1 Modeling Data {#occt_user_guides__modeling_data}
2 ========================
6 @section occt_modat_0 Introduction
8 Modeling Data supplies data structures to represent 2D and 3D geometric models.
10 This manual explains how to use Modeling Data. For advanced information on modeling data, see our <a href="http://www.opencascade.com/content/tutorial-learning">E-learning & Training</a> offerings.
12 @section occt_modat_1 Geometry Utilities
14 Geometry Utilities provide the following services:
15 * Creation of shapes by interpolation and approximation
16 * Direct construction of shapes
17 * Conversion of curves and surfaces to BSpline curves and surfaces
18 * Computation of the coordinates of points on 2D and 3D curves
19 * Calculation of extrema between shapes.
21 @subsection occt_modat_1_1 Interpolations and Approximations
23 In modeling, it is often required to approximate or interpolate points into curves and surfaces. In interpolation, the process is complete when the curve or surface passes through all the points; in approximation, when it is as close to these points as possible.
25 Approximation of Curves and Surfaces groups together a variety of functions used in 2D and 3D geometry for:
26 * the interpolation of a set of 2D points using a 2D BSpline or Bezier curve;
27 * the approximation of a set of 2D points using a 2D BSpline or Bezier curve;
28 * the interpolation of a set of 3D points using a 3D BSpline or Bezier curve, or a BSpline surface;
29 * the approximation of a set of 3D points using a 3D BSpline or Bezier curve, or a BSpline surface.
31 You can program approximations in two ways:
33 * Using high-level functions, designed to provide a simple method for obtaining approximations with minimal programming,
34 * Using low-level functions, designed for users requiring more control over the approximations.
36 @subsubsection occt_modat_1_1_1 Analysis of a set of points
38 The class *PEquation* from *GProp* package allows analyzing a collection or cloud of points and verifying if they are coincident, collinear or coplanar within a given precision. If they are, the algorithm computes the mean point, the mean line or the mean plane of the points. If they are not, the algorithm computes the minimal box, which includes all the points.
40 @subsubsection occt_modat_1_1_2 Basic Interpolation and Approximation
42 Packages *Geom2dAPI* and *GeomAPI* provide simple methods for approximation and interpolation with minimal programming
46 The class *Interpolate* from *Geom2dAPI* package allows building a constrained 2D BSpline curve, defined by a table of points through which the curve passes. If required, the parameter values and vectors of the tangents can be given for each point in the table.
50 The class *Interpolate* from *GeomAPI* package allows building a constrained 3D BSpline curve, defined by a table of points through which the curve passes. If required, the parameter values and vectors of the tangents can be given for each point in the table.
52 @figure{/user_guides/modeling_data/images/modeling_data_image003.png,"Approximation of a BSpline from scattered points",420}
54 This class may be instantiated as follows:
56 GeomAPI_Interpolate Interp(Points);
59 From this object, the BSpline curve may be requested as follows:
61 Handle(Geom_BSplineCurve) C = Interp.Curve();
66 The class *PointsToBSpline* from *Geom2dAPI* package allows building a 2DBSpline curve, which approximates a set of points. You have to define the lowest and highest degree of the curve, its continuity and a tolerance value for it.The tolerance value is used to check that points are not too close to each other, or tangential vectors not too small. The resulting BSpline curve will beC2 or second degree continuous, except where a tangency constraint is defined on a point through which the curve passes. In this case, it will be only C1continuous.
70 The class *PointsToBSpline* from GeomAPI package allows building a 3D BSplinecurve, which approximates a set of points. It is necessary to define the lowest and highest degree of the curve, its continuity and tolerance. The tolerance value is used to check that points are not too close to each other,or that tangential vectors are not too small.
72 The resulting BSpline curve will be C2 or second degree continuous, except where a tangency constraint is defined on a point, through which the curve passes. In this case, it will be only C1 continuous. This class is instantiated as follows:
75 GeomAPI_PointsToBSpline
76 Approx(Points,DegMin,DegMax,Continuity, Tol);
79 From this object, the BSpline curve may be requested as follows:
82 Handle(Geom_BSplineCurve) K = Approx.Curve();
85 #### Surface Approximation
87 The class **PointsToBSplineSurface** from GeomAPI package allows building a BSpline surface, which approximates or interpolates a set of points.
89 @subsubsection occt_modat_1_1_3 Advanced Approximation
91 Packages *AppDef* and *AppParCurves* provide low-level functions, allowing more control over the approximations.
93 The low-level functions provide a second API with functions to:
94 * Define compulsory tangents for an approximation. These tangents have origins and extremities.
95 * Approximate a set of curves in parallel to respect identical parameterization.
96 * Smooth approximations. This is to produce a faired curve.
98 You can also find functions to compute:
99 * The minimal box which includes a set of points
100 * The mean plane, line or point of a set of coplanar, collinear or coincident points.
102 #### Approximation by multiple point constraints
104 *AppDef* package provides low-level tools to allow parallel approximation of groups of points into Bezier or B-Spline curves using multiple point constraints.
106 The following low level services are provided:
108 * Definition of an array of point constraints:
110 The class *MultiLine* allows defining a given number of multi-point constraints in order to build the multi-line, multiple lines passing through ordered multiple point constraints.
112 @figure{/user_guides/modeling_data/images/modeling_data_image004.png,"Definition of a MultiLine using Multiple Point Constraints",240}
115 * *Pi*, *Qi*, *Ri* ... *Si* can be 2D or 3D points.
116 * Defined as a group: *Pn*, *Qn*, *Rn,* ... *Sn* form a MultipointConstraint. They possess the same passage, tangency and curvature constraints.
117 * *P1*, *P2*, ... *Pn*, or the *Q*, *R*, ... or *S* series represent the lines to be approximated.
119 * Definition of a set of point constraints:
121 The class *MultiPointConstraint* allows defining a multiple point constraint and computing the approximation of sets of points to several curves.
123 * Computation of an approximation of a Bezier curve from a set of points:
125 The class *Compute* allows making an approximation of a set of points to a Bezier curve
127 * Computation of an approximation of a BSpline curve from a set of points:
129 The class *BSplineCompute* allows making an approximation of a set of points to a BSpline curve.
131 * Definition of Variational Criteria:
133 The class *TheVariational* allows fairing the approximation curve to a given number of points using a least squares method in conjunction with a variational criterion, usually the weights at each constraint point.
135 #### Approximation by parametric or geometric constraints
138 *AppParCurves* package provides low-level tools to allow parallel approximation of groups of points into Bezier or B-Spline curve with parametric or geometric constraints, such as a requirement for the curve to pass through given points, or to have a given tangency or curvature at a particular point.
140 The algorithms used include:
141 - the least squares method
142 - a search for the best approximation within a given tolerance value.
144 The following low-level services are provided:
146 * Association of an index to an object:
148 The class *ConstraintCouple* allows you associating an index to an object to compute faired curves using *AppDef_TheVariational*.
150 * Definition of a set of approximations of Bezier curves:
152 The class *MultiCurve* allows defining the approximation of a multi-line made up of multiple Bezier curves.
154 * Definition of a set of approximations of BSpline curves:
156 The class *MultiBSpCurve* allows defining the approximation of a multi-line made up of multiple BSpline curves.
158 * Definition of points making up a set of point constraints
160 The class *MultiPoint* allows defining groups of 2D or 3D points making up a multi-line.
162 #### Example: How to approximate a curve with respect to tangency
164 To approximate a curve with respect to tangency, follow these steps:
166 1. Create an object of type <i> AppDef_MultiPointConstraints</i> from the set of points to approximate and use the method <i> SetTang </i>to set the tangency vectors.
167 2. Create an object of type <i> AppDef_MultiLine </i>from the <i> AppDef_MultiPointConstraint</i>.
168 3. Use <i> AppDef_BSplineCompute</i>, which instantiates <i>Approx_BSplineComputeLine</i> to perform the approximation.
170 @subsection occt_modat_1_2 Direct Construction
172 Direct Construction methods from *gce*, *GC* and *GCE2d* packages provide simplified algorithms to build elementary geometric entities such as lines, circles and curves. They complement the reference definitions provided by the *gp*, *Geom* and *Geom2d* packages.
174 The algorithms implemented by <i> gce</i>, <i> GCE2d</i> and <i> GC</i> packages are simple: there is no creation of objects defined by advanced positional constraints (for more information on this subject, see *Geom2dGcc* and *GccAna*, which describe geometry by constraints).
