Essential Mathematics for Computer Graphics fastBaffled by maths? Then don't give up hope. John Vince will show you how to understand many of the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. In ten chapters you will rediscover - and hopefully discover for the first time a new way of understanding - the mathematical techniques required to solve problems and design computer programs for computer graphic applications. Each chapter explores a specific mathematical topic and takes you forward into more advanced areas until you are able to understand 3D curves and surface patches, and solve problems using vectors. After reading the book, you should be able to refer to more challenging books with confidence and develop a greater insight into the design of computer graphics software. Get to grips with mathematics fast ... - Numbers - Algebra - Trigonometry - Coordinate geometry - Transforms - Vectors - Curves and surfaces - Analytic geometry Essential Mathematics for Computer Graphics fast The book you will read once, and refer to over and over again! |
Contents
TRIGONOMETRY | 25 |
CARTESIAN COORDINATES | 33 |
3D coordinates | 40 |
Homogeneous coordinates | 75 |
2D shearing | 82 |
2D rotation about an arbitrary point | 88 |
Gimbal lock | 95 |
Transforming vectors | 120 |
Summary | 128 |
INTERPOLATION | 129 |
CURVES AND PATCHES | 149 |
ANALYTIC GEOMETRY | 181 |
2D analytic geometry | 193 |
CONCLUSION 221 | 220 |
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Common terms and phrases
a₁ algebraic angle Ax² axial system axis B-splines b₁ Bernstein polynomials Bézier curves blending Cartesian chapter complex numbers components computer graphics control points cos(B cos(roll cos(ß cos(yaw cross product curve segments defined determinant direction cosines dot product equal example frame of reference functions geometry given graphs Hessian normal form homogeneous coordinates line equation line segments linear interpolation magnitude mathematician mathematics matrix form multiplying n₁ n₂ normal vector number line origin P₁ P₂ Pascal's triangle pitch plane point of intersection point P(x polygon polynomial terms position vector quaternion ratio relative roll rotate a point scalar scaling shape shown in Figure shows sin(B sin(pitch sin(roll sin(ß sine rule slope straight line subtraction surface normal surface patch t₁ t₂ transform translation trigonometric unit vector V₁ V₂ values vertex vertices virtual camera world space x-axis x₁ y-axis y-coordinates Y₁ z-axis zero