GAME ENGINE DESIGN. A Practical Approach to Real-Time Computer Graphics. ahhb. DAVID H. EBERLY Geometrie Tools, Inc.

Transcription

1 3D GAME ENGINE DESIGN A Practical Approach to Real-Time Computer Graphics SECOND EDITION DAVID H. EBERLY Geometrie Tools, Inc. ahhb _ jfw H NEW YORK-OXFORD-PARIS-SAN DIEGO fl^^h ' 4M arfcrgsbjlilhg, SAN FRANCISCO SINGAPORE SYDNEY TOKYO B^^H ^ ^ ELSEVIER Morgan Kaufmann is an imprint of Elsevier MORGAN KAUFMANN PUBLISHERS

2 CONTENTS TRADEMARKS ABOUT THE AUTHOR PREFACE v vi xxi i INTRODUCTION 1.1 THE EVOLUTION OF GRAPHICS HARDWARE AND GAMES 1.2 THE EVOLUTION OF THIS BOOK AND ITS SOFTWARE 1.3 A SUMMARY OF THE S 2 THE GRAPHICS SYSTEM 2.1 THE FOUNDATION Coordinate Systems Handedness and Cross Products Points and Vectors 2.2 TRANSFORMATIONS Linear Transformations Affine Transformations Projective Transformations Properties of Perspective Projection Homogeneous Points and Matrices 2.3 CAMERAS The Perspective Camera Model Model or Object Space World Space View, Camera, or Eye Space Clip, Projection, or Homogeneous Space Window Space Putting Them All Together 2.4 CULLING AND CLIPPING Object Culling vu

3 VÜi Contents Back-Face Culling Clipping to the View Frustum RASTERIZING Line Segments Circles Ellipses Triangles VERTEX ATTRIBUTES Colors Lighting and Materials Textures Transparency, Opacity, and Blending Fog And Many More Rasterizing Attributes ISSUES OF SOFTWARE, HARDWARE, AND APIS A General Discussion Portability versus Performance API CONVENTIONS Matrix Representation and Storage Matrix Composition ViewMatrices Projection Matrices Window Handedness Rotations Fast Computations Using the Graphics API RENDERERS SOFTWARE RENDERING Vertex Shaders Back-Face Culling Clipping Rasterizing Edge Buffers Scan Line Processi Pixel Shaders Stencil Buffering Depth Buffering Alpha Blending 170

4 Contents ix Color Masking Texture Sampling Frame Buffers HARDWARE RENDERING AN ABSTRACT RENDERING API Construction and Destruction Camera Management Global-State Management Buffer Clearing Object Drawing Text and 2D Drawing Miscellaneous Resource Management THE HEART OF THE RENDERER Drawing a Scene Drawing a Geometrie Primitive Applying an Effect Loading and Parsing Shader Programs Validation of Shader Programs 213 SCENE GRAPHS SCENE GRAPH DESIGN ISSUES The Core Classes Spatial Hierarchy Design Sharing ofobjects GEOMETRIC STATE Vertex Buffers and Index Buffers Transformations Bounding Volumes Geometric Types RENDER STATE Global State Lights Effects THE UPDATE PASS Geometric-State Updates Render-State Updates 280

5 X Contents 4.5 THE CULLING PASS Hierarchical Culling Sorted Culling 4.6 THE DRAWING PASS Single-Pass Drawing Single-Effect, Multipass Drawing Multiple-Effect Drawing 4.7 SCENE GRAPH COMPILERS A Scene Graph as an Expression Semantics of Compilation CONTROLLER-BASED ANIMATION 5.1 KEYFRAME ANIMATION Interpolation of Position Interpolation of Orientation Interpolation of Scale 5.2 KEYFRAME COMPRESSION Fitting Points with a B-Spline Curve Evaluation ofab-spline Curve Optimized Evaluation for Degree INVERSE KlNEMATICS Numerical Solution by Jacobian Methods Numerical Solution by Nonlinear Optimization Numerical Solution by Cyclic Coordinate Descent 5.4 SKINNING 5.5 VERTEX MORPHING 5.6 PARTICLE SYSTEMS SPATIAL SORTING BINARY SPACE PARTITIONING TREES BSP Tree Construction BSP Tree Usage NODE-BASED SORTING PORTALS

