Summary: Stratified Sampling of 2­Manifolds
James Arvo
State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis
SIGGRAPH 2001 Course Notes, volume 29
August 2001


Contents
1 Stratified Sampling of 2­Manifolds 5
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 A Recipe for Sampling Algorithms . . . . . . . . . . . . . . . . . 8
1.3 Analytic Area­Preserving Parametrizations . . . . . . . . . . . . 11
1.3.1 Sampling Planar Triangles . . . . . . . . . . . . . . . . . 12
1.3.2 Sampling the Unit Disk . . . . . . . . . . . . . . . . . . . 12
1.3.3 Sampling the Unit Hemisphere . . . . . . . . . . . . . . . 13
1.3.4 Sampling a Phong Lobe . . . . . . . . . . . . . . . . . . 14
1.3.5 Sampling Spherical Triangles . . . . . . . . . . . . . . . 15
1.4 Sampling Projected Spherical Polygons . . . . . . . . . . . . . . 19
1.4.1 The Cumulative Marginal Distribution . . . . . . . . . . . 21
1.4.2 The Sampling Algorithm . . . . . . . . . . . . . . . . . . 23

Source: Arvo, Jim - Departments of Information and Computer Science & Electrical and Computer Engineering, University of California, Irvine

Collections: Computer Technologies and Information Sciences