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 efficiently using overlapping bases. Cubic B-splines are used as an example to show the efficient solution of global illumination. B-splines have properties that give an efficient 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 final solution. They have an advantage over using Haar and multiwavelets bases which are discontinuous. They also have advantage over orthogonal bases like Legendre polynomials and Spherical harmonics which have global support. Computationally efficient 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 eff...

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Global illumination is the problem of rendering images by simulating the light transport in a scene, also considering the inter-reflection of light between surfaces. One general approach to global illumination that gained popularity during the last decade is the many-light formulation, whose idea is to approximate global illumination by many automatically generated virtual point lights. In this thesis, we address two fundamental issues that arise with the many-light formulation: scalability and generality. We present a new view of the many-light approach, by treating it as a large matrix of light-surface contributions. Our insight is that there is usually a significant amount of structure and redundancy in the matrix; this suggests that only a tiny subset of the elements might be needed for accurate reconstruction. First, we present a scalable rendering algorithm that exploits this insight by sampling a small subset of matrix rows and columns to reconstruct the image. This algorithm is very flexible in terms of the material and light types it can handle, and achieves high-quality rendering of complex scenes in several seconds