6 Contents xi 6.4 USER-DEFINED MAPS OCCLUSION CULLING 375 LEVEL OF DETAIL SPRITES AND BILLBOARDS DISCRETE LEVEL OF DETAIL CONTINUOUS LEVEL OF DETAIL Simplification Using Quadric Error Metrics Reordering ofvertices and Indices Terrain INFINITE LEVEL OF DETAIL 387 COLLISION DETECTION THE METHOD OF SEPARATING AXES Extrema of Convex Polygons or Convex Polyhedra Stationary Objects Objects Moving with Constant Linear Velocity Oriented Bounding Boxes FINDING COLLISIONS BETWEEN MOVING OBJECTS Pseudodistance Contact between Moving Intervals Computing the First Time of Contact Estimating the First Derivative A DYNAMIC COLLISION DETECTION SYSTEM The Abstract Base Class Pseudodistances for Specific Pairs of Object Types Collision Culling with Axis-Aligned Bounding Boxes OBJECT PICKING Constructing a Pick Ray Scene Graph Support Staying on Top of Things Staying Out of Things PATHFINDING TO AVOID COLLISIONS Environments, Levels, and Rooms 482

7 xii Contents Moving between Rooms Moving between Levels Moving through the Outdoor Environment Blueprints Visibility Graphs Envelope Construction Basic Data Structures Efficient Calculation ofthe Visibility Graph 504 PHYSICS PARTICLE SYSTEMS MASS-SPRING SYSTEMS Curve Masses Surface Masses Volume Masses Arbitrary Configurations DEFORMABLE BODIES RIGID BODIES The Rigid Body Class Computing the Inertia Tensor 527 i STANDARD OBJECTS LINEAR COMPONENTS PLANAR COMPONENTS BOXES QUADRICS Spheres Ellipsoids Cylinders Cones SPHERE-SWEPT VOLUMES Capsules Lozenges 539

8 Contents xiii CURVES DEFINITIONS REPARAMETERIZATION BY ARC LENGTH BEZIER CURVES Definitions Evaluation Degree Elevation Degree Reduction NATURAL, CLAMPED, AND CLOSED CUBIC SPLINES Natural Splines Clamped Splines Closed Splines B-SPLINE CURVES Types of Knot Vectors Evaluation LocalControl Closed Curves NURBS CURVES TENSION-CONTINUITY-BIAS SPLINES PARAMETRIC SUBDIVISION Subdivision by Uniform Sampling Subdivision by Arc Length Subdivision by Midpoint Distance Fast Subdivision for Cubic Curves ORIENTATION OF OBJECTS ON CURVED PATHS Orientation Using the Frenet Frame Orientation Using a Fixed Up-Vector 571 SURFACES INTRODUCTION BEZIER RECTANGLE PATCHES Definitions Evaluation 575

9 XIV Contents Degree Elevation Degree Reduction BEZIER TRIANGLE PATCHES Definitions Evaluation Degree Elevation Degree Reduction B-SPLINE RECTANGLE PATCHES NURBS RECTANGLE PATCHES SURFACES BUILT FROM CURVES Cylinder Surfaces Generalized Cylinder Surfaces Revolution Surfaces Tube Surfaces PARAMETRIC SUBDIVISION Subdivision of Rectangle Patches Subdivision of Triangle Patches 602 CONTAINMENT METHODS SPHERES Point in Sphere Sphere Containing Points Merging Spheres BOXES Point in Box Box Containing Points Merging Boxes CAPSULES Point in Capsule Capsule Containing Points Merging Capsules LOZENGES Point in Lozenge Lozenge Containing Points Merging Lozenges CYLINDERS Point in Cylinder 634

10 Contents XV Cylinder Containing Points Least-Squares Line Moved to Minimum-Area Center Merging Cylinders ELLIPSOIDS Point in Ellipsoid Ellipsoid Containing Points Merging Ellipsoids 638 u DISTANCE METHODS POINT TO LINEAR COMPONENT Point to Line Point to Ray Point to Segment LINEAR COMPONENT TO LINEAR COMPONENT Line to Line Line to Ray Line to Segment Ray to Ray Ray to Segment Segment to Segment POINT TO TRIANGLE LINEAR COMPONENT TO TRIANGLE Line to Triangle Ray to Triangle Segment to Triangle POINT TO RECTANGLE LINEAR COMPONENT TO RECTANGLE Line to Rectangle Ray to Rectangle Segment to Rectangle TRIANGLE OR RECTANGLE TO TRIANGLE OR RECTANGLE POINT TO ORIENTED BOX LINEAR COMPONENT TO ORIENTED BOX Line to Oriented Box Ray to Oriented Box Segment to Oriented Box TRIANGLE TO ORIENTED BOX 667