176 For example, to construct a circle from a point and a radius using the *gp* package, it is necessary to construct axis *Ax2d* before creating the circle. If *gce* package is used, and *Ox* is taken for the axis, it is possible to create a circle directly from a point and a radius.
178 Another example is the class <i>gce_MakeCirc</i> providing a framework for defining eight problems encountered in the geometric construction of circles and implementing the eight related construction algorithms.
180 The object created (or implemented) is an algorithm which can be consulted to find out, in particular:
182 * its result, which is a <i>gp_Circ</i>, and
183 * its status. Here, the status indicates whether or not the construction was successful.
185 If it was unsuccessful, the status gives the reason for the failure.
188 gp_Pnt P1 (0.,0.,0.);
189 gp_Pnt P2 (0.,10.,0.);
190 gp_Pnt P3 (10.,0.,0.);
191 gce_MakeCirc MC (P1,P2,P3);
193 const gp_Circ& C = MC.Value();
197 In addition, <i> gce</i>, <i> GCE2d</i> and <i> GC</i> each have a <i>Root</i> class. This class is the root of all classes in the package, which return a status. The returned status (successful
198 construction or construction error) is described by the enumeration <i>gce_ErrorType</i>.
200 Note, that classes, which construct geometric transformations do not return a status, and therefore do not inherit from *Root*.
203 @subsubsection occt_modat_1_2_1 Simple geometric entities
205 The following algorithms used to build entities from *gp* package are provided by *gce* package.
206 - 2D line parallel to another at a distance,
207 - 2D line parallel to another passing through a point,
208 - 2D circle passing through two points,
209 - 2D circle parallel to another at a distance,
210 - 2D circle parallel to another passing through a point,
211 - 2D circle passing through three points,
212 - 2D circle from a center and a radius,
213 - 2D hyperbola from five points,
214 - 2D hyperbola from a center and two apexes,
215 - 2D ellipse from five points,
216 - 2D ellipse from a center and two apexes,
217 - 2D parabola from three points,
218 - 2D parabola from a center and an apex,
219 - line parallel to another passing through a point,
220 - line passing through two points,
221 - circle coaxial to another passing through a point,
222 - circle coaxial to another at a given distance,
223 - circle passing through three points,
224 - circle with its center, radius, and normal to the plane,
225 - circle with its axis (center + normal),
226 - hyperbola with its center and two apexes,
227 - ellipse with its center and two apexes,
228 - plane passing through three points,
229 - plane from its normal,
230 - plane parallel to another plane at a given distance,
231 - plane parallel to another passing through a point,
232 - plane from an array of points,
233 - cylinder from a given axis and a given radius,
234 - cylinder from a circular base,
235 - cylinder from three points,
236 - cylinder parallel to another cylinder at a given distance,
237 - cylinder parallel to another cylinder passing through a point,
238 - cone from four points,
239 - cone from a given axis and two passing points,
240 - cone from two points (an axis) and two radii,
241 - cone parallel to another at a given distance,
242 - cone parallel to another passing through a point,
243 - all transformations (rotations, translations, mirrors,scaling transformations, etc.).
245 Each class from *gp* package, such as *Circ, Circ2d, Mirror, Mirror2d*, etc., has the corresponding *MakeCirc, MakeCirc2d, MakeMirror, MakeMirror2d*, etc. class from *gce* package.
247 It is possible to create a point using a *gce* package class, then question it to recover the corresponding *gp* object.
249 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
250 gp_Pnt2d Point1,Point2;
252 //Initialization of Point1 and Point2
253 gce_MakeLin2d L = gce_MakeLin2d(Point1,Point2);
254 if (L.Status() == gce_Done() ){
255 gp_Lin2d l = L.Value();
257 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
259 This is useful if you are uncertain as to whether the arguments can create the *gp* object without raising an exception. In the case above, if *Point1* and *Point2* are closer than the tolerance value required by *MakeLin2d*, the function *Status* will return the enumeration *gce_ConfusedPoint*. This tells you why the *gp* object cannot be created. If you know that the points *Point1* and *Point2* are separated by the value exceeding the tolerance value, then you may create the *gp* object directly, as follows:
261 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
262 gp_Lin2d l = gce_MakeLin2d(Point1,Point2);
263 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
265 @subsubsection occt_modat_1_2_2 Geometric entities manipulated by handle
267 *GC* and *GCE2d* packages provides an implementation of algorithms used to build entities from *Geom* and *Geom2D* packages.
268 They implement the same algorithms as the *gce* package, and also contain algorithms for trimmed surfaces and curves.
269 The following algorithms are available:
270 - arc of a circle trimmed by two points,
271 - arc of a circle trimmed by two parameters,
272 - arc of a circle trimmed by one point and one parameter,
273 - arc of an ellipse from an ellipse trimmed by two points,
274 - arc of an ellipse from an ellipse trimmed by two parameters,
275 - arc of an ellipse from an ellipse trimmed by one point and one parameter,
276 - arc of a parabola from a parabola trimmed by two points,
277 - arc of a parabola from a parabola trimmed by two parameters,
278 - arc of a parabola from a parabola trimmed by one point and one parameter,
279 - arc of a hyperbola from a hyperbola trimmed by two points,
280 - arc of a hyperbola from a hyperbola trimmed by two parameters,
281 - arc of a hyperbola from a hyperbola trimmed by one point and one parameter,
282 - segment of a line from two points,
283 - segment of a line from two parameters,
284 - segment of a line from one point and one parameter,
285 - trimmed cylinder from a circular base and a height,
286 - trimmed cylinder from three points,
287 - trimmed cylinder from an axis, a radius, and a height,
288 - trimmed cone from four points,
289 - trimmed cone from two points (an axis) and a radius,
290 - trimmed cone from two coaxial circles.
292 Each class from *GCE2d* package, such as *Circle, Ellipse, Mirror*, etc., has the corresponding *MakeCircle, MakeEllipse, MakeMirror*, etc. class from *Geom2d* package.
293 Besides, the class *MakeArcOfCircle* returns an object of type *TrimmedCurve* from *Geom2d*.
295 Each class from *GC* package, such as *Circle, Ellipse, Mirror*, etc., has the corresponding *MakeCircle, MakeEllipse, MakeMirror*, etc. class from *Geom* package.
296 The following classes return objects of type *TrimmedCurve* from *Geom*:
299 - *MakeArcOfHyperbola*
300 - *MakeArcOfParabola*
303 @subsection occt_modat_1_3 Conversion to and from BSplines
305 The Conversion to and from BSplines component has two distinct purposes:
306 * Firstly, it provides a homogeneous formulation which can be used to describe any curve or surface.
307 This is useful for writing algorithms for a single data structure model.
308 The BSpline formulation can be used to represent most basic geometric objects provided
309 by the components which describe geometric data structures ("Fundamental Geometry Types", "2D Geometry Types" and "3D Geometry Types" components).
310 * Secondly, it can be used to divide a BSpline curve or surface into a series of curves or surfaces,
311 thereby providing a higher degree of continuity. This is useful for writing algorithms
312 which require a specific degree of continuity in the objects to which they are applied.
313 Discontinuities are situated on the boundaries of objects only.
315 The "Conversion to and from BSplines" component is composed of three packages.
317 The <i> Convert </i> package provides algorithms to convert the following into a BSpline curve or surface:
319 * a bounded curve based on an elementary 2D curve (line, circle or conic) from the <i> gp </i> package,
320 * a bounded surface based on an elementary surface (cylinder, cone, sphere or torus) from the <i> gp</i> package,
321 * a series of adjacent 2D or 3D Bezier curves defined by their poles.
323 These algorithms compute the data needed to define the resulting BSpline curve or surface.
324 This elementary data (degrees, periodic characteristics, poles and weights, knots and multiplicities)
325 may then be used directly in an algorithm, or can be used to construct the curve or the surface
326 by calling the appropriate constructor provided by the classes <i>Geom2d_BSplineCurve, Geom_BSplineCurve </i> or <i>Geom_BSplineSurface</i>.
328 The <i>Geom2dConvert</i> package provides the following:
330 * a global function which is used to construct a BSpline curve from a bounded curve based on a 2D curve from the Geom2d package,
331 * a splitting algorithm which computes the points at which a 2D BSpline curve should be cut in order to obtain arcs with the same degree of continuity,
332 * global functions used to construct the BSpline curves created by this splitting algorithm, or by other types of segmentation of the BSpline curve,
333 * an algorithm which converts a 2D BSpline curve into a series of adjacent Bezier curves.
