Introduction to Implicit Surfaces
Jules Bloomenthal, Jim Blinn, Alyn Rockwood
332 pages, parution le 10/08/1997
Résumé
Implicit surfaces offer special effects animators, graphic
designers, CAD engineers, graphics students, and hobbyists
a new range of capabilities for the modeling of complex
geometric objects. In contrast to traditional parametric
surfaces, implicit surfaces can easily describe smooth,
intricate, and articulatable shapes. These powerful yet
easily understood surfaces are finding use in a growing
number of graphics applications.
This comprehensive introduction develops the fundamental concepts and techniques of implicit surface modeling, rendering, and animating in terms accessible to anyone with a basic background in computer graphics.
- provides a thorough overview of implicit surfaces with a focus on their applications in graphics
- explains the best methods for designing, representing, and visualizing implicit surfaces
- surveys the latest research
With contributions from seven graphics authorities, this innovative guide establishes implicit surfaces as a powerful and practical tool for animation and rendering.
Table of contents
Preface
Acknowledgments
1 The Geometry of Implicit Surfaces, by Jules Bloomenthal
2 The Algebraic Properties of Second-Order Surfaces, by Jim Blinn
3 Implicit Surface Patches, by Chandrajit L. Bajaj
4 Surface Tiling, by Jules Bloomenthal
Acknowledgments
1 The Geometry of Implicit Surfaces, by Jules Bloomenthal
1.1 Introduction
1.6 Patches
1.7 Procedural Definitions
1.8 Skeletal Design
1.9 Grids
1.10 Visualization
1.12 Surface Reconstruction
1.13 Interactivity
1.14 Conclusion
1.1.1 Mathematical
Foundations
1.1.2 Continuity and Differentiability
1.1.3 Manifolds and Models
1.1.4 Specification and Representation
1.2 Relation to Parametric Surfaces
1.1.2 Continuity and Differentiability
1.1.3 Manifolds and Models
1.1.4 Specification and Representation
1.2.1 Conversion between
Forms
1.3 Solid Modeling
1.3.1 Specification and
Representation
1.4 Algebraic Surfaces
1.4.1 Interpolation
1.4.2 Blends
1.4.3 Unions and Intersections
1.5 Deformations1.4.2 Blends
1.4.3 Unions and Intersections
1.6 Patches
1.7 Procedural Definitions
1.8 Skeletal Design
1.9 Grids
1.10 Visualization
1.10.1 Discrete Volumetric
Sets
1.10.2 Mathematical Functions
1.11 Details, Details1.10.2 Mathematical Functions
1.12 Surface Reconstruction
1.13 Interactivity
1.14 Conclusion
2 The Algebraic Properties of Second-Order Surfaces, by Jim Blinn
2.1 Introduction
2.1.1 Surface Definition
Techniques
2.1.2 First-Order Surfaces
2.1.3 Second-Order Surfaces
2.1.4 Homogeneous Representation
2.1.5 General Homogeneous Surfaces
2.2 Geometrical Operations Necessary for Drawing
2.1.2 First-Order Surfaces
2.1.3 Second-Order Surfaces
2.1.4 Homogeneous Representation
2.1.5 General Homogeneous Surfaces
2.2.1 Representation
2.2.2 Modeling
2.2.3 Transformation
2.2.4 Boundary Checking
2.2.5 Intersections
2.2.6 Surface Normals
2.3 Planar Curves
2.2.2 Modeling
2.2.3 Transformation
2.2.4 Boundary Checking
2.2.5 Intersections
2.2.6 Surface Normals
2.3.1 First-Order Algebraic
Curves
2.3.2 Second-Order Algebraic Curves
2.4 Surfaces
2.3.2 Second-Order Algebraic Curves
2.4.1 First-Order Algebraic
Surfaces
2.4.2 Second-Order Algebraic Surfaces
2.5 Rendering Algorithms
2.4.2 Second-Order Algebraic Surfaces
2.5.1 Coordinate
Systems
2.5.2 General Algorithm
2.5.3 Gross Clipping
2.5.4 Y and X Range Calculation
2.5.5 Pitfalls in Range Calculation
2.5.6 Z Calculation
2.5.7 Normal Vector Calculation
2.5.8 Texture Mapping
2.6 Applications to Higher-Order Curves
2.5.2 General Algorithm
2.5.3 Gross Clipping
