2d Pn = Projector.Point(Index);
851 Calling the parameter of a solution point
852 -----------------------------------------
853 For a given point corresponding to a given *Index*:
856 Standard_Real U = Projector.Parameter(Index);
859 This can also be programmed as:
863 Projector.Parameter(Index,U);
866 Calling the distance between the start and end points
867 -----------------------------------------------------
868 We can find the distance between the initial point and a point, which corresponds to the given *Index*:
871 Standard_Real D = Projector.Distance(Index);
874 Calling the nearest solution point
875 ---------------------------------
877 This class offers a method to return the closest solution point to the starting point. This solution is accessed as follows:
879 gp_Pnt2d P1 = Projector.NearestPoint();
882 Calling the parameter of the nearest solution point
883 ---------------------------------------------------
885 Standard_Real U = Projector.LowerDistanceParameter();
888 Calling the minimum distance from the point to the curve
889 -------------------------------------------------------
891 Standard_Real D = Projector.LowerDistance();
894 @subsubsection occt_modalg_2_12_3 Redefined operators
896 Some operators have been redefined to find the closest solution.
898 *Standard_Real()* returns the minimum distance from the point to the curve.
901 Standard_Real D = Geom2dAPI_ProjectPointOnCurve (P,C);
904 *Standard_Integer()* returns the number of solutions.
908 Geom2dAPI_ProjectPointOnCurve (P,C);
911 *gp_Pnt2d()* returns the nearest solution point.
914 gp_Pnt2d P1 = Geom2dAPI_ProjectPointOnCurve (P,C);
917 Using these operators makes coding easier when you only need the nearest point. Thus:
919 Geom2dAPI_ProjectPointOnCurve Projector (P, C);
920 gp_Pnt2d P1 = Projector.NearestPoint();
922 can be written more concisely as:
924 gp_Pnt2d P1 = Geom2dAPI_ProjectPointOnCurve (P,C);
926 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.
929 @subsubsection occt_modalg_2_12_4 Access to lower-level functionalities
931 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:
934 Extrema_ExtPC2d& TheExtrema = Projector.Extrema();
937 @subsubsection occt_modalg_2_12_5 GeomAPI_ProjectPointOnCurve
939 This class is instantiated as in the following example:
942 Handle(Geom_BezierCurve) C =
943 new Geom_BezierCurve(args);
944 GeomAPI_ProjectPointOnCurve Projector (P, C);
946 If you wish to restrict the search for normals to the given domain [U1,U2], use the following constructor:
948 GeomAPI_ProjectPointOnCurve Projector (P, C, U1, U2);
950 Having thus created the *GeomAPI_ProjectPointOnCurve* object, you can now interrogate it.
952 Calling the number of solution points
953 -------------------------------------
955 Standard_Integer NumSolutions = Projector.NbPoints();
958 Calling the location of a solution point
959 ----------------------------------------
960 The solutions are indexed in a range from 1 to *Projector.NbPoints()*. The point, which corresponds to a given index, may be found:
962 gp_Pnt Pn = Projector.Point(Index);
965 Calling the parameter of a solution point
966 -----------------------------------------
967 For a given point corresponding to a given index:
970 Standard_Real U = Projector.Parameter(Index);
973 This can also be programmed as:
976 Projector.Parameter(Index,U);
979 Calling the distance between the start and end point
980 ----------------------------------------------------
981 The distance between the initial point and a point, which corresponds to a given index, may be found:
983 Standard_Real D = Projector.Distance(Index);
986 Calling the nearest solution point
987 ----------------------------------
988 This class offers a method to return the closest solution point to the starting point. This solution is accessed as follows:
990 gp_Pnt P1 = Projector.NearestPoint();
993 Calling the parameter of the nearest solution point
994 ---------------------------------------------------
996 Standard_Real U = Projector.LowerDistanceParameter();
999 Calling the minimum distance from the point to the curve
1000 --------------------------------------------------------
1002 Standard_Real D = Projector.LowerDistance();
1006 --------------------
1007 Some operators have been redefined to find the nearest solution.
1009 *Standard_Real()* returns the minimum distance from the point to the curve.
1012 Standard_Real D = GeomAPI_ProjectPointOnCurve (P,C);
1015 *Standard_Integer()* returns the number of solutions.
1017 Standard_Integer N = GeomAPI_ProjectPointOnCurve (P,C);
1020 *gp_Pnt2d()* returns the nearest solution point.
1023 gp_Pnt P1 = GeomAPI_ProjectPointOnCurve (P,C);
1025 Using these operators makes coding easier when you only need the nearest point. In this way,
1028 GeomAPI_ProjectPointOnCurve Projector (P, C);
1029 gp_Pnt P1 = Projector.NearestPoint();
1032 can be written more concisely as:
1034 gp_Pnt P1 = GeomAPI_ProjectPointOnCurve (P,C);
1036 In the second case, however, no intermediate *GeomAPI_ProjectPointOnCurve* object is created, and it is impossible to access other solutions points.
1038 Access to lower-level functionalities
1039 -------------------------------------
1040 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:
1043 Extrema_ExtPC& TheExtrema = Projector.Extrema();
1046 @subsubsection occt_modalg_2_12_6 Projection of a Point on a Surface
1048 *GeomAPI_ProjectPointOnSurf* class allows calculation of all normals projected from a point from *gp_Pnt* onto a geometric surface from Geom_Surface.
1051 
1055 Note that the surface does not have to be of *Geom_RectangularTrimmedSurface* type.
1056 The algorithm will function with any class inheriting Geom_Surface.
1058 *GeomAPI_ProjectPointOnSurf* is instantiated as in the following example:
1061 Handle (Geom_Surface) S = new Geom_BezierSurface(args);
1062 GeomAPI_ProjectPointOnSurf Proj (P, S);
1065 To restrict the search for normals within the given rectangular domain [U1, U2, V1, V2], use the following constructor:
1068 GeomAPI_ProjectPointOnSurf Proj (P, S, U1, U2, V1, V2);
1071 The values of U1, U2, V1 and V2 lie at or within their maximum and minimum limits, i.e.:
1073 Umin <= U1 < U2 <= Umax
1074 Vmin <= V1 < V2 <= Vmax
1076 Having thus created the *GeomAPI_ProjectPointOnSurf* object, you can interrogate it.
1078 Calling the number of solution points
1079 -------------------------------------
1082 Standard_Integer NumSolutions = Proj.NbPoints();
1085 Calling the location of a solution point
1086 ----------------------------------------
1087 The solutions are indexed in a range from 1 to *Proj.NbPoints()*. The point corresponding to the given index may be found:
1090 gp_Pnt Pn = Proj.Point(Index);
1093 Calling the parameters of a solution point
1094 ------------------------------------------
1095 For a given point corresponding to the given index:
1099 Proj.Parameters(Index, U, V);
1102 Calling the distance between the start and end point
1103 ----------------------------------------------------
1105 The distance between the initial point and a point corresponding to the given index may be found:
1107 Standard_Real D = Projector.Distance(Index);
1110 Calling the nearest solution point
1111 ----------------------------------
1112 This class offers a method, which returns the closest solution point to the starting point. This solution is accessed as follows:
1114 gp_Pnt P1 = Proj.NearestPoint();
1117 Calling the parameters of the nearest solution point
1118 ----------------------------------------------------
1121 Proj.LowerDistanceParameters (U, V);
1124 Calling the minimum distance from a point to the surface
1125 --------------------------------------------------------
1127 Standard_Real D = Proj.LowerDistance();
1132 Some operators have been redefined to help you find the nearest solution.
1134 *Standard_Real()* returns the minimum distance from the point to the surface.