335 The <i> GeomConvert</i> package also provides the following:
337 * a global function used to construct a BSpline curve from a bounded curve based on a curve from the Geom package,
338 * a splitting algorithm, which computes the points at which a BSpline curve should be cut in order to obtain arcs with the same degree of continuity,
339 * global functions to construct BSpline curves created by this splitting algorithm, or by other types of BSpline curve segmentation,
340 * an algorithm, which converts a BSpline curve into a series of adjacent Bezier curves,
341 * a global function to construct a BSpline surface from a bounded surface based on a surface from the Geom package,
342 * a splitting algorithm, which determines the curves along which a BSpline surface should be cut in order to obtain patches with the same degree of continuity,
343 * global functions to construct BSpline surfaces created by this splitting algorithm, or by other types of BSpline surface segmentation,
344 * an algorithm, which converts a BSpline surface into a series of adjacent Bezier surfaces,
345 * an algorithm, which converts a grid of adjacent Bezier surfaces into a BSpline surface.
347 @subsection occt_modat_1_4 Points on Curves
349 The Points on Curves component comprises high level functions providing an API for complex algorithms that compute points on a 2D or 3D curve.
351 The following characteristic points exist on parameterized curves in 3d space:
352 - points equally spaced on a curve,
353 - points distributed along a curve with equal chords,
354 - a point at a given distance from another point on a curve.
356 *GCPnts* package provides algorithms to calculate such points:
357 - *AbscissaPoint* calculates a point on a curve at a given distance from another point on the curve.
358 - *UniformAbscissa* calculates a set of points at a given abscissa on a curve.
359 - *UniformDeflection* calculates a set of points at maximum constant deflection between the curve and the polygon that results from the computed points.
361 ### Example: Visualizing a curve.
363 Let us take an adapted curve **C**, i.e. an object which is an interface between the services provided by either a 2D curve from the package Geom2d (in case of an Adaptor_Curve2d curve) or a 3D curve from the package Geom (in case of an Adaptor_Curve curve), and the services required on the curve by the computation algorithm. The adapted curve is created in the following way:
366 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
367 Handle(Geom2d_Curve) mycurve = ... ;
368 Geom2dAdaptor_Curve C (mycurve) ;
369 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
372 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
373 Handle(Geom_Curve) mycurve = ... ;
374 GeomAdaptor_Curve C (mycurve) ;
375 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
377 The algorithm is then constructed with this object:
379 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
380 GCPnts_UniformDeflection myAlgo () ;
381 Standard_Real Deflection = ... ;
382 myAlgo.Initialize ( C , Deflection ) ;
383 if ( myAlgo.IsDone() )
385 Standard_Integer nbr = myAlgo.NbPoints() ;
386 Standard_Real param ;
387 for ( Standard_Integer i = 1 ; i <= nbr ; i++ )
389 param = myAlgo.Parameter (i) ;
393 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
396 @subsection occt_modat_1_5 Extrema
398 The classes to calculate the minimum distance between points, curves, and surfaces in 2d and 3d are provided by *GeomAPI* and *Geom2dAPI* packages.
400 These packages calculate the extrema of distance between:
402 - point and a surface,
404 - a curve and a surface,
407 ### Extrema between Point and Curve / Surface
409 The *GeomAPI_ProjectPointOnCurve* class allows calculation of all extrema between a point and a curve. Extrema are the lengths of the segments orthogonal to the curve.
410 The *GeomAPI_ProjectPointOnSurface* class allows calculation of all extrema between a point and a surface. Extrema are the lengths of the segments orthogonal to the surface.
411 These classes use the "Projection" criteria for optimization.
413 ### Extrema between Curves
415 The *Geom2dAPI_ExtremaCurveCurve* class allows calculation of all minimal distances between two 2D geometric curves.
416 The *GeomAPI_ExtremaCurveCurve* class allows calculation of all minimal distances between two 3D geometric curves.
417 These classes use Euclidean distance as the criteria for optimization.
419 ### Extrema between Curve and Surface
421 The *GeomAPI_ExtremaCurveSurface* class allows calculation of one extrema between a 3D curve and a surface. Extrema are the lengths of the segments orthogonal to the curve and the surface.
422 This class uses the "Projection" criteria for optimization.
424 ### Extrema between Surfaces
426 The *GeomAPI_ExtremaSurfaceSurface* class allows calculation of one minimal and one maximal distance between two surfaces.
427 This class uses Euclidean distance to compute the minimum, and "Projection" criteria to compute the maximum.
429 @section occt_modat_2 2D Geometry
431 *Geom2d* package defines geometric objects in 2dspace. All geometric entities are STEP processed. The objects are handled by reference.
433 In particular, <i>Geom2d</i> package provides classes for:
434 * description of points, vectors and curves,
435 * their positioning in the plane using coordinate systems,
436 * their geometric transformation, by applying translations, rotations, symmetries, scaling transformations and combinations thereof.
438 The following objects are available:
443 - vector with magnitude,
447 - conic: circle, ellipse, hyperbola, parabola,
448 - rounded curve: trimmed curve, NURBS curve, Bezier curve,
451 Before creating a geometric object, it is necessary to decide how the object is handled.
452 The objects provided by *Geom2d* package are handled by reference rather than by value. Copying an instance copies the handle, not the object, so that a change to one instance is reflected in each occurrence of it.
453 If a set of object instances is needed rather than a single object instance, *TColGeom2d* package can be used. This package provides standard and frequently used instantiations of one-dimensional arrays and sequences for curves from *Geom2d* package. All objects are available in two versions:
454 - handled by reference and
457 The key characteristic of <i> Geom2d </i> curves is that they are parameterized.
458 Each class provides functions to work with the parametric equation of the curve,
459 and, in particular, to compute the point of parameter u on a curve and the derivative vectors of order 1, 2.., N at this point.
461 As a consequence of the parameterization, a <i> Geom2d </i> curve is naturally oriented.
463 Parameterization and orientation differentiate elementary <i>Geom2d</i>curves from their
464 equivalent as provided by <i> gp</i> package. <i>Geom2d</i> package provides conversion
465 functions to transform a <i> Geom2d</i> object into a <i> gp</i> object, and vice-versa, when this is possible.
467 Moreover, <i> Geom2d</i> package provides more complex curves, including Bezier curves,
468 BSpline curves, trimmed curves and offset curves.
470 <i> Geom2d </i> objects are organized according to an inheritance structure over several levels.
472 Thus, an ellipse (specific class <i> Geom2d_Ellipse</i>) is also a conical curve and inherits from the abstract class <i> Geom2d_Conic</i>, while a Bezier curve (concrete class <i> Geom2d_BezierCurve</i>) is also a bounded curve and inherits from the abstract class <i> Geom2d_BoundedCurve</i>; both these examples are also curves (abstract class <i>Geom2d_Curve</i>). Curves, points and vectors inherit from the abstract class <i> Geom2d_Geometry,</i> which describes the properties common to any geometric object from the <i>Geom2d</i> package.
474 This inheritance structure is open and it is possible to describe new objects, which inherit from those provided in the <i>Geom2d</i> package, provided that they respect the behavior of the classes from which they are to inherit.
476 Finally, <i> Geom2d</i> objects can be shared within more complex data structures. This is why they are used within topological data structures, for example.
478 <i>Geom2d</i>package uses the services of the <i> gp</i> package to:
479 * implement elementary algebraic calculus and basic analytic geometry,
480 * describe geometric transformations which can be applied to <i> Geom2d</i> objects,
481 * describe the elementary data structures of <i>Geom2d</i> objects.
483 However, the <i> Geom2d</i> package essentially provides data structures and not algorithms.
484 You can refer to the <i> GCE2d </i> package to find more evolved construction algorithms for <i> Geom2d </i> objects.
486 @section occt_modat_3 3D Geometry
488 The *Geom* package defines geometric objects in 3d space and contains all basic geometric transformations, such as identity, rotation, translation, mirroring, scale transformations, combinations of transformations, etc. as well as special functions depending on the reference definition of the geometric object (e.g. addition of a control point on a B-Spline curve,modification of a curve, etc.). All geometrical entities are STEP processed.
490 In particular, it provides classes for:
491 * description of points, vectors, curves and surfaces,
492 * their positioning in 3D space using axis or coordinate systems, and
493 * their geometric transformation, by applying translations, rotations, symmetries, scaling transformations and combinations thereof.
