Diaphony of Uniform Samples over Hemisphere and Sphere
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The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Using two algorithms we obtain samples in orthogonal spherical triangle and spherical quadrangle. Our aim is to prove uniform distribution of the obtained samples. The importance of the uniformly distributed samples is determined by the effectiveness of the algorithms for numerical solution of the rendering equation. We use numerical characteristic for uniform distribution of points, called diaphony. The diaphony of these samples is calculated numerically. Analysis and comparison of the obtained results are made.
KeywordsSampling Point Solid Angle Light Propagation Uniform Sample Closed Domain
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- 5.Hellekalek, P., Leeb, H.: Dyadic Diaphony. Acta Arithmetica LXXX(2), 187–196Google Scholar