1137 Standard_Real D = GeomAPI_ProjectPointOnSurf (P,S);
1140 *Standard_Integer()* returns the number of solutions.
1143 Standard_Integer N = GeomAPI_ProjectPointOnSurf (P,S);
1146 *gp_Pnt2d()* returns the nearest solution point.
1149 gp_Pnt P1 = GeomAPI_ProjectPointOnSurf (P,S);
1152 Using these operators makes coding easier when you only need the nearest point. In this way,
1155 GeomAPI_ProjectPointOnSurface Proj (P, S);
1156 gp_Pnt P1 = Proj.NearestPoint();
1159 can be written more concisely as:
1162 gp_Pnt P1 = GeomAPI_ProjectPointOnSurface (P,S);
1165 In the second case, however, no intermediate *GeomAPI_ProjectPointOnSurf* object is created, and it is impossible to access other solution points.
1167 @subsubsection occt_modalg_2_12_7 Access to lower-level functionalities
1169 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:
1172 Extrema_ExtPS& TheExtrema = Proj.Extrema();
1176 @subsubsection occt_modalg_2_12_8 Switching from 2d and 3d Curves
1177 The To2d and To3d methods are used to;
1179 * build a 2d curve from a 3d Geom_Curve lying on a gp_Pln plane
1180 * build a 3d curve from a Geom2d_Curve and a gp_Pln plane.
1182 These methods are called as follows:
1184 Handle(Geom2d_Curve) C2d = GeomAPI::To2d(C3d, Pln);
1185 Handle(Geom_Curve) C3d = GeomAPI::To3d(C2d, Pln);
1189 @section occt_modalg_3 Topological Tools
1191 Open CASCADE Technology topological tools include:
1193 * Standard topological objects combining topological data structure and boundary representation
1194 * Geometric Transformations
1195 * Conversion to NURBS geometry
1197 * Duplicating Shapes
1201 @subsection occt_modalg_3_1 Creation of Standard Topological Objects
1203 The standard topological objects include
1211 There are two root classes for their construction and modification:
1212 * 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.
1213 * The deferred *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.
1215 @subsubsection occt_modalg_3_1_1 Vertex
1217 *BRepBuilderAPI_MakeVertex* creates a new vertex from a 3D point from gp.
1220 TopoDS_Vertex V = BRepBuilderAPI_MakeVertex(P);
1223 This class always creates a new vertex and has no other methods.
1225 @subsubsection occt_modalg_3_1_2 Edge
1227 Use *BRepBuilderAPI_MakeEdge* to create from a curve and vertices. The basic method is to construct an edge from a curve, two vertices, and two parameters. All other constructions are derived from this one. The basic method and its arguments are described first, followed by the other methods. The BRepBuilderAPI_MakeEdge class can provide extra information and return an error status.
1229 Basic Edge construction
1230 -----------------------
1233 Handle(Geom_Curve) C = ...; // a curve
1234 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1235 Standard_Real p1 = ..., p2 = ..;// two parameters
1236 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(C,V1,V2,p1,p2);
1239 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.
1241 
1243 The following rules apply to the arguments:
1246 * Must not be a Null Handle.
1247 * If the curve is a trimmed curve, the basis curve is used.
1250 * 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()).
1251 * 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).
1254 * Must be increasing and in the range of the curve, i.e.:
1256 C->FirstParameter() <= p1 < p2 <= C->LastParameter()
1259 * If the parameters are decreasing, the Vertices are switched, i.e. V2 becomes V1 and V1 becomes V2.
1260 * 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.
1261 * Can be infinite but the corresponding vertex must be Null (see above).
1262 * The distance between the Vertex 3d location and the point evaluated on the curve with the parameter must be lower than the default precision.
1264 The figure below illustrates two special cases, a semi-infinite edge and an edge on a periodic curve.
1266 
1269 Other Edge constructions
1270 ------------------------
1271 *BRepBuilderAPI_MakeEdge* class provides methods, which are all simplified calls of the previous one:
1273 * The parameters can be omitted. They are computed by projecting the vertices on the curve.
1274 * 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.
1275 * The vertices or points can be omitted if the parameters are given. The points are computed by evaluating the parameters on the curve.
1276 * The vertices or points and the parameters can be omitted. The first and the last parameters of the curve are used.
1278 The five following methods are thus derived from the basic construction:
1281 Handle(Geom_Curve) C = ...; // a curve
1282 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1283 Standard_Real p1 = ..., p2 = ..;// two parameters
1284 gp_Pnt P1 = ..., P2 = ...;// two points
1286 // project the vertices on the curve
1287 E = BRepBuilderAPI_MakeEdge(C,V1,V2);
1288 // Make vertices from points
1289 E = BRepBuilderAPI_MakeEdge(C,P1,P2,p1,p2);
1290 // Make vertices from points and project them
1291 E = BRepBuilderAPI_MakeEdge(C,P1,P2);
1292 // Computes the points from the parameters
1293 E = BRepBuilderAPI_MakeEdge(C,p1,p2);
1294 // Make an edge from the whole curve
1295 E = BRepBuilderAPI_MakeEdge(C);
1299 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:
1301 *gp_Lin* creates a *Geom_Line*
1302 *gp_Circ* creates a *Geom_Circle*
1303 *gp_Elips* creates a *Geom_Ellipse*
1304 *gp_Hypr* creates a *Geom_Hyperbola*
1305 *gp_Parab* creates a *Geom_Parabola*
1307 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.
1311 TopoDS_Vertex V1 = ...,V2 = ...;// two Vertices
1312 gp_Pnt P1 = ..., P2 = ...;// two points
1315 // linear edge from two vertices
1316 E = BRepBuilderAPI_MakeEdge(V1,V2);
1318 // linear edge from two points
1319 E = BRepBuilderAPI_MakeEdge(P1,P2);
1322 Other information and error status
1323 ----------------------------------
1324 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.
1326 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:
1328 * **EdgeDone** - No error occurred, *IsDone* returns True.
1329 * **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.
1330 * **ParameterOutOfRange** - The given parameters are not in the range *C->FirstParameter()*, *C->LastParameter()*
1331 * **DifferentPointsOnClosedCurve** - The two vertices or points have different locations but they are the extremities of a closed curve.
1332 * **PointWithInfiniteParameter** - A finite coordinate point was associated with an infinite parameter (see the Precision package for a definition of infinite values).
1333 * **DifferentsPointAndParameter** - The distance of the 3D point and the point evaluated on the curve with the parameter is greater than the precision.
1334 * **LineThroughIdenticPoints** - Two identical points were given to define a line (construction of an edge without curve), *gp::Resolution* is used to test confusion .
1336 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.
1338 
1341 #include <BRepBuilderAPI_MakeEdge.hxx>
1342 #include <TopoDS_Shape.hxx>
1343 #include <gp_Circ.hxx>
1345 #include <TopoDS_Wire.hxx>
1346 #include <TopTools_Array1OfShape.hxx>
1347 #include <BRepBuilderAPI_MakeWire.hxx>
1349 // Use MakeArc method to make an edge and two vertices
1350 void MakeArc(Standard_Real x,Standard_Real y,
1353 TopoDS_Shape& E,
1354 TopoDS_Shape& V1,
1355 TopoDS_Shape& V2)
1357 gp_Ax2 Origin = gp::XOY();
1358 gp_Vec Offset(x, y, 0.);
1359 Origin.Translate(Offset);
1360 BRepBuilderAPI_MakeEdge
1361 ME(gp_Circ(Origin,R), ang, ang+PI/2);
1367 TopoDS_Wire MakeFilletedRectangle(const Standard_Real H,
1368 const Standard_Real L,
1369 const Standard_Real R)
1371 TopTools_Array1OfShape theEdges(1,8);
1372 TopTools_Array1OfShape theVertices(1,8);
1374 // First create the circular edges and the vertices
1375 // using the MakeArc function described above.