495 The following objects are available:
500 - Vector with magnitude
504 - Conic: circle, ellipse, hyperbola, parabola
506 - Elementary surface: plane, cylinder, cone, sphere, torus
507 - Bounded curve: trimmed curve, NURBS curve, Bezier curve
508 - Bounded surface: rectangular trimmed surface, NURBS surface,Bezier surface
509 - Swept surface: surface of linear extrusion, surface of revolution
512 The key characteristic of *Geom* curves and surfaces is that they are parameterized.
513 Each class provides functions to work with the parametric equation of the curve or
514 surface, and, in particular, to compute:
515 * the point of parameter u on a curve, or
516 * the point of parameters (u, v) on a surface.
517 together with the derivative vectors of order 1, 2, ... N at this point.
519 As a consequence of this parameterization, a Geom curve or surface is naturally oriented.
521 Parameterization and orientation differentiate elementary Geom curves and surfaces from the classes of the same (or similar) names found in <i> gp</i> package.
522 <i>Geom</i> package also provides conversion functions to transform a Geom object into a <i> gp</i> object, and vice-versa, when such transformation is possible.
524 Moreover, <i> Geom </i>package provides more complex curves and surfaces, including:
525 * Bezier and BSpline curves and surfaces,
526 * swept surfaces, for example surfaces of revolution and surfaces of linear extrusion,
527 * trimmed curves and surfaces, and
528 * offset curves and surfaces.
530 Geom objects are organized according to an inheritance structure over several levels.
531 Thus, a sphere (concrete class <i> Geom_SphericalSurface</i>) is also an elementary surface and inherits from the abstract class <i> Geom_ElementarySurface</i>, while a Bezier surface (concrete class <i> Geom_BezierSurface</i>) is also a bounded surface and inherits from the abstract class <i> Geom_BoundedSurface</i>; both these examples are also surfaces (abstract class <i> Geom_Surface</i>). Curves, points and vectors inherit from the abstract class <i> Geom_Geometry,</i> which describes the properties common to any geometric object from the <i>Geom</i> package.
533 This inheritance structure is open and it is possible to describe new objects, which inherit from those provided in the Geom package, on the condition that they respect the behavior of the classes from which they are to inherit.
535 Finally, Geom objects can be shared within more complex data structures. This is why they are used within topological data structures, for example.
537 If a set of object instances is needed rather than a single object instance, *TColGeom* package can be used. This package provides instantiations of one- and two-dimensional arrays and sequences for curves from *Geom* package. All objects are available in two versions:
538 - handled by reference and
541 The <i> Geom</i> package uses the services of the <i> gp</i> package to:
542 * implement elementary algebraic calculus and basic analytic geometry,
543 * describe geometric transformations which can be applied to Geom objects,
544 * describe the elementary data structures of Geom objects.
546 However, the Geom package essentially provides data structures, not algorithms.
548 You can refer to the <i> GC</i> package to find more evolved construction algorithms for
551 @section occt_modat_4 Properties of Shapes
553 @subsection occt_modat_4_1 Local Properties of Shapes
555 <i>BRepLProp</i> package provides the Local Properties of Shapes component,
556 which contains algorithms computing various local properties on edges and faces in a BRep model.
558 The local properties which may be queried are:
560 * for a point of parameter u on a curve which supports an edge :
562 * the derivative vectors, up to the third degree,
563 * the tangent vector,
565 * the curvature, and the center of curvature;
566 * for a point of parameter (u, v) on a surface which supports a face :
568 * the derivative vectors, up to the second degree,
569 * the tangent vectors to the u and v isoparametric curves,
571 * the minimum or maximum curvature, and the corresponding directions of curvature;
572 * the degree of continuity of a curve which supports an edge, built by the concatenation of two other edges, at their junction point.
574 Analyzed edges and faces are described as <i> BRepAdaptor</i> curves and surfaces,
575 which provide shapes with an interface for the description of their geometric support.
576 The base point for local properties is defined by its u parameter value on a curve, or its (u, v) parameter values on a surface.
578 @subsection occt_modat_4_2 Local Properties of Curves and Surfaces
580 The "Local Properties of Curves and Surfaces" component provides algorithms for computing various local properties on a Geom curve (in 2D or 3D space) or a surface. It is composed of:
582 * <i> Geom2dLProp</i> package, which allows computing Derivative and Tangent vectors (normal and curvature) of a parametric point on a 2D curve;
583 * <i> GeomLProp </i> package, which provides local properties on 3D curves and surfaces
584 * <i> LProp </i> package, which provides an enumeration used to characterize a particular point on a 2D curve.
586 Curves are either <i> Geom_Curve </i> curves (in 3D space) or <i> Geom2d_Curve </i> curves (in the plane).
587 Surfaces are <i> Geom_Surface </i> surfaces. The point on which local properties are calculated
588 is defined by its u parameter value on a curve, and its (u,v) parameter values on a surface.
590 It is possible to query the same local properties for points as mentioned above, and additionally for 2D curves:
592 * the points corresponding to a minimum or a maximum of curvature;
593 * the inflection points.
596 #### Example: How to check the surface concavity
598 To check the concavity of a surface, proceed as follows:
600 1. Sample the surface and compute at each point the Gaussian curvature.
601 2. If the value of the curvature changes of sign, the surface is concave or convex depending on the point of view.
602 3. To compute a Gaussian curvature, use the class <i> SLprops</i> from <i> GeomLProp</i>, which instantiates the generic class <i> SLProps </i>from <i> LProp</i> and use the method <i> GaussianCurvature</i>.
604 @subsection occt_modat_4_2a Continuity of Curves and Surfaces
606 Types of supported continuities for curves and surfaces are described in *GeomAbs_Shape* enumeration.
608 In respect of curves, the following types of continuity are supported (see the figure below):
609 * C0 (*GeomAbs_C0*) - parametric continuity. It is the same as G0 (geometric continuity), so the last one is not represented by separate variable.
610 * G1 (*GeomAbs_G1*) - tangent vectors on left and on right are parallel.
611 * C1 (*GeomAbs_C1*) - indicates the continuity of the first derivative.
612 * G2 (*GeomAbs_G2*) - in addition to G1 continuity, the centers of curvature on left and on right are the same.
613 * C2 (*GeomAbs_C2*) - continuity of all derivatives till the second order.
614 * C3 (*GeomAbs_C3*) - continuity of all derivatives till the third order.
615 * CN (*GeomAbs_CN*) - continuity of all derivatives till the N-th order (infinite order of continuity).
617 *Note:* Geometric continuity (G1, G2) means that the curve can be reparametrized to have parametric (C1, C2) continuity.
619 @figure{/user_guides/modeling_data/images/modeling_data_continuity_curves.svg,"Continuity of Curves",420}
621 The following types of surface continuity are supported:
622 * C0 (*GeomAbs_C0*) - parametric continuity (the surface has no points or curves of discontinuity).
623 * G1 (*GeomAbs_G1*) - surface has single tangent plane in each point.
624 * C1 (*GeomAbs_C1*) - indicates the continuity of the first derivatives.
625 * G2 (*GeomAbs_G2*) - in addition to G1 continuity, principal curvatures and directions are continuous.
626 * C2 (*GeomAbs_C2*) - continuity of all derivatives till the second order.
627 * C3 (*GeomAbs_C3*) - continuity of all derivatives till the third order.
628 * CN (*GeomAbs_CN*) - continuity of all derivatives till the N-th order (infinite order of continuity).
630 @figure{/user_guides/modeling_data/images/modeling_data_continuity_surfaces.svg,"Continuity of Surfaces",420}
632 Against single surface, the connection of two surfaces (see the figure above) defines its continuity in each intersection point only. Smoothness of connection is a minimal value of continuities on the intersection curve.
635 @subsection occt_modat_4_2b Regularity of Shared Edges
637 Regularity of an edge is a smoothness of connection of two faces sharing this edge. In other words, regularity is a minimal continuity between connected faces in each point on edge.
639 Edge's regularity can be set by *BRep_Builder::Continuity* method. To get the regularity use *BRep_Tool::Continuity* method.
641 Some algorithms like @ref occt_modalg_6 "Fillet" set regularity of produced edges by their own algorithms. On the other hand, some other algorithms (like @ref occt_user_guides__boolean_operations "Boolean Operations", @ref occt_user_guides__shape_healing "Shape Healing", etc.) do not set regularity. If the regularity is needed to be set correctly on a shape, the method *BRepLib::EncodeRegularity* can be used. It calculates and sets correct values for all edges of the shape.
