Mathematics for Computer Graphics ApplicationsThis completely revised Second Edition of "Computer Graphics" includes valuable information on major organizational changes within the last few years. This edition brings to the fore the basic mathematical tools of computer graphics, including vectors, matrices, and transformations. Additionally, it provides a strong, comprehensive base in exploring math, computer science, physics, engineering, and in special subjects such as algebraic and computational geometry, geometric modeling, and CAD/CAM. A highly diversified book that can be utilized as a primary textbook, supplemental teaching resource, individual tutorial, or key reference text. Features
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Contents
Vectors | 1 |
Matrix Methods | 28 |
Transformations | 47 |
Symmetry and Groups | 73 |
Limit and Continuity | 90 |
Topology | 129 |
Halfspaces | 152 |
Points | 165 |
Polyhedra | 205 |
Constructive Solid Geometry | 226 |
Curves | 244 |
The Bézier Curve | 264 |
Surfaces | 277 |
Computer Graphics Display Geometry | 286 |
Display and Scene Transformations | 313 |
| 326 | |
Common terms and phrases
affine transformations algebraic angle angle excess arbitrary axes axis Bézier curve Boolean boundary Chapter closed curve closed path coefficients components computer graphics construct control points convex hull coordinate system cube define deformed denote display distance edges elements endpoints equal Euler characteristic Euler's formula example Exercise faces Figure function geometric modeling given halfspaces hypernumbers icosahedron inside interior interval inversion limit line segments linear mathematical mathematician matrix Möbius strip node object octahedron operations p₁ parametric equations parametric variable perpendicular picture plane piecewise flat surface point of intersection polyhedron produces projection properties real numbers regular polygon regular polyhedra scalar sequence set of points shape simple solid space sphere straight line symmetry group symmetry transformations tangent vectors tetrahedron theorem three-dimensional torus total curvature total turning translation triangle Truncated two-dimensional u₁ vector equation vertex vertices W₁ wallpaper groups window zero