1376 void MakeArc(Standard_Real, Standard_Real,
1377 Standard_Real, Standard_Real,
1378 TopoDS_Shape&, TopoDS_Shape&, TopoDS_Shape&);
1380 Standard_Real x = L/2 - R, y = H/2 - R;
1381 MakeArc(x,-y,R,3.*PI/2.,theEdges(2),theVertices(2),
1383 MakeArc(x,y,R,0.,theEdges(4),theVertices(4),
1385 MakeArc(-x,y,R,PI/2.,theEdges(6),theVertices(6),
1387 MakeArc(-x,-y,R,PI,theEdges(8),theVertices(8),
1389 // Create the linear edges
1390 for (Standard_Integer i = 1; i <= 7; i += 2)
1392 theEdges(i) = BRepBuilderAPI_MakeEdge
1393 (TopoDS::Vertex(theVertices(i)),TopoDS::Vertex
1394 (theVertices(i+1)));
1396 // Create the wire using the BRepBuilderAPI_MakeWire
1397 BRepBuilderAPI_MakeWire MW;
1398 for (i = 1; i <= 8; i++)
1400 MW.Add(TopoDS::Edge(theEdges(i)));
1406 @subsubsection occt_modalg_3_1_3 Edge 2D
1408 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).
1410 *BRepBuilderAPI_MakeEdge2d* class is strictly similar to BRepBuilderAPI_MakeEdge, but it uses 2D geometry from gp and Geom2d instead of 3D geometry.
1412 @subsubsection occt_modalg_3_1_4 Polygon
1414 *BRepBuilderAPI_MakePolygon* class is used to build polygonal wires from vertices or points. Points are automatically changed to vertices as in *BRepBuilderAPI_MakeEdge*.
1416 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.
1419 #include <TopoDS_Wire.hxx>
1420 #include <BRepBuilderAPI_MakePolygon.hxx>
1421 #include <TColgp_Array1OfPnt.hxx>
1423 TopoDS_Wire ClosedPolygon(const TColgp_Array1OfPnt& Points)
1425 BRepBuilderAPI_MakePolygon MP;
1426 for(Standard_Integer i=Points.Lower();i=Points.Upper();i++)
1435 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.
1439 Example of a closed triangle from three vertices:
1441 TopoDS_Wire W = BRepBuilderAPI_MakePolygon(V1,V2,V3,Standard_True);
1444 Example of an open polygon from four points:
1446 TopoDS_Wire W = BRepBuilderAPI_MakePolygon(P1,P2,P3,P4);
1449 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.
1451 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.
1453 @subsubsection occt_modalg_3_1_5 Face
1455 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.
1457 Basic face construction
1458 -----------------------
1460 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.
1463 Handle(Geom_Surface) S = ...; // a surface
1464 Standard_Real umin,umax,vmin,vmax; // parameters
1465 TopoDS_Face F = BRepBuilderAPI_MakeFace(S,umin,umax,vmin,vmax);
1468 
1470 To make a face from the natural boundary of a surface, the parameters are not required:
1473 Handle(Geom_Surface) S = ...; // a surface
1474 TopoDS_Face F = BRepBuilderAPI_MakeFace(S);
1477 Constraints on the parameters are similar to the constraints in *BRepBuilderAPI_MakeEdge*.
1478 * umin,umax (vmin,vmax) must be in the range of the surface and must be increasing.
1479 * On a U (V) periodic surface umin and umax (vmin,vmax) are adjusted.
1480 * umin, umax, vmin, vmax can be infinite. There will be no edge in the corresponding direction.
1483 Other face constructions
1484 ------------------------
1485 The two basic constructions (from a surface and from a surface and parameters) are implemented for all the gp package surfaces, which are transformed in the corresponding Surface from Geom.
1487 *gp_Pln* creates a *Geom_Plane*
1488 *gp_Cylinder* creates a *Geom_CylindricalSurface*
1489 *gp_Cone* creates a *Geom_ConicalSurface*
1490 *gp_Sphere* creates a *Geom_SphericalSurface*
1491 *gp_Torus* creates a *Geom_ToroidalSurface*
1493 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.
1496 gp_Cylinder C = ..; // a cylinder
1497 TopoDS_Wire W = ...;// a wire
1498 BRepBuilderAPI_MakeFace MF(C);
1503 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.
1505 If there is no parametric curve for an edge of the wire on the Face it is computed by projection.
1507 For one wire, a simple syntax is provided to construct the face from the surface and the wire. The above lines could be written:
1510 TopoDS_Face F = BRepBuilderAPI_MakeFace(C,W);
1513 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*.
1516 #include <TopoDS_Face.hxx>
1517 #include <TColgp_Array1OfPnt.hxx>
1518 #include <BRepBuilderAPI_MakePolygon.hxx>
1519 #include <BRepBuilderAPI_MakeFace.hxx>
1521 TopoDS_Face PolygonalFace(const TColgp_Array1OfPnt& thePnts)
1523 BRepBuilderAPI_MakePolygon MP;
1524 for(Standard_Integer i=thePnts.Lower();
1525 i<=thePnts.Upper(); i++)
1530 TopoDS_Face F = BRepBuilderAPI_MakeFace(MP.Wire());
1535 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:
1538 TopoDS_Face F = ...; // a face
1539 TopoDS_Wire W = ...; // a wire
1540 F = BRepBuilderAPI_MakeFace(F,W);
1543 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.
1547 The Error method returns an error status, which is a term from the *BRepBuilderAPI_FaceError* enumeration.
1549 * *FaceDone* - no error occurred.
1550 * *NoFace* - no initialization of the algorithm; an empty constructor was used.
1551 * *NotPlanar* - no surface was given and the wire was not planar.
1552 * *CurveProjectionFailed* - no curve was found in the parametric space of the surface for an edge.
1553 * *ParametersOutOfRange* - the parameters umin,umax,vmin,vmax are out of the surface.
1555 @subsubsection occt_modalg_3_1_6 Wire
1556 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.
1558 Up to four edges can be used directly, for example:
1561 TopoDS_Wire W = BRepBuilderAPI_MakeWire(E1,E2,E3,E4);
1564 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).
1567 TopTools_Array1OfShapes theEdges;
1568 BRepBuilderAPI_MakeWire MW;
1569 for (Standard_Integer i = theEdge.Lower();
1570 i <= theEdges.Upper(); i++)
1571 MW.Add(TopoDS::Edge(theEdges(i));
1575 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:
1578 #include <TopoDS_Wire.hxx>
1579 #include <BRepBuilderAPI_MakeWire.hxx>
1581 TopoDS_Wire MergeWires (const TopoDS_Wire& W1,
1582 const TopoDS_Wire& W2)
1584 BRepBuilderAPI_MakeWire MW(W1);
1590 *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.
1592 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.
1594 The Error method returns a term of the *BRepBuilderAPI_WireError* enumeration:
1595 *WireDone* - no error occurred.
1596 *EmptyWire* - no initialization of the algorithm, an empty constructor was used.
1597 *DisconnectedWire* - the last added edge was not connected to the wire.
1598 *NonManifoldWire* - the wire with some singularity.
1600 @subsubsection occt_modalg_3_1_7 Shell
1601 The shell is a composite shape built not from a geometry, but by the assembly of faces.
1602 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.
1604 @subsubsection occt_modalg_3_1_8 Solid
1605 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.
1608 @subsubsection occt_modalg_3_2 Modification Operators
1610 @subsubsection occt_modalg_3_2_1 Transformation
1611 *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.