643 The regularity flag is extensively used by the following high level algorithms: @ref occt_modalg_6_1_2 "Chamfer", @ref occt_modalg_7_3 "Draft Angle", @ref occt_modalg_10 "Hidden Line Removal", @ref occt_modalg_9_2_3 "Gluer".
646 @subsection occt_modat_4_3 Global Properties of Shapes
648 The Global Properties of Shapes component provides algorithms for computing the global
649 properties of a composite geometric system in 3D space, and frameworks to query the computed results.
651 The global properties computed for a system are :
655 * moment about an axis,
656 * radius of gyration about an axis,
657 * principal properties of inertia such as principal axis, principal moments, and principal radius of gyration.
659 Geometric systems are generally defined as shapes. Depending on the way they are analyzed, these shapes will give properties of:
661 * lines induced from the edges of the shape,
662 * surfaces induced from the faces of the shape, or
663 * volumes induced from the solid bounded by the shape.
665 The global properties of several systems may be brought together to give the global properties of the system composed of the sum of all individual systems.
667 The Global Properties of Shapes component is composed of:
668 * seven functions for computing global properties of a shape: one function for lines, two functions for surfaces and four functions for volumes. The choice of functions depends on input parameters and algorithms used for computation (<i>BRepGProp</i> global functions),
669 * a framework for computing global properties for a set of points (<i>GProp_PGProps</i>),
670 * a general framework to bring together the global properties retained by several more elementary frameworks, and provide a general programming interface to consult computed global properties.
672 Packages *GeomLProp* and *Geom2dLProp* provide algorithms calculating the local properties of curves and surfaces
674 A curve (for one parameter) has the following local properties:
680 - Center of curvature.
682 A surface (for two parameters U and V) has the following local properties:
684 - derivative for U and V)
685 - tangent line (for U and V)
689 - main directions of curvature
693 The following methods are available:
694 * *CLProps* -- calculates the local properties of a curve (tangency, curvature,normal);
695 * *CurAndInf2d* -- calculates the maximum and minimum curvatures and the inflection points of 2d curves;
696 * *SLProps* -- calculates the local properties of a surface (tangency, the normal and curvature).
697 * *Continuity* -- calculates regularity at the junction of two curves.
699 Note that the B-spline curve and surface are accepted but they are not cut into pieces of the desired continuity. It is the global continuity, which is seen.
701 @subsection occt_modat_4_4 Adaptors for Curves and Surfaces
703 Some Open CASCADE Technology general algorithms may work theoretically on numerous types of curves or surfaces.
705 To do this, they simply get the services required of the analyzed curve or surface through an interface so as to a single API, whatever the type of curve or surface. These interfaces are called adaptors.
707 For example, <i> Adaptor3d_Curve </i> is the abstract class which provides the required services by an algorithm which uses any 3d curve.
709 <i> GeomAdaptor </i> package provides interfaces:
711 * On a curve lying on a Geom surface;
714 <i> Geom2dAdaptor</i> package provides interfaces :
715 * On a <i>Geom2d</i> curve.
717 <i> BRepAdaptor </i> package provides interfaces:
721 When you write an algorithm which operates on geometric objects, use <i> Adaptor3d</i> (or <i> Adaptor2d</i>) objects.
723 As a result, you can use the algorithm with any kind of object, if you provide for this object an interface derived from *Adaptor3d* or *Adaptor2d*.
724 These interfaces are easy to use: simply create an adapted curve or surface from a *Geom2d* curve, and then use this adapted curve as an argument for the algorithm? which requires it.
727 @section occt_modat_5 Topology
729 OCCT Topology allows accessing and manipulating data of objects without dealing with their 2D or 3D representations. Whereas OCCT Geometry provides a description of objects in terms of coordinates or parametric values, Topology describes data structures of objects in parametric space. These descriptions use location in and restriction of parts of this space.
731 Topological library allows you to build pure topological data structures. Topology defines relationships between simple geometric entities. In this way, you can model complex shapes as assemblies of simpler entities. Due to a built-in non-manifold (or mixed-dimensional) feature, you can build models mixing:
732 * 0D entities such as points;
733 * 1D entities such as curves;
734 * 2D entities such as surfaces;
735 * 3D entities such as volumes.
737 You can, for example, represent a single object made of several distinct bodies containing embedded curves and surfaces connected or non-connected to an outer boundary.
739 Abstract topological data structure describes a basic entity -- a shape, which can be divided into the following component topologies:
740 * Vertex -- a zero-dimensional shape corresponding to a point in geometry;
741 * Edge -- a shape corresponding to a curve, and bound by a vertex at each extremity;
742 * Wire -- a sequence of edges connected by their vertices;
743 * Face -- part of a plane (in 2D geometry) or a surface (in 3D geometry) bounded by a closed wire;
744 * Shell -- a collection of faces connected by some edges of their wire boundaries;
745 * Solid -- a part of 3D space bound by a shell;
746 * Compound solid -- a collection of solids.
748 The wire and the solid can be either infinite or closed.
750 A face with 3D underlying geometry may also refer to a collection of connected triangles that approximate the underlying surface. The surfaces can be undefined leaving the faces represented by triangles only. If so, the model is purely polyhedral.
752 Topology defines the relationship between simple geometric entities, which can thus be linked together to represent complex shapes.
754 Abstract Topology is provided by six packages.
755 The first three packages describe the topological data structure used in Open CASCADE Technology:
757 * <i> TopAbs</i> package provides general resources for topology-driven applications. It contains enumerations that are used to describe basic topological notions: topological shape, orientation and state. It also provides methods to manage these enumerations.
758 * <i> TopLoc </i>package provides resources to handle 3D local coordinate systems: <i> Datum3D</i>and <i> Location</i>. <i> Datum3D</i> describes an elementary coordinate system, while <i> Location</i> comprises a series of elementary coordinate systems.
759 * <i> TopoDS</i> package describes classes to model and build data structures that are purely topological.
761 Three additional packages provide tools to access and manipulate this abstract topology:
763 * <i> TopTools</i> package provides basic tools to use on topological data structures.
764 * <i> TopExp</i> package provides classes to explore and manipulate the topological data structures described in the TopoDS package.
765 * <i> BRepTools </i> package provides classes to explore, manipulate, read and write BRep data structures. These more complex data structures combine topological descriptions with additional geometric information, and include rules for evaluating equivalence of different possible representations of the same object, for example, a point.
767 @subsection occt_modat_5_1 Shape Location
769 A local coordinate system can be viewed as either of the following:
770 - A right-handed trihedron with an origin and three orthonormal vectors. The *gp_Ax2* package corresponds to this definition.
771 - A transformation of a +1 determinant, allowing the transformation of coordinates between local and global references frames. This corresponds to the *gp_Trsf*.
773 *TopLoc* package distinguishes two notions:
774 - *TopLoc_Datum3D* class provides the elementary reference coordinate, represented by a right-handed orthonormal system of axes or by a right-handed unitary transformation.
775 - *TopLoc_Location* class provides the composite reference coordinate made from elementary ones. It is a marker composed of a chain of references to elementary markers. The resulting cumulative transformation is stored in order to avoid recalculating the sum of the transformations for the whole list.
777 @figure{/user_guides/modeling_data/images/modeling_data_image005.png,"Structure of TopLoc_Location",420}
779 Two reference coordinates are equal if they are made up of the same elementary coordinates in the same order. There is no numerical comparison. Two coordinates can thus correspond to the same transformation without being equal if they were not built from the same elementary coordinates.
781 For example, consider three elementary coordinates:
783 The composite coordinates are:
789 **NOTE** C3 and C4 are equal because they are both R1 * R2 * R3.
791 The *TopLoc* package is chiefly targeted at the topological data structure, but it can be used for other purposes.
793 Change of coordinates
794 ---------------------
796 *TopLoc_Datum3D* class represents a change of elementary coordinates. Such changes must be shared so this class inherits from *MMgt_TShared*. The coordinate is represented by a transformation *gp_Trsfpackage*. This transformation has no scaling factor.
798 @subsection occt_modat_5_2 Naming shapes, sub-shapes, their orientation and state
800 The **TopAbs** package provides general enumerations describing the basic concepts of topology and methods to handle these enumerations. It contains no classes. This package has been separated from the rest of the topology because the notions it contains are sufficiently general to be used by all topological tools. This avoids redefinition of enumerations by remaining independent of modeling resources. The TopAbs package defines three notions:
801 - **Type** *TopAbs_ShapeEnum*;
802 - **Orientation** *TopAbs_Orientation* ;
803 - **State** *StateTopAbs_State*
805 @subsubsection occt_modat_5_2_1 Topological types
807 TopAbs contains the *TopAbs_ShapeEnum* enumeration,which lists the different topological types:
808 - COMPOUND -- a group of any type of topological objects.