2.5.4 Y and X Range Calculation
2.5.5 Pitfalls in Range Calculation
2.5.6 Z Calculation
2.5.7 Normal Vector Calculation
2.5.8 Texture Mapping
2.6.1 Taylor Series
2.6.2 Stationary Points
2.6.3 Level Curves
2.6.4 Inflection Points
2.7 Conclusions2.6.2 Stationary Points
2.6.3 Level Curves
2.6.4 Inflection Points
3 Implicit Surface Patches, by Chandrajit L. Bajaj
3.1 Introduction
3.2 Mathematical Preliminaries
3.2 Mathematical Preliminaries
3.2.1 Algebraic
Surfaces
3.2.2 Polynomial Patch Representations
3.2.3 A-Patch Representation
3.2.4 Continuity
3.3 Curvilinear Mesh Schemes
3.2.2 Polynomial Patch Representations
3.2.3 A-Patch Representation
3.2.4 Continuity
3.3.1 Algorithm Sketch
3.4 Simplex- and Box-Based Schemes
3.4.1 Smooth Interpolation of
a Polyhedron with $C^1$ A-patches
3.4.2 Smooth Approximation with $C^2$ A-patches
3.4.3 Smooth Reconstruction of Surfaces and Functions-on-Surfaces from Scattered Data
3.5 Subdivision-Based Schemes3.4.2 Smooth Approximation with $C^2$ A-patches
3.4.3 Smooth Reconstruction of Surfaces and Functions-on-Surfaces from Scattered Data
4 Surface Tiling, by Jules Bloomenthal
4.1 Introduction
5 Ray Tracing Implicit Surfaces, by Geoff Wyvill
6 Blending, by Alyn Rockwood
7 Convolution of Skeletons, by Jules Bloomenthal
8 Animation and Special Effects, by Brian Wyvill
9 Implicit Surfaces in Physically Based Animation, by Marie-Paule Cani-Gascuel
Index
4.1.1 Classes of Tilers
4.2 Spatial Partitioning
4.2.1 Subdivision
4.2.2 Exhaustive Enumeration
4.2.3 Continuation
4.2.4 Robustness
4.3 Cell Polygonization
4.2.2 Exhaustive Enumeration
4.2.3 Continuation
4.2.4 Robustness
4.3.1 Surface Vertex
Computation
4.3.2 Table Generation
4.3.3 Polygon Formats
4.3.4 Ambiguities
4.3.5 Tetrahedral Decomposition
4.3.6 Surface Orientation
4.3.7 Optimized Polygons
4.4 Adaptive Methods
4.3.2 Table Generation
4.3.3 Polygon Formats
4.3.4 Ambiguities
4.3.5 Tetrahedral Decomposition
4.3.6 Surface Orientation
4.3.7 Optimized Polygons
4.4.1 Adaptive Criteria
4.4.2 Cracks and Honeycombs
4.4.3 Hybrid Continuation
4.4.4 Iterative Surface Refinement
4.4.5 Interactive Methods
4.5 Ad Hoc Polygonization
4.4.2 Cracks and Honeycombs
4.4.3 Hybrid Continuation
4.4.4 Iterative Surface Refinement
4.4.5 Interactive Methods
4.5.1 Nonmanifold
Polygonization
4.5.2 Constructive Solid Geometry Polygonization 4.6 Conclusion
4.5.2 Constructive Solid Geometry Polygonization 4.6 Conclusion
5 Ray Tracing Implicit Surfaces, by Geoff Wyvill
5.1 Introduction
5.1.1 The Basic Process
5.2 Intersection Tests
5.2.1 Intersection with a
Sphere
5.2.2 Intersection with a Triangle
5.2.3 Intersection with a Blended Implicit Surface
5.2.4 Intersections with Transformed Objects
5.2.5 Intersection with CSG Trees
5.3 Efficiency
5.2.2 Intersection with a Triangle
5.2.3 Intersection with a Blended Implicit Surface
5.2.4 Intersections with Transformed Objects
5.2.5 Intersection with CSG Trees
5.3.1 Bounding Boxes
5.3.2 Ray Sorting
5.3.3 Space Subdivision
5.3.4 Octrees
5.3.5 Creating the Space Division
5.3.6 Space Division of Blended Implicit Surfaces
5.3.7 Signatures and Mailboxes
5.4 General Implicit Surfaces
5.3.2 Ray Sorting
5.3.3 Space Subdivision
5.3.4 Octrees
5.3.5 Creating the Space Division
5.3.6 Space Division of Blended Implicit Surfaces
5.3.7 Signatures and Mailboxes
5.4.1 Lipschitz
Constants
5.4.2 L-G Surfaces
5.4.3 Sphere Tracing
5.5 Conclusion5.4.2 L-G Surfaces
5.4.3 Sphere Tracing
6 Blending, by Alyn Rockwood
6.1 Introduction
6.2 Background
6.4 Blending on Blends
6.5 The Development of a General Blending Facility
6.6 The Displacement Blending Form
6.2 Background
6.2.1 Potential Methods
6.2.2 Design Taxonomy
