3D COMPUTER GRAPHICS

Transcription

1 ч 3D COMPUTER GRAPHICS S E C O N D E D I T I O N A L A N W A T T Instituto de Matemätica Рига e Aplicada Rio de Janeiro, Brasil and University of Sheffield, England A D D I S О N - W E S L E Y Publishing Company Wokingham, England Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Amsterdam Bonn Sydney Singapore Tokyo Madrid San Juan Milan Paris Mexico City Seoul Taipei

2 Contents Preface vii 1 Three-dimensional Geometry in Computer Graphics Manipulating three-dimensional structures Affine transformations Transformations for changing coordinate systems Structure-deforming transformations Vectors in computer graphics 13 Projects, notes and suggestions 19 2 Representation of Objects Representation and modelling of geometric objects Polygonal representation Bicubic parametric patch nets Constructive solid geometry Space subdivision techniques Rendering strategies 45 Projects, notes and suggestions 53 3 Viewing Systems Introduction Viewing system I Viewing system II Viewing system III View plane projection for viewing systems I III Viewing system IV View plane projection for viewing system IV Clipping for viewing system IV Viewing system V (PHIGS) Implementing viewing system V 83 Projects, notes and suggestions 85 xiii

3 4 Reflection and Illumination Models Introduction Theoretical considerations in light reflection The Phong reflection model Geometric considerations Colour Summary of Phong model The 20 spheres - an example Using look-up tables with reflection models Empirical transparency The Cook and Torrance model Illumination source models 122 Projects, notes and suggestions Rendering Algorithms Introduction Culling and clipping Incremental shading techniques Rasterization Hidden surface removal 149 Projects, notes and suggestions Parametric Representation and Practice Parametric representation of three-dimensional solids Parametric representation of three-dimensional curves B-spline curves Biparametric cubic surfaces Rendering parametric surfaces Approximation to a surface patch using a polygon mesh Extending the control: NURBS and ß-splines Interpolation using B-splines Modelling objects with bicubic parametric nets 210 Projects, notes and suggestions Shadows and Textures Introduction Shadows: their function Simple shadows on a ground plane Shadow algorithms Texture Two-dimensional texture mapping Three-dimensional texture domain techniques Bump mapping Anti-aliasing and texture mapping Environment mapping 259 Projects, notes and suggestions 262

4 Contents xv 8 Ray Tracing Introduction Basic algorithm A historical digression - the optics of the rainbow Recursive implementation of ray tracing Ray tracing geometry Reflection-illumination model Shadows Distributed ray tracing Ray tracing and anti-aliasing operations Making ray tracing efficient 298 Projects, notes and suggestions Volume Rendering Introduction Volume rendering algorithms Case study Parallel versus perspective projection Lighting model 325 Projects, notes and suggestions Radiosity Introduction Radiosity theory Form factor determination Increasing the accuracy of the solution Reordering the solution for progressive refinement Further development of the radiosity method: 347 hybrid radiosity and ray tracing Projects, notes and suggestions Anti-aliasing Introduction Aliasing artefacts and Fourier theory Supersampling or postfiltering Prefiltering or area sampling techniques A mathematical comparison Stochastic sampling 365 Projects, notes and suggestions Functionally Based Modelling Methods Introduction Particle systems Fractal systems Functions suitable for three-dimensional texture 377 Projects, notes and suggestions 380

5 Appendix A Appendix В Appendix С Appendix D References Index Three-dimensional Computer Animation Introduction Keyframing systems Explicit motion specification - curve editing Other approaches to three-dimensional computer animation Temporal anti-aliasing Projects, notes and suggestions Colour Spaces and Monitor Considerations Introduction Specifying a colour with three labels Colour spaces in computer graphics Monitor considerations Projects, notes and suggestion Viewing Transformation for a Simple Four-parameter Viewing System A Wireframe System An Implementation of a Renderer The Utah Teapot Trademark notice Luxo is a trademark of Jac Jacobson Industries Kodak is a trademark of Eastman Kodak Company VAX is a trademark of Digital Equipment Corporation