809 - COMPSOLID -- a composite solid is a set of solids connected by their faces. It expands the notions of WIRE and SHELL to solids.
810 - SOLID -- a part of space limited by shells. It is three dimensional.
811 - SHELL -- a set of faces connected by their edges. A shell can be open or closed.
812 - FACE -- in 2D it is a part of a plane; in 3D it is a part of a surface. Its geometry is constrained (trimmed) by contours. It is two dimensional.
813 - WIRE -- a set of edges connected by their vertices. It can be an open or closed contour depending on whether the edges are linked or not.
814 - EDGE -- a topological element corresponding to a restrained curve. An edge is generally limited by vertices. It has one dimension.
815 - VERTEX -- a topological element corresponding to a point. It has zero dimension.
816 - SHAPE -- a generic term covering all of the above.
818 A topological model can be considered as a graph of objects with adjacency relationships. When modeling a part in 2D or 3D space it must belong to one of the categories listed in the ShapeEnum enumeration. The TopAbspackage lists all the objects, which can be found in any model. It cannot be extended but a subset can be used. For example, the notion of solid is useless in 2D.
820 The terms of the enumeration appear in order from the most complex to the most simple, because objects can contain simpler objects in their description. For example, a face references its wires, edges, and vertices.
821 @figure{/user_guides/modeling_data/images/modeling_data_image006.png,"ShapeEnum",420}
823 @subsubsection occt_modat_5_2_2 Orientation
825 The notion of orientation is represented by the **TopAbs_Orientation** enumeration. Orientation is a generalized notion of the sense of direction found in various modelers. This is used when a shape limits a geometric domain; and is closely linked to the notion of boundary. The three cases are the following:
826 - Curve limited by a vertex.
827 - Surface limited by an edge.
828 - Space limited by a face.
830 In each case the topological form used as the boundary of a geometric domain of a higher dimension defines two local regions of which one is arbitrarily considered as the **default region**.
832 For a curve limited by a vertex the default region is the set of points with parameters greater than the vertex. That is to say it is the part of the curve after the vertex following the natural direction along the curve.
834 For a surface limited by an edge the default region is on the left of the edge following its natural direction. More precisely it is the region pointed to by the vector product of the normal vector to the surface and the vector tangent to the curve.
836 For a space limited by a face the default region is found on the negative side of the normal to the surface.
838 Based on this default region the orientation allows definition of the region to be kept, which is called the *interior* or *material*. There are four orientations defining the interior.
840 | Orientation | Description |
841 | :--------- | :--------------------------------- |
842 | FORWARD | The interior is the default region. |
843 | REVERSED | The interior is the region complementary to the default. |
844 | INTERNAL | The interior includes both regions. The boundary lies inside the material. For example a surface inside a solid. |
845 | EXTERNAL | The interior includes neither region. The boundary lies outside the material. For example an edge in a wire-frame model. |
847 @figure{/user_guides/modeling_data/images/modeling_data_image007.png,"Four Orientations",420}
849 The notion of orientation is a very general one, and it can be used in any context where regions or boundaries appear. Thus, for example, when describing the intersection of an edge and a contour it is possible to describe not only the vertex of intersection but also how the edge crosses the contour considering it as a boundary. The edge would therefore be divided into two regions: exterior and interior and the intersection vertex would be the boundary. Thus an orientation can be associated with an intersection vertex as in the following figure:
851 | Orientation | Association |
852 | :-------- | :-------- |
853 | FORWARD | Entering |
854 | REVERSED | Exiting |
855 | INTERNAL | Touching from inside |
856 | EXTERNAL | Touching from outside |
858 @figure{/user_guides/modeling_data/images/modeling_data_image008.png,"Four orientations of intersection vertices",420}
861 Along with the Orientation enumeration the *TopAbs* package defines four methods:
863 @subsubsection occt_modat_5_2_3 State
865 The **TopAbs_State** enumeration described the position of a vertex or a set of vertices with respect to a region. There are four terms:
867 |Position | Description |
868 | :------ | :------- |
869 |IN | The point is interior. |
870 |OUT | The point is exterior. |
871 |ON | The point is on the boundary(within tolerance). |
872 |UNKNOWN | The state of the point is indeterminate. |
874 The UNKNOWN term has been introduced because this enumeration is often used to express the result of a calculation, which can fail. This term can be used when it is impossible to know if a point is inside or outside, which is the case with an open wire or face.
876 @figure{/user_guides/modeling_data/images/modeling_data_image009.png,"The four states",420}
878 The State enumeration can also be used to specify various parts of an object. The following figure shows the parts of an edge intersecting a face.
880 @figure{/user_guides/modeling_data/images/modeling_data_image010.png,"State specifies the parts of an edge intersecting a face",420}
882 @subsection occt_modat_5_3 Manipulating shapes and sub-shapes
884 The *TopoDS* package describes the topological data structure with the following characteristics:
885 - reference to an abstract shape with neither orientation nor location.
886 - Access to the data structure through the tool classes.
888 As stated above, OCCT Topology describes data structures of objects in parametric space. These descriptions use localization in and restriction of parts of this space. The types of shapes, which can be described in these terms, are the vertex, the face and the shape. The vertex is defined in terms of localization in parametric space, and the face and shape, in terms of restriction of this space.
890 OCCT topological descriptions also allow the simple shapes defined in these terms to be combined into sets. For example, a set of edges forms a wire; a set of faces forms a shell, and a set of solids forms a composite solid (CompSolid in Open CASCADE Technology). You can also combine shapes of either sort into compounds. Finally, you can give a shape an orientation and a location.
892 Listing shapes in order of complexity from vertex to composite solid leads us to the notion of the data structure as knowledge of how to break a shape down into a set of simpler shapes. This is in fact, the purpose of the *TopoDS* package.
894 The model of a shape is a shareable data structure because it can be used by other shapes. (An edge can be used by more than one face of a solid). A shareable data structure is handled by reference. When a simple reference is insufficient, two pieces of information are added: an orientation and a local coordinate reference.
895 - An orientation tells how the referenced shape is used in a boundary (*Orientation* from *TopAbs*).
896 - A local reference coordinate (*Location* from *TopLoc*) allows referencing a shape at a position different from that of its definition.
898 The **TopoDS_TShape** class is the root of all shape descriptions. It contains a list of shapes. Classes inheriting **TopoDS_TShape** can carry the description of a geometric domain if necessary (for example, a geometric point associated with a TVertex). A **TopoDS_TShape** is a description of a shape in its definition frame of reference. This class is manipulated by reference.
900 The **TopoDS_Shape** class describes a reference to a shape. It contains a reference to an underlying abstract shape, an orientation,and a local reference coordinate. This class is manipulated by value and thus cannot be shared.
902 The class representing the underlying abstract shape is never referenced directly. The *TopoDS_Shape* class is always used to refer to it.
904 The information specific to each shape (the geometric support) is always added by inheritance to classes deriving from **TopoDS_TShape**. The following figures show the example of a shell formed from two faces connected by an edge.
906 @figure{/user_guides/modeling_data/images/modeling_data_image011.png,"Structure of a shell formed from two faces",420}
908 @figure{/user_guides/modeling_data/images/modeling_data_image012.png,"Data structure of the above shell",420}
910 In the previous diagram, the shell is described by the underlying shape TS, and the faces by TF1 and TF2. There are seven edges from TE1 to TE7 and six vertices from TV1 to TV6.
912 The wire TW1 references the edges from TE1 to TE4; TW2 references from TE4 to TE7.
914 The vertices are referenced by the edges as follows:TE1(TV1,TV4), TE2(TV1,TV2), TE3(TV2,TV3), TE4(TV3,TV4), TE5(TV4,TV5), TE6(T5,TV6),TE7(TV3,TV6).
916 **Note** that this data structure does not contain any *back references*. All references go from more complex underlying shapes to less complex ones. The techniques used to access the information are described later. The data structure is as compact as possible. Sub-objects can be shared among different objects.
918 Two very similar objects, perhaps two versions of the same object, might share identical sub-objects. The usage of local coordinates in the data structure allows the description of a repetitive sub-structure to be shared.
920 The compact data structure avoids the loss of information associated with copy operations which are usually used in creating a new version of an object or when applying a coordinate change.