6.3 Algebraic Surfaces6.2.2 Design Taxonomy
6.4 Blending on Blends
6.5 The Development of a General Blending Facility
6.6 The Displacement Blending Form
6.6.1 Interrogability
6.7 Conclusion7 Convolution of Skeletons, by Jules Bloomenthal
7.1 Introduction
7.2 Algebraic Blends
7.3 Convolution Surfaces
7.4 Branching Objects
7.6 Three-Dimensional Skeletal Elements
7.7 Conclusion and Future Work
7.2 Algebraic Blends
7.3 Convolution Surfaces
7.4 Branching Objects
7.4.1 Interpolation of
Surfaces
7.5 Two-Dimensional Skeletal Elements7.6 Three-Dimensional Skeletal Elements
7.7 Conclusion and Future Work
8 Animation and Special Effects, by Brian Wyvill
8.1 Introduction
8.2 Geometric Motion of Skeletal Elements
8.2 Geometric Motion of Skeletal Elements
8.2.1 Path Following
8.3 Changing Skeletal Element Characteristics
8.3.1 Geometry
8.3.2 Weight
8.3.3 Field Function
8.4 Metamorphosis
8.3.2 Weight
8.3.3 Field Function
8.4.1 Heuristics for Skeleton
Matching in Metamorphosis
8.4.2 Hand Matching
8.4.3 Hierarchical Matching
8.4.4 Cellular Inbetweening
8.4.5 Surface Inbetweening
8.4.6 Example: Metamorhposis Between a Rabbit and a Man
8.4.7 Other Methods
8.5 Warping
8.4.2 Hand Matching
8.4.3 Hierarchical Matching
8.4.4 Cellular Inbetweening
8.4.5 Surface Inbetweening
8.4.6 Example: Metamorhposis Between a Rabbit and a Man
8.4.7 Other Methods
8.5.1 Squash and
Stretch
8.5.2 Warping Space and Time
8.5.3 Using Barr's Deformations
8.5.4 Affine Transformations Implemented as Warps
8.6 Unrendered Surfaces
8.5.2 Warping Space and Time
8.5.3 Using Barr's Deformations
8.5.4 Affine Transformations Implemented as Warps
8.6.1 Making Objects
Glow
8.6.2 Synthetic Topiary
8.7 Conclusion8.6.2 Synthetic Topiary
9 Implicit Surfaces in Physically Based Animation, by Marie-Paule Cani-Gascuel
9.1 Introduction
References9.1.1 Deformable Models
9.1.2 Collision Detection and Response
9.2 The Use of Implicit Surfaces within a Layered Model
9.1.2 Collision Detection and Response
9.2.1 Skeletal and Implicit
Components
9.2.2 Benefits for Animation and Collision Processing
9.3 Deformation of Surfaces under Collisions
9.2.2 Benefits for Animation and Collision Processing
9.3.1 Modeling Contacts
between Objects
9.3.2 Response to Collisions
9.3.3 Implementation: The Use of Sampling
9.4 Volume Preservation
9.3.2 Response to Collisions
9.3.3 Implementation: The Use of Sampling
9.4.1 The Need for Local
Control
9.4.2 Local Volume Approximation
9.4.3 Control of Local Volume
9.5 An Example: Simulating Soft Substances
9.4.2 Local Volume Approximation
9.4.3 Control of Local Volume
9.5.1 Structure Used
9.5.2 Modeling Separations
9.5.3 Modeling Fusion under Compression
9.6 Conclusion9.5.2 Modeling Separations
9.5.3 Modeling Fusion under Compression
Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Morgan Kaufmann |
| Auteur(s) | Jules Bloomenthal, Jim Blinn, Alyn Rockwood |
| Parution | 10/08/1997 |
| Nb. de pages | 332 |
| Format | 19 x 24 |
| Couverture | Relié |
| Poids | 800g |
| EAN13 | 9781558602335 |
Avantages Eyrolles.com
Livraison à partir de 0,01 € en France métropolitaine
Paiement en ligne SÉCURISÉ
Livraison dans le monde
Retour sous 15 jours
+ d'un million et demi de livres disponibles
Consultez aussi
- Les meilleures ventes en Graphisme & Photo
- Les meilleures ventes en Informatique
- Les meilleures ventes en Construction
- Les meilleures ventes en Entreprise & Droit
- Les meilleures ventes en Sciences
- Les meilleures ventes en Littérature
- Les meilleures ventes en Arts & Loisirs
- Les meilleures ventes en Vie pratique
- Les meilleures ventes en Voyage et Tourisme
- Les meilleures ventes en BD et Jeunesse
