3D Math Primer for Graphics and Game DevelopmentCRC Press, 2 nov. 2011 - 846 pages This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for |
Table des matières
| 1 | |
2 Vectors | 31 |
3 Multiple Coordinate Spaces | 79 |
4 Introduction to Matrices | 113 |
5 Matrices and Linear Transformations | 137 |
6 More on Matrices | 161 |
7 Polar Coordinate Systems | 191 |
8 Rotation in Three Dimensions | 217 |
10 Mathematical Topics from 3D Graphics | 343 |
Linear Kinematics and Calculus | 479 |
Linear and Rotational Dynamics | 553 |
13 Curves in 3D | 645 |
14 Afterword | 715 |
A Geometric Tests | 717 |
B Answers to the Exercises | 745 |
| 801 | |
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Expressions et termes fréquents
AABB acceleration algebra angular displacement angular velocity arbitrary axes axis barycentric coordinates basic basis vectors Bézier curves Bézier form calculations camera Cartesian coordinates center of mass chapter collision color column vectors common complex numbers compute constant control points convert coordinate space coordinate system defined denoted depth buffer derivative describe determine direction discussed distance dot product endpoint Equation Euler angles example float force function geometric graphics important input integral interpolation intersection inverse length light linear magnitude math mathematical mesh model space momentum Newton’s notation object space orientation origin orthogonal output perpendicular pixel shader plane polar coordinates polygon polynomial position projection quaternion rendering result rotation matrix scalar scale Section segment shown in Figure simulation specular sphere spline surface normal tangent techniques texture map tion transformation triangle unit vector upright space vertex normal vertex shader vertices video game world space zero