1613 The following example deals with the rotation of shapes.
1617 TopoDS_Shape myShape1 = ...;
1618 // The original shape 1
1619 TopoDS_Shape myShape2 = ...;
1620 // The original shape2
1622 T.SetRotation(gp_Ax1(gp_Pnt(0.,0.,0.),gp_Vec(0.,0.,1.)),
1624 BRepBuilderAPI_Transformation theTrsf(T);
1625 theTrsf.Perform(myShape1);
1626 TopoDS_Shape myNewShape1 = theTrsf.Shape()
1627 theTrsf.Perform(myShape2,Standard_True);
1628 // Here duplication is forced
1629 TopoDS_Shape myNewShape2 = theTrsf.Shape()
1632 @subsubsection occt_modalg_3_2_2 Duplication
1634 Use the BRepBuilderAPI_Copy class to duplicate a shape. A new shape is thus created.
1635 In the following example, a solid is copied:
1638 TopoDS Solid MySolid;
1639 ....// Creates a solid
1641 TopoDS_Solid myCopy = BRepBuilderAPI_Copy(mySolid);
1644 @section occt_modalg_4 Construction of Primitives
1645 @subsection occt_modalg_4_1 Making Primitives
1646 @subsubsection occt_modalg_4_1_1 Box
1648 BRepPrimAPI_MakeBox class allows building a parallelepiped box. The result is either a Shell or a Solid. There are four ways to build a box:
1650 * From three dimensions dx,dy,dz. The box is parallel to the axes and extends for [0,dx] [0,dy] [0,dz].
1651 * From a point and three dimensions. The same as above but the point is the new origin.
1652 * From two points, the box is parallel to the axes and extends on the intervals defined by the coordinates of the two points.
1653 * 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.
1655 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:
1657 TopoDS_Solid theBox = BRepPrimAPI_MakeBox(10.,20.,30.);
1660 The four methods to build a box are shown in the figure:
1662 
1664 @subsubsection occt_modalg_4_1_2 Wedge
1665 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.
1667 The following figure shows two ways to build wedges. One is to add an ltx dimension, which is the length in x of the face at dy. The second is to add xmin, xmax, zmin, zmax to describe the face at dy.
1669 The first method is a particular case of the second with xmin = 0, xmax = ltx, zmin = 0, zmax = dz.
1670 To make a centered pyramid you can use xmin = xmax = dx / 2, zmin = zmax = dz / 2.
1672 
1674 @subsubsection occt_modalg_4_1_3 Rotation object
1675 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.
1677 The particular constructions of these primitives are described, but they all have some common arguments, which are:
1679 * A system of coordinates, where the Z axis is the rotation axis..
1680 * An angle in the range [0,2*PI].
1681 * A vmin, vmax parameter range on the curve.
1683 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.
1685 
1687 @subsubsection occt_modalg_4_1_4 Cylinder
1688 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:
1690 * Radius and height, to build a full cylinder.
1691 * Radius, height and angle to build a portion of a cylinder.
1693 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, a length of DY, and a radius R.
1697 Standard_Real X = 20, Y = 10, Z = 15, R = 10, DY = 30;
1698 // Make the system of coordinates
1699 gp_Ax2 axes = gp::ZOX();
1700 axes.Translate(gp_Vec(X,Y,Z));
1702 BRepPrimAPI_MakeCylinder(axes,R,DY,PI/2.);
1704 
1706 @subsubsection occt_modalg_4_1_5 Cone
1707 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:
1709 * Two radii and height, to build a full cone. One of the radii can be null to make a sharp cone.
1710 * Radii, height and angle to build a truncated cone.
1712 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.
1715 Standard_Real R1 = 30, R2 = 10, H = 15;
1716 TopoDS_Solid S = BRepPrimAPI_MakeCone(R1,R2,H);
1719 
1721 @subsubsection occt_modalg_4_1_6 Sphere
1722 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:
1724 * From a radius - builds a full sphere.
1725 * From a radius and an angle - builds a lune (digon).
1726 * From a radius and two angles - builds a wraparound spherical segment between two latitudes. The angles a1, a2 must follow the relation: PI/2 <= a1 < a2 <= PI/2.
1727 * From a radius and three angles - a combination of two previous methods builds a portion of spherical segment.
1729 The following code builds four spheres from a radius and three angles.
1732 Standard_Real R = 30, ang =
1733 PI/2, a1 = -PI/2.3, a2 = PI/4;
1734 TopoDS_Solid S1 = BRepPrimAPI_MakeSphere(R);
1735 TopoDS_Solid S2 = BRepPrimAPI_MakeSphere(R,ang);
1736 TopoDS_Solid S3 = BRepPrimAPI_MakeSphere(R,a1,a2);
1737 TopoDS_Solid S4 = BRepPrimAPI_MakeSphere(R,a1,a2,ang);
1740 Note that we could equally well choose to create Shells instead of Solids.
1742 
1745 @subsubsection occt_modalg_4_1_7 Torus
1746 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:
1748 * Two radii - builds a full torus.
1749 * Two radii and an angle - builds an angular torus segment.
1750 * 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.
1751 * Two radii and three angles - a combination of two previous methods builds a portion of torus segment.
1753 
1755 The following code builds four toroidal shells from two radii and three angles.
1758 Standard_Real R1 = 30, R2 = 10, ang = PI, a1 = 0,
1760 TopoDS_Shell S1 = BRepPrimAPI_MakeTorus(R1,R2);
1761 TopoDS_Shell S2 = BRepPrimAPI_MakeTorus(R1,R2,ang);
1762 TopoDS_Shell S3 = BRepPrimAPI_MakeTorus(R1,R2,a1,a2);
1764 BRepPrimAPI_MakeTorus(R1,R2,a1,a2,ang);
1767 Note that we could equally well choose to create Solids instead of Shells.
1769 @subsubsection occt_modalg_4_1_8 Revolution
1770 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.
1772 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:
1774 * From a curve, use the full curve and make a full rotation.
1775 * From a curve and an angle of rotation.
1776 * From a curve and two parameters to trim the curve. The two parameters must be growing and within the curve range.
1777 * From a curve, two parameters, and an angle. The two parameters must be growing and within the curve range.
1780 @subsection occt_modalg_4_2 Sweeping: Prism, Revolution and Pipe
1781 @subsubsection occt_modalg_4_2_1 Sweeping
1783 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:
1785 * Vertices generate Edges
1786 * Edges generate Faces.
1787 * Wires generate Shells.
1788 * Faces generate Solids.
1789 * Shells generate Composite Solids
1791 It is forbidden to sweep Solids and Composite Solids. A Compound generates a Compound with the sweep of all its elements.
1793 
1795 *BRepPrimAPI_MakeSweep class* is a deferred class used as a root of the the following sweep classes:
1796 * *BRepPrimAPI_MakePrism* - produces a linear sweep
1797 * *BRepPrimAPI_MakeRevol* - produces a rotational sweep
1798 * *BRepPrimAPI_MakePipe* - produces a general sweep.
1801 @subsubsection occt_modalg_4_2_2 Prism
1802 BRepPrimAPI_MakePrism class allows creating a linear **prism** from a shape and a vector or a direction.
1803 * A vector allows creating a finite prism;
1804 * 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).
1805 The following code creates a finite, an infinite and a semi-infinite solid using a face, a direction and a length
1808 TopoDS_Face F = ..; // The swept face
1809 gp_Dir direc(0,0,1);
1810 Standard_Real l = 10;
1811 // create a vector from the direction and the length
1814 TopoDS_Solid P1 = BRepPrimAPI_MakePrism(F,v);
1816 TopoDS_Solid P2 = BRepPrimAPI_MakePrism(F,direc);
1818 TopoDS_Solid P3 = BRepPrimAPI_MakePrism(F,direc,Standard_False);
1822 
1824 @subsubsection occt_modalg_4_2_3 Rotation
1825 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.