922 The following figure shows a data structure containing two versions of a solid. The second version presents a series of identical holes bored at different positions. The data structure is compact and yet keeps all information on the sub-elements.
924 The three references from *TSh2* to the underlying face *TFcyl* have associated local coordinate systems, which correspond to the successive positions of the hole.
925 @figure{/user_guides/modeling_data/images/modeling_data_image013.png,"Data structure containing two versions of a solid",420}
927 Classes inheriting TopoDS_Shape
928 ------------------------------
929 *TopoDS* is based on class *TopoDS_Shape* and the class defining its underlying shape. This has certain advantages, but the major drawback is that these classes are too general. Different shapes they could represent do not type them (Vertex, Edge, etc.) hence it is impossible to introduce checks to avoid incoherences such as inserting a face in an edge.
931 *TopoDS* package offers two sets of classes, one set inheriting the underlying shape with neither orientation nor location and the other inheriting *TopoDS_Shape*, which represent the standard topological shapes enumerated in *TopAbs* package.
933 The following classes inherit Shape : *TopoDS_Vertex, TopoDS_Edge, TopoDS_Wire, TopoDS_Face, TopoDS_Shell, TopoDS_Solid,TopoDS_CompSolid,* and *TopoDS_Compound*. In spite of the similarity of names with those inheriting from **TopoDS_TShape** there is a profound difference in the way they are used.
935 *TopoDS_Shape* class and the classes, which inherit from it, are the natural means to manipulate topological objects. *TopoDS_TShape* classes are hidden. *TopoDS_TShape* describes a class in its original local coordinate system without orientation. *TopoDS_Shape* is a reference to *TopoDS_TShape* with an orientation and a local reference.
937 *TopoDS_TShape* class is deferred; *TopoDS_Shape* class is not. Using *TopoDS_Shape* class allows manipulation of topological objects without knowing their type. It is a generic form. Purely topological algorithms often use the *TopoDS_Shape* class.
939 *TopoDS_TShape* class is manipulated by reference; TopoDS_Shape class by value. A TopoDS_Shape is nothing more than a reference enhanced with an orientation and a local coordinate. The sharing of *TopoDS_Shapes* is meaningless. What is important is the sharing of the underlying *TopoDS_TShapes*. Assignment or passage in argument does not copy the data structure: this only creates new *TopoDS_Shapes* which refer to the same *TopoDS_TShape*.
941 Although classes inheriting *TopoDS_TShape* are used for adding extra information, extra fields should not be added in a class inheriting from TopoDS_Shape. Classes inheriting from TopoDS_Shape serve only to specialize a reference in order to benefit from static type control (carried out by the compiler). For example, a routine that receives a *TopoDS_Face* in argument is more precise for the compiler than the one, which receives a *TopoDS_Shape*. It is pointless to derive other classes than those found inTopoDS. All references to a topological data structure are made with the Shape class and its inheritors defined in *TopoDS*.
943 There are no constructors for the classes inheriting from the *TopoDS_Shape* class, otherwise the type control would disappear through **implicit casting** (a characteristic of C++). The TopoDS package provides package methods for **casting** an object of the TopoDS_Shape class in one of these sub-classes, with type verification.
945 The following example shows a routine receiving an argument of the *TopoDS_Shape* type, then putting it into a variable V if it is a vertex or calling the method ProcessEdge if it is an edge.
948 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
949 #include <TopoDS_Vertex.hxx>
950 #include <TopoDS_Edge.hxx>
951 #include <TopoDS_Shape.hxx>
954 void ProcessEdge(const TopoDS_Edge&);
956 void Process(const TopoDS_Shape& aShape) {
957 if (aShape.Shapetype() == TopAbs_VERTEX) {
959 V = TopoDS::Vertex(aShape); // Also correct
960 TopoDS_Vertex V2 = aShape; // Rejected by the compiler
961 TopoDS_Vertex V3 = TopoDS::Vertex(aShape); // Correct
963 else if (aShape.ShapeType() == TopAbs_EDGE){
964 ProcessEdge(aShape) ; // This is rejected
965 ProcessEdge(TopoDS::Edge(aShape)) ; // Correct
968 cout <<"Neither a vertex nor an edge ?";
969 ProcessEdge(TopoDS::Edge(aShape)) ;
970 // OK for compiler but an exception will be raised at run-time
973 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
977 @subsection occt_modat_5_4 Exploration of Topological Data Structures
979 The *TopExp* package provides tools for exploring the data structure described with the *TopoDS* package. Exploring a topological structure means finding all sub-objects of a given type, for example, finding all the faces of a solid.
981 The TopExp package provides the class *TopExp_Explorer* to find all sub-objects of a given type. An explorer is built with:
982 - The shape to be explored.
983 - The type of shapes to be found e.g. VERTEX, EDGE with the exception of SHAPE, which is not allowed.
984 - The type of Shapes to avoid. e.g. SHELL, EDGE. By default, this type is SHAPE. This default value means that there is no restriction on the exploration.
988 The Explorer visits the whole structure in order to find the shapes of the requested type not contained in the type to avoid. The example below shows how to find all faces in the shape *S*:
991 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
995 for (Ex.Init(S,TopAbs_FACE); Ex.More(); Ex.Next()) {
996 ProcessFace(Ex.Current());
999 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1001 Find all the vertices which are not in an edge
1003 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1004 for (Ex.Init(S,TopAbs_VERTEX,TopAbs_EDGE); ...)
1005 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1008 Find all the faces in a SHELL, then all the faces not in a SHELL:
1011 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1013 TopExp_Explorer Ex1, Ex2;
1015 for (Ex1.Init(S,TopAbs_SHELL);Ex1.More(); Ex1.Next()){
1017 for (Ex2.Init(Ex1.Current(),TopAbs_FACE);Ex2.More();
1019 //visit all the faces of the current shell
1020 ProcessFaceinAshell(Ex2.Current());
1024 for(Ex1.Init(S,TopAbs_FACE,TopAbs_SHELL);Ex1.More(); Ex1.Next()){
1025 // visit all faces not ina shell.
1026 ProcessFace(Ex1.Current());
1029 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1031 The Explorer presumes that objects contain only objects of an equal or inferior type. For example, if searching for faces it does not look at wires, edges, or vertices to see if they contain faces.
1033 The *MapShapes* method from *TopExp* package allows filling a Map. An exploration using the Explorer class can visit an object more than once if it is referenced more than once. For example, an edge of a solid is generally referenced by two faces. To process objects only once, they have to be placed in a Map.
1036 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1037 void TopExp::MapShapes (const TopoDS_Shape& S,
1038 const TopAbs_ShapeEnum T,
1039 TopTools_IndexedMapOfShape& M)
1041 TopExp_Explorer Ex(S,T);
1043 M.Add(Ex.Current());
1047 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1049 In the following example all faces and all edges of an object are drawn in accordance with the following rules:
1050 - The faces are represented by a network of *NbIso* iso-parametric lines with *FaceIsoColor* color.
1051 - The edges are drawn in a color, which indicates the number of faces sharing the edge:
1052 - *FreeEdgeColor* for edges, which do not belong to a face (i.e. wireframe element).
1053 - *BorderEdgeColor* for an edge belonging to a single face.
1054 - *SharedEdgeColor* for an edge belonging to more than one face.
1055 - The methods *DrawEdge* and *DrawFaceIso* are also available to display individual edges and faces.
1057 The following steps are performed:
1058 1. Storing the edges in a map and create in parallel an array of integers to count the number of faces sharing the edge. This array is initialized to zero.
1059 2. Exploring the faces. Each face is drawn.
1060 3. Exploring the edges and for each of them increment the counter of faces in the array.
1061 4. From the Map of edges, drawing each edge with the color corresponding to the number of faces.
1063 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1064 void DrawShape ( const TopoDS_Shape& aShape,
1065 const Standard_Integer nbIsos,
1066 const Color FaceIsocolor,
1067 const Color FreeEdgeColor,
1068 const Color BorderEdgeColor,
1069 const Color SharedEdgeColor)
1071 // Store the edges in aMap.
1072 TopTools_IndexedMapOfShape edgemap;
1073 TopExp::MapShapes(aShape,TopAbs_EDGE,edgeMap);
1074 // Create an array set to zero.
1075 TColStd_Array1OfInteger faceCount(1,edgeMap.Extent());
1077 // Explore the faces.
