Object Libraries Modeling Data User's Guide Version 6.6.0 / April 2013 1 Copyright © 2013, by OPEN CASCADE S.A.S. PROPRIETARY RIGHTS NOTICE: All rights reserved. Verbatim copying and distribution of this entire document are permitted worldwide, without royalty, in any medium, provided the copyright notice and this permission notice are preserved. The information in this document is subject to change without notice and should not be construed as a commitment by OPEN CASCADE S.A.S. OPEN CASCADE S.A.S. assures no responsibility for any errors that may appear in this document. The software described in this document is furnished under a license and may be used or copied only in accordance with the terms of such a license. CAS.CADE, Open CASCADE and Open CASCADE Technology are registered trademarks of OPEN CASCADE S.A.S. Other brand or product names are trademarks or registered trademarks of their respective holders. NOTICE FOR USERS: This User Guide is a general instruction for Open CASCADE Technology study. It may be incomplete and even contain occasional mistakes, particularly in examples, samples, etc. OPEN CASCADE S.A.S. bears no responsibility for such mistakes. If you find any mistakes or imperfections in this document, or if you have suggestions for improving this document, please, contact us and contribute your share to the development of Open CASCADE Technology: [email protected] http://www.opencascade.com/contact/ 2 TABLE OF CONTENTS 1. INTRODUCTION .................................................................................................................................... 4 2. GEOMETRY UTILITIES ....................................................................................................................... 5 2. 1 OVERVIEW ............................................................................................................................................ 5 2. 2 INTERPOLATIONS AND APPROXIMATIONS ............................................................................................. 5 2. 2. 1 The services provided .................................................................................................................. 5 2. 3 DIRECT CONSTRUCTION ....................................................................................................................... 9 2. 3. 1 The services provided .................................................................................................................. 9 2. 3. 2 The packages ..............................................................................................................................11 2. 4 CONVERSION TO AND FROM BSPLINES ................................................................................................14 2. 4. 1 Services provided ........................................................................................................................14 2. 5 POINTS ON CURVES .............................................................................................................................14 2. 5. 1 The services provided .................................................................................................................14 2. 5. 2 Example ......................................................................................................................................14 2. 6 EXTREMA ............................................................................................................................................15 2. 6. 1 The services provided .................................................................................................................15 2. 6. 2 Extrema between Curves ............................................................................................................16 2. 6. 3 Extrema between Curve and Surface ..........................................................................................16 2. 6. 4 Extrema between Surfaces .........................................................................................................16 3. 2D GEOMETRY .....................................................................................................................................17 3. 1 OVERVIEW ...........................................................................................................................................17 3. 2 GEOM2D ..............................................................................................................................................17 3. 3 COLLECTIONS OF 2D GEOMETRIC OBJECTS .........................................................................................17 3. 3. 1 TColGeom2d ...............................................................................................................................17 4. 3D GEOMETRY .....................................................................................................................................18 4. 1 OVERVIEW ...........................................................................................................................................18 4. 2 GEOM ..................................................................................................................................................18 4. 3 LOCAL PROPERTIES OF CURVES AND SURFACES ..................................................................................19 4. 4 THE SERVICES PROVIDED .....................................................................................................................19 4. 5 TCOLGEOM .........................................................................................................................................20 5. TOPOLOGY ............................................................................................................................................21 5.1 KEEPING TRACK OF SHAPE LOCATION ..................................................................................................21 5. 1. 1 Implementation of TopLoc ..........................................................................................................22 5. 1. 2 The TopLoc_Datum class ...........................................................................................................22 5. 1. 3 The TopLoc_Location class ........................................................................................................22 5. 2 NAMING SHAPES, SUBSHAPES, THEIR ORIENTATIONS AND STATES .......................................................23 5. 2. 1 Topological types ........................................................................................................................24 5. 2. 2 Orientation .................................................................................................................................25 5. 2. 3 State ............................................................................................................................................27 5. 3 MANIPULATING SHAPES AND SUBSHAPES ............................................................................................30 3 5. 3. 1 The TopoDS_Shape class ...........................................................................................................30 5. 3. 2 Classes inheriting TopoDS_Shape .............................................................................................33 5. 4 EXPLORATION OF TOPOLOGICAL DATA STRUCTURES .........................................................................36 5. 4. 1 The TopExp_Explorer Class .......................................................................................................36 5. 4. 2 Example of using TopExp ...........................................................................................................37 5. 5 LISTS AND MAPS OF SHAPES ................................................................................................................39 5. 5. 1 Use of TopTools_Map ................................................................................................................40 5. 5. 2 Wire Explorer .............................................................................................................................43 1. Introduction 4 1. Introduction This manual explains how to use Modeling Data. It provides basic documentation on modeling data. For advanced information on modeling data, see our offerings on our web site at www.opencascade.org/support/training/ Modeling Data supplies data structures to represent 2D and 3D geometric models. These services are grouped in the following libraries and dealt with in the chapters listed under each: • Geometry Utilities • Interpolations and Approximations • Direct Construction • Conversion to BSplines • Points on Curves • Extrema • 2D Geometry • 2D Geometry Types • Collections of 2D Geometric Objects • 2D Adaptors • Topological Types and Orientation • 3D Geometry • 3D Geometry Types • Collections of 3D Geometric Objects • 3D Adaptors • Local Properties of Curves and Surfaces • Topology 2. Geometry Utilities 5 2. Geometry Utilities 2. 1 Overview Open CASCADE Technology Technology (OCCT) geometry utilities provide the following services: • Creation of shapes by interpolation and approximation • Direct construction of shapes • Conversion of curves and surfaces to bspline curves and surfaces • Computation of the coordinates of points on 2D and 3D curves • Calculation of extrema between shapes. 2. 2 Interpolations and Approximations In modeling, you often need