11 xvi Contents RECTANGLE TO ORIENTED BOX ORIENTED BOX TO ORIENTED BOX MlSCELLANEOUS Point to Ellipse Point to Ellipsoid Point to Quadratic Curve or to Quadric Surface PointtoCirclein3D Circle to Circle in 3D 676 INTERSECTION METHODS LINEAR COMPONENTS AND CONVEX OBJECTS LINEAR COMPONENT AND PLANAR COMPONENT LINEAR COMPONENT AND ORIENTED BOX Test-Intersection Query Find-Intersection Query LINEAR COMPONENT AND SPHERE Line and Sphere Ray and Sphere Segment and Sphere LINE AND SPHERE-SWEPT VOLUME Line and Capsule Line and Lozenge LINE AND QUADRIC SURFACE Line and Ellipsoid Line and Cylinder Line and Cone CULLING OBJECTS BY PLANES Oriented Boxes Spheres Capsules Lozenges Ellipsoids Cylinders Cones Convex Polygons or Convex Polyhedra 717

12 Contents XVÜ NUMERICAL METHODS SYSTEMS OF EQUATIONS Linear Systems Polynomial Systems EIGENSYSTEMS Extrema of Quadratic Forms Extrema of Constrained Quadratic Forms LEAST-SQUARES FITTING Linear Fitting of Points (x, /(*)) Linear Fitting of Points Using Orthogonal Regression Planar Fitting of Points (x,y,f{x,y)) Planar Fitting of Points Using Orthogonal Regression Fitting a Circle to 2D Points Fitting a Sphere to 3D Points Fitting a Quadratic Curve to 2D Points Fitting a Quadric Surface to 3D Points MlNIMIZATlON Methods in One Dimension Methods in Many Dimensions ROOT FlNDlNG Methods in One Dimension Methods in Many Dimensions INTEGRATION Romberg Integration Gaussian Quadrature DIFFERENTIAL EQUATIONS Ordinary Differential Equations Partial Differential Equations FAST FUNCTION EVALUATION Square Root and Inverse Square Root Sine, Cosine, and Tangent Inverse Tangent 756

13 XVlll Contents 17 ROTATIONS ROTATION MATRICES Axis/Angle to Matrix Matrix to Axis/Angle Interpolation QUATERNIONS The Linear Algebraic View of Quaternions Rotation ofavector Productof Rotations The Classical View of Quaternions Axis/Angle to Quaternion Quaternion to Axis/Angle Matrix to Quaternion Quaternion to Matrix Interpolation EULER ANGLES PERFORMANCE ISSUES THE CURSE OF NONUNIFORM SCALING Gram-Schmidt Orthonormalization Eigendecomposition Polar Decomposition Singular Value Decomposition 781 lo OBJECT-ORIENTED INFRASTRUCTURE OBJECT-ORIENTED SOFTWARE CONSTRUCTION Software Quality Modularity Reusability Functions and Data Object Orientation STYLE, NAMING CONVENTIONS, AND NAMESPACES RUN-TIME TYPE INFORMATION Single-Inheritance Systems Multiple-Inheritance Systems Macro Support TEMPLATES 800

14 Contents xix 18.5 SHARED OBJECTS AND REFERENCE COUNTING STREAMING The Stream API TheObjectAPI NAMES AND UNIQUE IDENTIFIERS NameString Unique Identification INITIALIZATION AND TERMINATION Potential Problems A Generic Solution for Classes AN APPLICATION LAYER Processing Command-Line Parameters The Application Class The ConsoleApplication Class The WindowApplication Class The WindowApplication3 Class Managing the Engines 867 MEMORY MANAGEMENT MEMORY BUDGETS FOR GAME CONSOLES LEAK DETECTION AND COLLECTING STATISTICS GENERAL MEMORY MANAGEMENT CONCEPTS Allocation Using Sequential-Fit Methods Allocation Using Buddy-System Methods Allocation Using Segregated-Storage Methods Memory Compaction 895 SPECIAL EFFECTS USING SHADERS VERTEX COLORS LlGHTING AND MATERIALS Ambient Lights Directional Lights Point Lights Spotlights TEXTURES 909

15 XX Contents 20.4 MULTITEXTURES BUMP MAPS Generating Normal Maps Generating Tangent-Space Information The Shader Programs GLOSS MAPS SPHERE MAPS CUBE MAPS REFRACTION PLANAR REFLECTION PLANAR SHADOWS PROJECTED TEXTURES SHADOW MAPS VOLUMETRIC FOG SKINNING IRIDESCENCE WATER EFFECTS 955 APPENDIX CREATING A SHADER IN WILD MAGIC 957 A.1 SHADER PROGRAMS FOR AN ILLUSTRATIVE APPLICATION 958 A.2 CREATING THE GEOMETRIC DATA 963 A.3 A CLASSLESS SHADER EFFECT 965 A.4 CREATING A CLASS DERIVED FROM SHADEREFFECT 968 A.5 DYNAMIC UPDATES FOR THE SHADER CONSTANTS 970 REFERENCES 973 INDEX 981 ABOUT THE CD-ROM 1017