1827 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.
1830 TopoDS_Face F = ...; // the profile
1831 gp_Ax1 axis(gp_Pnt(0,0,0),gp_Dir(0,0,1));
1832 Standard_Real ang = PI/3;
1833 TopoDS_Solid R1 = BRepPrimAPI_MakeRevol(F,axis);
1835 TopoDS_Solid R2 = BRepPrimAPI_MakeRevol(F,axis,ang);
1838 
1840 @section occt_modalg_5 Boolean Operations
1842 Boolean operations are used to create new shapes from the combinations of two shapes.
1843 |Fuse | all points in S1 or S2 |
1844 |Common | all points in S1 and S2 |
1845 |Cut S1 by S2| all points in S1 and not in S2 |
1847 BRepAlgoAPI_BooleanOperation class is the deferred root class for Boolean operations.
1849 
1851 @subsection occt_modalg_5_1 Fuse
1853 BRepAlgoAPI_Fuse performs the Fuse operation.
1855 TopoDS_Shape A = ..., B = ...;
1856 TopoDS_Shape S = BRepAlgoAPI_Fuse(A,B);
1859 @subsection occt_modalg_5_2 Common
1860 BRepAlgoAPI_Common performs the Common operation.
1863 TopoDS_Shape A = ..., B = ...;
1864 TopoDS_Shape S = BRepAlgoAPI_Common(A,B);
1867 @subsection occt_modalg_5_3 Cut
1868 BRepAlgoAPI_Cut performs the Cut operation.
1871 TopoDS_Shape A = ..., B = ...;
1872 TopoDS_Shape S = BRepAlgoAPI_Cut(A,B);
1875 @subsection occt_modalg_5_4 Section
1877 BRepAlgoAPI_Section performs the section, described as a *TopoDS_Compound* made of *TopoDS_Edge*.
1879 
1882 TopoDS_Shape A = ..., TopoDS_ShapeB = ...;
1883 TopoDS_Shape S = BRepAlgoAPI_Section(A,B);
1886 @section occt_modalg_6 Fillets and Chamfers
1887 @subsection occt_modalg_6_1 Fillets
1888 @subsection occt_modalg_6_1_1 Fillet on shape
1890 A fillet is a smooth face replacing a sharp edge.
1892 *BRepFilletAPI_MakeFillet* class allows filleting a shape.
1894 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.
1895 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.
1896 It is not an error to Add a fillet twice, the last description holds.
1898 
1900 In the following example a filleted box with dimensions a,b,c and radius r is created.
1906 #include <TopoDS_Shape.hxx>
1907 #include <TopoDS.hxx>
1908 #include <BRepPrimAPI_MakeBox.hxx>
1909 #include <TopoDS_Solid.hxx>
1910 #include <BRepFilletAPI_MakeFillet.hxx>
1911 #include <TopExp_Explorer.hxx>
1913 TopoDS_Shape FilletedBox(const Standard_Real a,
1914 const Standard_Real b,
1915 const Standard_Real c,
1916 const Standard_Real r)
1918 TopoDS_Solid Box = BRepPrimAPI_MakeBox(a,b,c);
1919 BRepFilletAPI_MakeFillet MF(Box);
1921 // add all the edges to fillet
1922 TopExp_Explorer ex(Box,TopAbs_EDGE);
1925 MF.Add(r,TopoDS::Edge(ex.Current()));
1932 
1938 void CSampleTopologicalOperationsDoc::OnEvolvedblend1()
1940 TopoDS_Shape theBox = BRepPrimAPI_MakeBox(200,200,200);
1942 BRepFilletAPI_MakeFillet Rake(theBox);
1943 ChFi3d_FilletShape FSh = ChFi3d_Rational;
1944 Rake.SetFilletShape(FSh);
1946 TColgp_Array1OfPnt2d ParAndRad(1, 6);
1947 ParAndRad(1).SetCoord(0., 10.);
1948 ParAndRad(1).SetCoord(50., 20.);
1949 ParAndRad(1).SetCoord(70., 20.);
1950 ParAndRad(1).SetCoord(130., 60.);
1951 ParAndRad(1).SetCoord(160., 30.);
1952 ParAndRad(1).SetCoord(200., 20.);
1954 TopExp_Explorer ex(theBox,TopAbs_EDGE);
1955 Rake.Add(ParAndRad, TopoDS::Edge(ex.Current()));
1956 TopoDS_Shape evolvedBox = Rake.Shape();
1960 
1962 @subsection occt_modalg_6_1_2 Chamfer
1964 A chamfer is a rectilinear edge replacing a sharp vertex of the face.
1966 The use of *BRepFilletAPI_MakeChamfer* class is similar to the use of *BRepFilletAPI_MakeFillet*, except for the following:
1968 *The surfaces created are ruled and not smooth.
1969 *The *Add* syntax for selecting edges requires one or two distances, one edge and one face (contiguous to the edge):
1973 Add(d1, d2, E, F) with d1 on the face F.
1976 
1978 @subsection occt_modalg_6_1_3 Fillet on a planar face
1980 BRepFilletAPI_MakeFillet2d class allows constructing fillets and chamfers on planar faces.
1981 To create a fillet on planar face: define it, indicate, which vertex is to be deleted, and give the fillet radius with *AddFillet* method.
1982 A chamfer can be calculated with *AddChamfer* method. It can be described by
1983 * two edges and two distances
1984 * one edge, one vertex, one distance and one angle.
1985 Fillets and chamfers are calculated when addition is complete.
1987 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:
1989 BRepFilletAPI_MakeFillet2d builder;
1990 builder.Init(F1,F2);
1997 #include “BRepPrimAPI_MakeBox.hxx”
1998 #include “TopoDS_Shape.hxx”
1999 #include “TopExp_Explorer.hxx”
2000 #include “BRepFilletAPI_MakeFillet2d.hxx”
2001 #include “TopoDS.hxx”
2002 #include “TopoDS_Solid.hxx”
2004 TopoDS_Shape FilletFace(const Standard_Real a,
2005 const Standard_Real b,
2006 const Standard_Real c,
2007 const Standard_Real r)
2010 TopoDS_Solid Box = BRepPrimAPI_MakeBox (a,b,c);
2011 TopExp_Explorer ex1(Box,TopAbs_FACE);
2013 const TopoDS_Face& F = TopoDS::Face(ex1.Current());
2014 BRepFilletAPI_MakeFillet2d MF(F);
2015 TopExp_Explorer ex2(F, TopAbs_VERTEX);
2018 MF.AddFillet(TopoDS::Vertex(ex2.Current()),r);
2026 @section occt_modalg_7 Offsets, Drafts, Pipes and Evolved shapes
2027 @subsection occt_modalg_7_1 Shelling
2029 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.
2031 The constructor *BRepOffsetAPI_MakeThickSolid* shelling operator takes the solid, the list of faces to remove and an offset value as input.
2034 TopoDS_Solid SolidInitial = ...;
2036 Standard_Real Of = ...;
2037 TopTools_ListOfShape LCF;
2038 TopoDS_Shape Result;
2039 Standard_Real Tol = Precision::Confusion();
2041 for (Standard_Integer i = 1 ;i <= n; i++) {
2042 TopoDS_Face SF = ...; // a face from SolidInitial
2046 Result = BRepOffsetAPI_MakeThickSolid (SolidInitial,
2052 
2055 @subsection occt_modalg_7_2 Draft Angle
2057 *BRepOffsetAPI_DraftAngle* class allows modifying a shape by applying draft angles to its planar, cylindrical and conical faces.