1078 TopExp_Explorer expFace(aShape,TopAbs_FACE);
1079 while (expFace.More()) {
1080 //Draw the current face.
1081 DrawFaceIsos(TopoDS::Face(expFace.Current()),nbIsos,FaceIsoColor);
1082 // Explore the edges ofthe face.
1083 TopExp_Explorer expEdge(expFace.Current(),TopAbs_EDGE);
1084 while (expEdge.More()) {
1085 //Increment the face count for this edge.
1086 faceCount(edgemap.FindIndex(expEdge.Current()))++;
1091 //Draw the edges of theMap
1093 for (i=1;i<=edgemap.Extent();i++) {
1094 switch (faceCount(i)) {
1096 DrawEdge(TopoDS::Edge(edgemap(i)),FreeEdgeColor);
1099 DrawEdge(TopoDS::Edge(edgemap(i)),BorderEdgeColor);
1102 DrawEdge(TopoDS::Edge(edgemap(i)),SharedEdgeColor);
1107 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1109 @subsection occt_modat_5_5 Lists and Maps of Shapes
1111 **TopTools** package contains tools for exploiting the *TopoDS* data structure. It is an instantiation of the tools from *TCollection* package with the Shape classes of *TopoDS*.
1114 * *TopTools_Array1OfShape, HArray1OfShape* -- instantiation of the *TCollection_Array1* and *TCollection_HArray1* with *TopoDS_Shape*.
1115 * *TopTools_SequenceOfShape* -- instantiation of the *TCollection_Sequence* with *TopoDS_Shape*.
1116 * *TopTools_MapOfShape* - instantiation of the *TCollection_Map*. Allows the construction of sets of shapes.
1117 * *TopTools_IndexedMapOfShape* - instantiation of the *TCollection_IndexedMap*. Allows the construction of tables of shapes and other data structures.
1119 With a *TopTools_Map*, a set of references to Shapes can be kept without duplication.
1120 The following example counts the size of a data structure as a number of *TShapes*.
1123 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1124 #include <TopoDS_Iterator.hxx>
1125 Standard_Integer Size(const TopoDS_Shape& aShape)
1127 // This is a recursive method.
1128 // The size of a shape is1 + the sizes of the subshapes.
1130 Standard_Integer size = 1;
1131 for (It.Initialize(aShape);It.More();It.Next()) {
1132 size += Size(It.Value());
1136 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1138 This program is incorrect if there is sharing in the data structure.
1140 Thus for a contour of four edges it should count 1 wire + 4 edges +4 vertices with the result 9, but as the vertices are each shared by two edges this program will return 13. One solution is to put all the Shapes in a Map so as to avoid counting them twice, as in the following example:
1143 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1144 #include <TopoDS_Iterator.hxx>
1145 #include <TopTools_MapOfShape.hxx>
1147 void MapShapes(const TopoDS_Shape& aShape,
1148 TopTools_MapOfShape& aMap)
1150 //This is a recursive auxiliary method. It stores all subShapes of aShape in a Map.
1151 if (aMap.Add(aShape)) {
1152 //Add returns True if aShape was not already in the Map.
1154 for (It.Initialize(aShape);It.More();It.Next()){
1155 MapShapes(It.Value(),aMap);
1160 Standard_Integer Size(const TopoDS_Shape& aShape)
1162 // Store Shapes in a Mapand return the size.
1163 TopTools_MapOfShape M;
1164 MapShapes(aShape,M);
1167 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1169 **Note** For more details about Maps please, refer to the TCollection documentation. (Foundation Classes Reference Manual)
1171 The following example is more ambitious and writes a program which copies a data structure using an *IndexedMap*. The copy is an identical structure but it shares nothing with the original. The principal algorithm is as follows:
1172 - All Shapes in the structure are put into an *IndexedMap*.
1173 - A table of Shapes is created in parallel with the map to receive the copies.
1174 - The structure is copied using the auxiliary recursive function,which copies from the map to the array.
1176 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1177 #include <TopoDS_Shape.hxx>
1178 #include <TopoDS_Iterator.hxx>
1179 #include <TopTools_IndexedMapOfShape.hxx>
1180 #include <TopTools_Array1OfShape.hxx>
1181 #include <TopoDS_Location.hxx>
1183 TopoDS_Shape Copy(const TopoDS_Shape& aShape,
1184 const TopoDS_Builder& aBuilder)
1186 // Copies the wholestructure of aShape using aBuilder.
1187 // Stores all thesub-Shapes in an IndexedMap.
1188 TopTools_IndexedMapOfShape theMap;
1192 TopLoc_Location Identity;
1194 S.Location(Identity);
1195 S.Orientation(TopAbs_FORWARD);
1197 for (i=1; i<= theMap.Extent(); i++) {
1198 for(It.Initialize(theMap(i)); It.More(); It.Next()) {
1200 S.Location(Identity);
1201 S.Orientation(TopAbs_FORWARD);
1206 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1209 In the above example, the index *i* is that of the first object not treated in the Map. When *i* reaches the same size as the Map this means that everything has been treated. The treatment consists in inserting in the Map all the sub-objects, if they are not yet in the Map, they are inserted with an index greater than *i*.
1211 **Note** that the objects are inserted with a local reference set to the identity and a FORWARD orientation. Only the underlying TShape is of great interest.
1214 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1215 //Create an array to store the copies.
1216 TopTools_Array1OfShapetheCopies(1,theMap.Extent());
1218 // Use a recursivefunction to copy the first element.
1219 void AuxiliaryCopy (Standard_Integer,
1220 const TopTools_IndexedMapOfShape &,
1221 TopTools_Array1OfShape &,
1222 const TopoDS_Builder&);
1224 AuxiliaryCopy(1,theMap,theCopies,aBuilder);
1226 // Get the result with thecorrect local reference and orientation.
1228 S.Location(aShape.Location());
1229 S.Orientation(aShape.Orientation());
1231 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1233 Below is the auxiliary function, which copies the element of rank *i* from the map to the table. This method checks if the object has been copied; if not copied, then an empty copy is performed into the table and the copies of all the sub-elements are inserted by finding their rank in the map.
1236 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1237 void AuxiliaryCopy(Standard_Integer index,
1238 const TopTools_IndexedMapOfShapes& sources,
1239 TopTools_Array1OfShape& copies,
1240 const TopoDS_Builder& aBuilder)
1242 //If the copy is a null Shape the copy is not done.
1243 if (copies(index).IsNull()) {
1244 copies(index) =sources(index).EmptyCopied();
1245 //Insert copies of the sub-shapes.
1248 TopLoc_Location Identity;
1249 for(It.Initialize(sources(index)),It.More(), It.Next ()) {
1251 S.Location(Identity);
1252 S.Orientation(TopAbs_FORWARD);
1253 AuxiliaryCopy(sources.FindIndex(S),sources,copies,aBuilder);
1254 S.Location(It.Value().Location());S.Orientation(It.Value().Orientation()); aBuilder.Add(copies(index),S);
1258 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1260 @subsubsection occt_modat_5_5_1 Wire Explorer
1262 *BRepTools_WireExplorer* class can access edges of a wire in their order of connection.
1264 For example, in the wire in the image we want to recuperate the edges in the order {e1, e2, e3,e4, e5} :
1266 @figure{/user_guides/modeling_data/images/modeling_data_image014.png,"A wire composed of 6 edges.",320}
1268 *TopExp_Explorer*, however, recuperates the lines in any order.
1270 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1271 TopoDS_Wire W = ...;
1272 BRepTools_WireExplorer Ex;
1273 for(Ex.Init(W); Ex.More(); Ex.Next()) {
1274 ProcessTheCurrentEdge(Ex.Current());
1275 ProcessTheVertexConnectingTheCurrentEdgeToThePrevious
1276 One(Ex.CurrentVertex());
1278 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1280 @subsection occt_modat_5_6 Storage of shapes
1282 *BRepTools* and *BinTools* packages contain methods *Read* and *Write* allowing to read and write a Shape to/from a stream or a file.
1283 The methods provided by *BRepTools* package use ASCII storage format; *BinTools* package uses binary format.
1284 Each of these methods has two arguments:
1285 - a *TopoDS_Shape* object to be read/written;
1286 - a stream object or a file name to read from/write to.
1288 The following sample code reads a shape from ASCII file and writes it to a binary one:
1290 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.cpp}
1291 TopoDS_Shape aShape;
1292 if (BRepTools::Read (aShape, "source_file.txt")) {
1293 BinTools::Write (aShape, "result_file.bin");
1295 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~