Geometry for Computer Graphics Formulae Examples and Proofs 1st Edition by John Vince ISBN 1852338342 9781852338343 by John Vince 9781846281167, 9781852338343, 1846281164, 1852338342 instant download after payment.

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ISBN 10: 1852338342 
ISBN 13: 9781852338343
Author: John Vince

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.

Geometry for Computer Graphics draws together a wide variety of geometric information that will provide a sourcebook of facts, examples, and proofs for students, academics, researchers, and professional practitioners.

The book is divided into 4 sections: the first summarizes hundreds of formulae used to solve 2D and 3D geometric problems. The second section places these formulae in context in the form of worked examples. The third provides the origin and proofs of these formulae, and communicates mathematical strategies for solving geometric problems. The last section is a glossary of terms used in geometry.

Geometry for Computer Graphics Formulae Examples and Proofs 1st Table of contents:

Part I: Fundamental Concepts and Vector Algebra

• Chapter 1: Points, Vectors, and Coordinate Systems
  • Defining Points and Vectors in 2D and 3D
  • Coordinate Systems: Cartesian, Polar, Cylindrical, Spherical (Formulae & Conversions)
  • Vector Operations: Addition, Subtraction, Scalar Multiplication (Examples & Proofs)
  • Magnitude, Normalization, and Direction Cosines
• Chapter 2: Vector Products
  • The Dot Product: Definition, Properties, and Geometric Interpretation (Angle, Projection)
  • The Cross Product: Definition, Properties, and Geometric Interpretation (Area, Normal Vector)
  • Triple Products (Scalar and Vector)
  • Applications in Lighting and Surface Normals (Examples)
• Chapter 3: Lines and Planes
  • Representations of Lines: Parametric, Implicit, Explicit (Formulae & Examples)
  • Representations of Planes: Normal Form, General Form, Three Points (Formulae & Examples)
  • Distances: Point to Line, Point to Plane, Line to Line (Formulae & Proofs)
  • Intersections: Line-Line, Line-Plane, Plane-Plane (Examples)

Part II: Geometric Transformations

• Chapter 4: Introduction to Transformations and Matrices
  • Why Transformations are Essential in CG
  • Introduction to Matrices: Definitions, Operations (Addition, Multiplication)
  • Matrix Inverses and Determinants
  • Homogeneous Coordinates for 2D and 3D (Proof for Unification)
• Chapter 5: 2D Transformations
  • Translation Matrix (Formulae & Derivation)
  • Scaling Matrix (Formulae & Derivation)
  • Rotation Matrix (around origin) (Formulae & Derivation)
  • Shear Matrix (Formulae & Derivation)
  • Composition of 2D Transformations (Examples)
• Chapter 6: 3D Transformations
  • Translation, Scaling, and Shear in 3D (Formulae & Derivations)
  • 3D Rotations: Around X, Y, Z Axes (Euler Angles) (Formulae & Derivations)
  • Rotation about an Arbitrary Axis (Rodrigues' Rotation Formula, Quaternions Introduction)
  • Composition of 3D Transformations (Examples)
• Chapter 7: Projections
  • Orthographic Projection (Formulae & Derivation)
  • Perspective Projection (Formulae & Derivation)
  • Viewports and Canonical View Volume

Part III: Curves and Surfaces

• Chapter 8: Parametric Curves
  • Introduction to Parametric Representation
  • Hermite Curves (Cubic Hermite) (Formulae & Derivations)
  • Bézier Curves: Definition, de Casteljau's Algorithm, Properties (Examples & Proofs)
  • Continuity of Curves (C0,C1,C2)
• Chapter 9: Spline Curves
  • B-Spline Curves: Definition, Basis Functions (NURBS introduction, but possibly in later chapter)
  • Properties of B-Splines (Local Control, Convex Hull)
  • Knot Vectors and Their Influence
  • Catmull-Rom Splines (Examples)
• Chapter 10: Parametric Surfaces
  • Tensor Product Surfaces
  • Bilinear Patches
  • Bézier Surfaces (Formulae & Examples)
  • B-Spline Surfaces and NURBS Surfaces (brief introduction or advanced chapter)
  • Surface Normals and Tangent Planes (Formulae)

Part IV: Advanced Topics and Applications

• Chapter 11: Intersections and Collisions
  • Line-Sphere Intersection (Formulae & Proofs)
  • Ray-Triangle Intersection (Moller-Trumbore Algorithm or similar)
  • Bounding Volumes: Spheres, AABBs, OBBs
  • Collision Detection Algorithms (Conceptual Overview)
• Chapter 12: Quaternions for Rotations
  • Introduction to Complex Numbers and Quaternions
  • Quaternion Algebra and Properties
  • Quaternion Rotations (Formulae & Derivations)
  • Spherical Linear Interpolation (SLERP)
  • Advantages and Disadvantages over Euler Angles/Matrices
• Chapter 13: Geometric Algorithms and Data Structures
  • Convex Hull Algorithms (2D and 3D)
  • Triangulation of Polygons
  • Spatial Partitioning Structures (Kd-Trees, Octrees, BSP Trees - conceptual)
• Chapter 14: Mesh Representations and Operations
  • Polygon Meshes: Vertex, Edge, Face Data Structures
  • Mesh Simplification Techniques
  • Subdivision Surfaces (Conceptual Introduction)

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Tags: John Vince, Geometry, Graphics