2058 The class is created or initialized from a shape, then faces to be modified are added; for each face, three arguments are used:
2060 * Direction: the direction with which the draft angle is measured
2061 * Angle: value of the angle
2062 * Neutral plane: intersection between the face and the neutral plane is invariant.
2064 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:
2067 TopoDS_Shape myShape = ...
2068 // The original shape
2069 TopTools_ListOfShape ListOfFace;
2070 // Creation of the list of faces to be modified
2073 gp_Dir Direc(0.,0.,1.);
2075 Standard_Real Angle = 5.*PI/180.;
2077 gp_Pln Neutral(gp_Pnt(0.,0.,5.), Direc);
2078 // Neutral plane Z=5
2079 BRepOffsetAPI_DraftAngle theDraft(myShape);
2080 TopTools_ListIteratorOfListOfShape itl;
2081 for (itl.Initialize(ListOfFace); itl.More(); itl.Next()) {
2082 theDraft.Add(TopoDS::Face(itl.Value()),Direc,Angle,Neutral);
2083 if (!theDraft.AddDone()) {
2084 // An error has occurred. The faulty face is given by // ProblematicShape
2088 if (!theDraft.AddDone()) {
2089 // An error has occurred
2090 TopoDS_Face guilty = theDraft.ProblematicShape();
2094 if (!theDraft.IsDone()) {
2095 // Problem encountered during reconstruction
2099 TopoDS_Shape myResult = theDraft.Shape();
2104 
2106 @subsection occt_modalg_7_3 Pipe Constructor
2108 *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.
2109 The angle between the spine and the profile is preserved throughout the pipe.
2112 TopoDS_Wire Spine = ...;
2113 TopoDS_Shape Profile = ...;
2114 TopoDS_Shape Pipe = BRepOffsetAPI_MakePipe(Spine,Profile);
2117 
2119 @subsection occt_modalg_7_4 Evolved Solid
2121 *BRepOffsetAPI_MakeEvolved* class allows creating an evolved solid from a Spine (planar face or wire) and a profile (wire).
2122 The evolved solid is an unlooped sweep generated by the spine and the profile.
2123 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.
2125 The reference axes of the profile can be defined following two distinct modes:
2127 * The reference axes of the profile are the origin axes.
2128 * The references axes of the profile are calculated as follows:
2129 + the origin is given by the point on the spine which is the closest to the profile
2130 + the X axis is given by the tangent to the spine at the point defined above
2131 + the Z axis is the normal to the plane which contains the spine.
2134 TopoDS_Face Spine = ...;
2135 TopoDS_Wire Profile = ...;
2137 BRepOffsetAPI_MakeEvolved(Spine,Profile);
2140 @section occt_modalg_8 Sewing operators
2141 @subsection occt_modalg_8_1 Sewing
2143 *BRepOffsetAPI_Sewing* class allows sewing TopoDS Shapes together along their common edges. The edges can be partially shared as in the following example.
2145 
2147 The constructor takes as arguments the tolerance (default value is 10-6) and a flag, which is used to mark the degenerate shapes.
2148 The following methods are used in this class:
2149 * *Add* adds shapes, as it is needed;
2150 * *Perform* forces calculation of the sewed shape.
2151 * *SewedShape* returns the result.
2152 Additional methods can be used to give information on the number of free boundaries, multiple edges and degenerate shapes.
2154 @subsection occt_modalg_8_2 Find Contiguous Edges
2155 *BRepOffsetAPI_FindContiguousEdges* class is used to find edges, which coincide among a set of shapes within the given tolerance; these edges can be analyzed for tangency, continuity (C1, G2, etc.)...
2157 The constructor takes as arguments the tolerance defining the edge proximity (10-6 by default) and a flag used to mark degenerated shapes.
2158 The following methods are used in this class:
2159 * *Add* adds shapes, which are to be analyzed;
2160 * *NbEdges* returns the total number of edges;
2161 * *NbContiguousEdges* returns the number of contiguous edges within the given tolerance as defined above;
2162 * *ContiguousEdge* takes an edge number as an argument and returns the *TopoDS* edge contiguous to another edge;
2163 * *ContiguousEdgeCouple* gives all edges or sections, which are common to the edge with the number given above.
2164 * *SectionToBoundary* finds the original edge on the original shape from the section.
2166 @section occt_modalg_9 Features
2168 @subsection occt_modalg_9_1 The BRepFeat Classes and their use
2169 BRepFeat package is used to manipulate extensions of the classical boundary representation of shapes closer to features. In that sense, BRepFeat is an extension of BRepBuilderAPI package.
2171 @subsubsection occt_modalg_9_1_1 Form classes
2172 The Form from BRepFeat class 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.
2176 MakePrism from BRepFeat class is used to build a prism interacting with a shape. It is created or initialized from
2177 * a shape (the basic shape),
2178 * the base of the prism,
2179 * 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),
2181 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2182 * another Boolean indicating if the self-intersections have to be found (not used in every case).
2184 There are six Perform methods:
2186 |Perform(Height) | The resulting prism is of the given length. |
2187 |Perform(Until) | The prism is defined between the position of the base and the given face. |
2188 |Perform(From, Until) | The prism is defined between the two faces From and Until. |
2189 |PerformUntilEnd() | The prism is semi-infinite, limited by the actual position of the base. |
2190 |PerformFromEnd(Until) | The prism is semi-infinite, limited by the face Until. |
2191 | 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. |
2193 **Note** *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.
2195 In the following sequence, a protrusion is performed, i.e. a face of the shape is changed into a prism.
2198 TopoDS_Shape Sbase = ...; // an initial shape
2199 TopoDS_Face Fbase = ....; // a base of prism
2201 gp_Dir Extrusion (.,.,.);
2203 // An empty face is given as the sketch face
2205 BRepFeat_MakePrism thePrism(Sbase, Fbase, TopoDS_Face(), Extrusion, Standard_True, Standard_True);
2207 thePrism, Perform(100.);
2208 if (thePrism.IsDone()) {
2209 TopoDS_Shape theResult = thePrism;
2214 
2216 
2220 MakeDPrism from BRepFeat class 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
2221 * a shape (basic shape),
2222 * the base of the prism,
2223 * 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),
2225 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2226 * another Boolean indicating if self-intersections have to be found (not used in every case).
2228 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.
2229 The semantics of draft prism feature creation is based on the construction of shapes:
2231 * up to a limiting face
2232 * from a limiting face to a height.
2234 The shape defining construction of the draft prism feature can be either the supporting edge or the concerned area of a face.
2236 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.
2237 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 .
2239 The *Perform* methods are the same as for *MakePrism*.
2242 TopoDS_Shape S = BRepPrimAPI_MakeBox(400.,250.,300.);
2244 Ex.Init(S,TopAbs_FACE);
2250 TopoDS_Face F = TopoDS::Face(Ex.Current());
2251 Handle(Geom_Surface) surf = BRep_Tool::Surface(F);
2253 c(gp_Ax2d(gp_Pnt2d(200.,130.),gp_Dir2d(1.,0.)),50.);
2254 BRepBuilderAPI_MakeWire MW;
2255 Handle(Geom2d_Curve) aline = new Geom2d_Circle(c);
2256 MW.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,PI));
2257 MW.Add(BRepBuilderAPI_MakeEdge(aline,surf,PI,2.*PI));
2258 BRepBuilderAPI_MakeFace MKF;
2259 MKF.Init(surf,Standard_False);
2261 TopoDS_Face FP = MKF.Face();
2262 BRepLib::BuildCurves3d(FP);
2263 BRepFeat_MakeDPrism MKDP (S,FP,F,10*PI180,Standard_True,
2266 TopoDS_Shape res1 = MKDP.Shape();
2269 
2273 The MakeRevol from BRepFeat class is used to build a revolution interacting with a
2274 shape. It is created or initialized from
2276 * a shape (the basic shape,)
2277 * the base of the revolution,
2278 * 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),
2279 * an axis of revolution,
2280 * a boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2281 * another boolean indicating whether the self-intersections have to be found (not used in every case).
