Eecient Global Illumination Using Compactly Supported Overlapping Bases
نویسندگان
چکیده
This paper deals with solving the global illumination problem using compactly supported overlapping bases. Overlapping bases have not been used for their computational complexities. This paper is a step towards solving illumination ee-ciently using overlapping bases. Cubic B-splines are used as an example to show the eecient solution of global illumination. B-splines have properties that give an eecient representation of smooth functions, giving rise to a compact representation. In this paper cubic B-splines are used as the basis function to provide C 2 continuity in the nal solution. They have an advantage over using Haar and multi-wavelets bases which are discontinuous. They also have advantage over orthogonal bases like Legendre polynomials and Spherical harmonics which have global support. Computationally eecient integrals involving B-splines cannot be obtained using Gauss quadrature methods. We show how equi-distant sampling and Newton Coates methods can be used very eeciently for solving integral equations involving overlapping bases. We use directional parameterization to solve scenes containing glossy objects. A new directional parameterization is deened over a hemisphere. Finally, results are shown on various test scenes along with their computational timings.
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