Open Geometry: OpenGL® + Advanced Geometry Opengl + Advanced Geometry

This book is about graphics programming based on OPENGL. The program­ ming language is C++. The programs will run under various operating systems, among them WINDOWS 9x, ALPHA-STATIONS (Digital workstations) and SILI­ CON GRAPHICS workstations. Hardware is used if accessible. The book provides a graphics library. This library is based on OPENGL and expands the elemen­ tary routines. Thus, the reader is enabled to realize direct geometrical thinking without having to care much about implementation. The enclosed modules provide the reader with solutions for: • The most common intersection problems and measuring tasks of both pla­ nar and spatial geometry. • The creation ofarbitrary geometric objects, e.g., by means ofdifferent kinds of "sweeping." • The creation of the most general solids by means of Boolean operations (intersection, union, and complements of solid polyhedra). The book presents: • A well documented, versatile, and robust geometry library. The reader can use it very easily and expand it in any way he/she likes. vi Preface • A programming course that provides a deeper insight into object-oriented thinking and programming.It contains an introduction to C++ (for begin­ ners and intermediate programmers) that is influenced by the experience gained from thousands of programming hours (which may even be useful to experienced programmers).

1 Graphics Programming.- 1.1 Think Geometrically!.- 1.2 OPENGL.- 1.3 The Programming Language C++.- 1.4 How to Develop Solid Code.- 1.5 The Implementation of a Vector.- 1.6 Classes That Contain Dynamic Memory.- 2 Getting Started.- 2.1 A Simple 2D Program.- 2.2 A Simple 3D Program.- 2.3 Simple Animations.- 2.4 What to Do with Existing OPENGL Code.- 3 Basic Objects.- 3.1 Some Useful Routines.- 3.2 Vectors and Points.- 3.3 Straight Lines.- 3.4 Planes.- 3.5 Geometrical “Objects”.- 3.6 Circles.- 4 Curved Lines and Polygons.- 4.1 Polylines, Path Curves, Parameterized Curves.- 4.2 Spline Curves.- 4.3 Closed Polygons.- 4.4 Texture Mapping.- 4.5 Complex Polygons, Tesselation.- 4.6 Conics.- 5 Primitive Elements in Space.- 5.1 Boxes.- 5.2 Prisms and Pyramids.- 5.3 Spheres.- 5.4 Groups of 3D Objects.- 5.5 The Virtual Camera.- 6 Complex Surfaces.- 6.1 Parameterized Surfaces.- 6.2 Swept Surfaces.- 6.3 Surfaces of Revolution.- 6.4 Helical Surfaces.- 6.5 Tubular Surfaces.- 6.6 Function Graphs.- 7 Solids.- 7.1 What Is a Solid?.- 7.2 How to Represent Solids.- 7.3 Boundary Representation of Polyhedral Models.- 7.4 Polyhedra in OPEN GEOMETRY.- 7.5 Consistency Conditions for Polyhedra.- 8 Boolean Operations.- 8.1 Types of Boolean Operations.- 8.2 Three Main Steps.- 8.3 Intersection of Faces, Generic Case.- 8.4 The Geometry of Particular Cases.- 8.5 Intersection of Faces, Particular Cases.- 8.6 Steps Two and Three.- 8.7 Practical Applications.- 9 Kinematics—Geometry of Motion.- 9.1 Basic Concepts of Planar Kinematics.- 9.2 Theory of Curvature.- 9.3 The Elliptic Motion.- 9.4 The Trochoid Motion.- 9.5 The Coupler Motion.- 9.6 Special Four-Bar Linkages.- 9.7 Sample Kinematics Programs.- 9.8 Geometry of Gearing.- 10 Interesting Classes of Surfaces.- 10.1 Spiral Surfaces.- 10.2 HelispiralSurfaces.- 10.3 DUPIN-Cyclides.- 10.4 Rotoid Surfaces.- 11 Data Exchange, Printouts.- 11.1 DXF File Output.- 11.2 How to Import 3D Objects from 3D STUDIO.- 11.3 How to Add Textures to Your Objects.- 11.4 Export as BMP File, Animated GIF Files.- 11.5 How to Make Proper Printouts.- 12 More Classes and Examples.- 12.1 Sample 2D Programs.- 12.2 Sample 3D-Programs.- References.