2283 There are four Perform methods:
2284 |Perform(Angle) | The resulting revolution is of the given magnitude. |
2285 |Perform(Until) |The revolution is defined between the actual position of the base and the given face. |
2286 |Perform(From, Until) | The revolution is defined between the two faces, From and Until. |
2287 |PerformThruAll() | The result is similar to Perform(2*PI). |
2289 **Note** *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.
2292 In the following sequence, a face is revolved and the revolution is limited by a face of the base shape.
2295 TopoDS_Shape Sbase = ...; // an initial shape
2296 TopoDS_Face Frevol = ....; // a base of prism
2297 TopoDS_Face FUntil = ....; // face limiting the revol
2299 gp_Dir RevolDir (.,.,.);
2300 gp_Ax1 RevolAx(gp_Pnt(.,.,.), RevolDir);
2302 // An empty face is given as the sketch face
2304 BRepFeat_MakeRevol theRevol(Sbase, Frevol, TopoDS_Face(), RevolAx, Standard_True, Standard_True);
2306 theRevol.Perform(FUntil);
2307 if (theRevol.IsDone()) {
2308 TopoDS_Shape theResult = theRevol;
2315 This method constructs compound shapes with pipe features: depressions or protrusions. A class object is created or initialized from
2316 * a shape (basic shape),
2317 * a base face (profile of the pipe)
2318 * 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),
2320 * a Boolean indicating the type of operation (fusion=protrusion or cut=depression) on the basic shape,
2321 * another Boolean indicating if self-intersections have to be found (not used in every case).
2323 There are three Perform methods:
2325 | Perform() | The pipe is defined along the entire path (spine wire) |
2326 | Perform(Until) | The pipe is defined along the path until a given face |
2327 | Perform(From, Until) | The pipe is defined between the two faces From and Until |
2330 TopoDS_Shape S = BRepPrimAPI_MakeBox(400.,250.,300.);
2332 Ex.Init(S,TopAbs_FACE);
2335 TopoDS_Face F1 = TopoDS::Face(Ex.Current());
2336 Handle(Geom_Surface) surf = BRep_Tool::Surface(F1);
2337 BRepBuilderAPI_MakeWire MW1;
2339 p1 = gp_Pnt2d(100.,100.);
2340 p2 = gp_Pnt2d(200.,100.);
2341 Handle(Geom2d_Line) aline = GCE2d_MakeLine(p1,p2).Value();
2343 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2345 p2 = gp_Pnt2d(150.,200.);
2346 aline = GCE2d_MakeLine(p1,p2).Value();
2348 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2350 p2 = gp_Pnt2d(100.,100.);
2351 aline = GCE2d_MakeLine(p1,p2).Value();
2353 MW1.Add(BRepBuilderAPI_MakeEdge(aline,surf,0.,p1.Distance(p2)));
2354 BRepBuilderAPI_MakeFace MKF1;
2355 MKF1.Init(surf,Standard_False);
2356 MKF1.Add(MW1.Wire());
2357 TopoDS_Face FP = MKF1.Face();
2358 BRepLib::BuildCurves3d(FP);
2359 TColgp_Array1OfPnt CurvePoles(1,3);
2360 gp_Pnt pt = gp_Pnt(150.,0.,150.);
2362 pt = gp_Pnt(200.,100.,150.);
2364 pt = gp_Pnt(150.,200.,150.);
2366 Handle(Geom_BezierCurve) curve = new Geom_BezierCurve
2368 TopoDS_Edge E = BRepBuilderAPI_MakeEdge(curve);
2369 TopoDS_Wire W = BRepBuilderAPI_MakeWire(E);
2370 BRepFeat_MakePipe MKPipe (S,FP,F1,W,Standard_False,
2373 TopoDS_Shape res1 = MKPipe.Shape();
2376 
2378 @subsubsection occt_modalg_9_1_2 Linear Form
2380 *MakeLinearForm* class creates a rib or a groove along a planar surface.
2381 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.
2383 The development contexts differ, however, in the case of mechanical features.
2384 Here they include extrusion:
2385 * to a limiting face of the basis shape;
2386 * to or from a limiting plane;
2388 A class object is created or initialized from
2389 * a shape (basic shape);
2390 * a wire (base of rib or groove);
2391 * a plane (plane of the wire);
2392 * direction1 (a vector along which thickness will be built up);
2393 * direction2 (vector opposite to the previous one along which thickness will be built up, may be null);
2394 * a Boolean indicating the type of operation (fusion=rib or cut=groove) on the basic shape;
2395 * another Boolean indicating if self-intersections have to be found (not used in every case).
2397 There is one Perform() method, which performs a prism from the wire along the direction1 and direction2 interacting base shape Sbase. The height of the prism is Magnitude(Direction1)+Magnitude(direction2).
2400 BRepBuilderAPI_MakeWire mkw;
2401 gp_Pnt p1 = gp_Pnt(0.,0.,0.);
2402 gp_Pnt p2 = gp_Pnt(200.,0.,0.);
2403 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2405 p2 = gp_Pnt(200.,0.,50.);
2406 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2408 p2 = gp_Pnt(50.,0.,50.);
2409 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2411 p2 = gp_Pnt(50.,0.,200.);
2412 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2414 p2 = gp_Pnt(0.,0.,200.);
2415 mkw.Add(BRepBuilderAPI_MakeEdge(p1,p2));
2417 mkw.Add(BRepBuilderAPI_MakeEdge(p2,gp_Pnt(0.,0.,0.)));
2418 TopoDS_Shape S = BRepBuilderAPI_MakePrism(BRepBuilderAPI_MakeFace
2419 (mkw.Wire()),gp_Vec(gp_Pnt(0.,0.,0.),gp_P
2421 TopoDS_Wire W = BRepBuilderAPI_MakeWire(BRepBuilderAPI_MakeEdge(gp_Pnt
2423 gp_Pnt(100.,45.,50.)));
2424 Handle(Geom_Plane) aplane =
2425 new Geom_Plane(gp_Pnt(0.,45.,0.), gp_Vec(0.,1.,0.));
2426 BRepFeat_MakeLinearForm aform(S, W, aplane, gp_Dir
2427 (0.,5.,0.), gp_Dir(0.,-3.,0.), 1, Standard_True);
2429 TopoDS_Shape res = aform.Shape();
2432 
2434 @subsubsection occt_modalg_9_1_3 Gluer
2436 The Gluer from BRepFeat class 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.
2437 The class is created or initialized from two shapes: the “glued” shape and the basic shape (on which the other shape is glued).
2438 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.
2440 **Note** Every face and edge has to be bounded, if two edges of two glued faces are coincident they must be explicitly bounded.
