GPGPU Programming for Games and Science

x Contents

6.3.6.9 Euler Angles to and from Quaternion or Axis-

Angle...................... 317

6.4 CoordinateSystems ....................... 318

6.4.1 GeometryandAffineAlgebra.............. 319

6.4.2 Transformations ..................... 322

6.4.2.1 Composition of Affine Transformations . . . 322

6.4.2.2 Decomposition of Affine Transformations . . 327

6.4.2.3 A Simple Transformation Factory . . . . . . 330

6.4.3 Coordinate System Conventions . . . . . . . . . . . . 332

6.4.4 Converting between Coordinate Systems . . . . . . . . 336

7 Sample Applications 341

7.1 VideoStreams .......................... 341

7.1.1 The

VideoStream Class .................. 341

7.1.2 The

VideoStreamManager Class.............. 342

7.2 RootFinding ........................... 346

7.2.1