2443 TopoDS_Shape Sbase = ...; // the basic shape
2444 TopoDS_Shape Sglued = ...; // the glued shape
2446 TopTools_ListOfShape Lfbase;
2447 TopTools_ListOfShape Lfglued;
2448 // Determination of the glued faces
2451 BRepFeat_Gluer theGlue(Sglue, Sbase);
2452 TopTools_ListIteratorOfListOfShape itlb(Lfbase);
2453 TopTools_ListIteratorOfListOfShape itlg(Lfglued);
2454 for (; itlb.More(); itlb.Next(), itlg(Next()) {
2455 const TopoDS_Face& f1 = TopoDS::Face(itlg.Value());
2456 const TopoDS_Face& f2 = TopoDS::Face(itlb.Value());
2457 theGlue.Bind(f1,f2);
2458 // for example, use the class FindEdges from LocOpe to
2459 // determine coincident edges
2460 LocOpe_FindEdge fined(f1,f2);
2461 for (fined.InitIterator(); fined.More(); fined.Next()) {
2462 theGlue.Bind(fined.EdgeFrom(),fined.EdgeTo());
2466 if (theGlue.IsDone() {
2467 TopoDS_Shape theResult = theGlue;
2472 @subsubsection occt_modalg_9_1_3 Split Shape
2474 SplitShape from BRepFeat class is used to split faces of a shape with wires or edges. The shape containing the new entities is rebuilt, sharing the unmodified ones.
2476 The class is created or initialized from a shape (the basic shape).
2477 Three Add methods are available:
2479 | Add(Wire, Face) | Adds a new wire on a face of the basic shape. |
2480 | Add(Edge, Face) | Adds a new edge on a face of the basic shape. |
2481 | Add(EdgeNew, EdgeOld) | Adds a new edge on an existing one (the old edge must contain the new edge). |
2483 **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.
2486 TopoDS_Shape Sbase = ...; // basic shape
2487 TopoDS_Face Fsplit = ...; // face of Sbase
2488 TopoDS_Wire Wsplit = ...; // new wire contained in Fsplit
2489 BRepFeat_SplitShape Spls(Sbase);
2490 Spls.Add(Wsplit, Fsplit);
2491 TopoDS_Shape theResult = Spls;
2496 @section occt_modalg_10 Hidden Line Removal
2498 To provide the precision required in industrial design, drawings need to offer the possibility of removing lines, which are hidden in a given projection.
2500 For this the Hidden Line Removal component provides two algorithms: HLRBRep_Algo and HLRBRep_PolyAlgo.
2502 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.
2503 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.
2505 HLRBRep_Algo takes the shape itself into account 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.
2507 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.
2509 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.
2511 However, there some restrictions in HLR use:
2512 * Points are not processed;
2513 * Z-clipping planes are not used;
2514 * Infinite faces or lines are not processed.
2517 
2519 
2521 
2523 
2526 @subsection occt_modalg_10_2 Services
2527 The following services are related to Hidden Lines Removal :
2531 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.
2533 Setting view parameters
2534 -----------------------
2535 HLRBRep_Algo::Projector and HLRBRep_PolyAlgo::Projector set a projector object which defines the parameters of the view. This object is an HLRAlgo_Projector.
2537 Computing the projections
2538 -------------------------
2539 HLRBRep_PolyAlgo::Update launches the calculation of outlines of the shape visualized by the HLRBRep_PolyAlgo framework.
2540 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.
2544 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:
2545 * visible/hidden sharp edges;
2546 * visible/hidden smooth edges;
2547 * visible/hidden sewn edges;
2548 * visible/hidden outline edges.
2550 To perform extraction on an *HLRBRep_PolyHLRToShape* object, use *HLRBRep_PolyHLRToShape::Update* function.
2551 For an *HLRBRep_HLRToShape* object built from an *HLRBRepAlgo* object you can also highlight:
2552 * visible isoparameters and
2553 * hidden isoparameters.
2555 @subsection occt_modalg_10_3 Examples
2560 // Build The algorithm object
2561 myAlgo = new HLRBRep_Algo();
2563 // Add Shapes into the algorithm
2564 TopTools_ListIteratorOfListOfShape anIterator(myListOfShape);
2565 for (;anIterator.More();anIterator.Next())
2566 myAlgo-Add(anIterator.Value(),myNbIsos);
2568 // Set The Projector (myProjector is a
2570 myAlgo-Projector(myProjector);
2575 // Set The Edge Status
2578 // Build the extraction object :
2579 HLRBRep_HLRToShape aHLRToShape(myAlgo);
2581 // extract the results :
2582 TopoDS_Shape VCompound = aHLRToShape.VCompound();
2583 TopoDS_Shape Rg1LineVCompound =
2584 aHLRToShape.Rg1LineVCompound();
2585 TopoDS_Shape RgNLineVCompound =
2586 aHLRToShape.RgNLineVCompound();
2587 TopoDS_Shape OutLineVCompound =
2588 aHLRToShape.OutLineVCompound();
2589 TopoDS_Shape IsoLineVCompound =
2590 aHLRToShape.IsoLineVCompound();
2591 TopoDS_Shape HCompound = aHLRToShape.HCompound();
2592 TopoDS_Shape Rg1LineHCompound =
2593 aHLRToShape.Rg1LineHCompound();
2594 TopoDS_Shape RgNLineHCompound =
2595 aHLRToShape.RgNLineHCompound();
2596 TopoDS_Shape OutLineHCompound =
2597 aHLRToShape.OutLineHCompound();
2598 TopoDS_Shape IsoLineHCompound =
2599 aHLRToShape.IsoLineHCompound();
2607 // Build The algorithm object
2608 myPolyAlgo = new HLRBRep_PolyAlgo();
2610 // Add Shapes into the algorithm
2611 TopTools_ListIteratorOfListOfShape
2612 anIterator(myListOfShape);
2613 for (;anIterator.More();anIterator.Next())
2614 myPolyAlgo-Load(anIterator.Value());
2616 // Set The Projector (myProjector is a
2618 myPolyAlgo->Projector(myProjector);
2621 myPolyAlgo->Update();
2623 // Build the extraction object :
2624 HLRBRep_PolyHLRToShape aPolyHLRToShape;
2625 aPolyHLRToShape.Update(myPolyAlgo);
2627 // extract the results :
2628 TopoDS_Shape VCompound =
2629 aPolyHLRToShape.VCompound();
2630 TopoDS_Shape Rg1LineVCompound =
2631 aPolyHLRToShape.Rg1LineVCompound();
2632 TopoDS_Shape RgNLineVCompound =
2633 aPolyHLRToShape.RgNLineVCompound();
2634 TopoDS_Shape OutLineVCompound =
2635 aPolyHLRToShape.OutLineVCompound();
2636 TopoDS_Shape HCompound =
2637 aPolyHLRToShape.HCompound();
2638 TopoDS_Shape Rg1LineHCompound =
2639 aPolyHLRToShape.Rg1LineHCompound();
2640 TopoDS_Shape RgNLineHCompound =
2641 aPolyHLRToShape.RgNLineHCompound();
2642 TopoDS_Shape OutLineHCompound =
2643 aPolyHLRToShape.OutLineHCompound();
2646 @section occt_modalg_10_4 Meshing of Shapes
2648 The *HLRBRep_PolyAlgo* algorithm works with triangulation of shapes. This is provided by the function *BRepMesh::Mesh*, which adds a triangulation of the shape to its topological data structure. This triangulation is computed with a given deflection.
2651 Standard_Real radius=10. ;
2652 Standard_Real height=25. ;
2653 BRepBuilderAPI_MakeCylinder myCyl (radius, height) ;
2654 TopoDS_Shape myShape = myCyl.Shape() ;
2655 Standard_Real Deflection = 0.01 ;
2656 BRepMesh::Mesh (myShape, Deflection);
2659 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, for example.
2661 You can obtain information on the shape by first exploring it. To then access triangulation of a face in the shape, use *BRepTool::Triangulation*. To access a polygon which is the approximation of an edge of the face, use *BRepTool::PolygonOnTriangulation*.
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