This paper discusses techniques for the computation of global illumination in environments with a participating medium using a Monte Carlo simulation of the particle model of light. Efficient algorithms and data structures for tracking the particles inside the volume have been developed. The necessary equation for computing the illumination along any given direction has been derived for rendering a scene with a participating medium. A major issue in any Monte Carlo simulation is the uncertainty in the final simulation results. Various steps of the algorithm have been analysed to identify major sources of uncertainty. To reduce the uncertainty, suitable modifications to the simulation algorithm have been suggested using variance reduction methods of forced collision, absorption suppression and particle divergence. Some sample scenes showing the results of applying these methods are also included.
We present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape B min is non-intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex BC min . BC min and B min can be expressed similarly by parametrizing a topological constraint. A close approximation of BC min , termed BC 0 can be computed fast using a greedy algorithm. BC 0 is then transformed into a closed interpolating boundary B out in two steps to satisfy B min 's topological and minimization requirements. Computing B min exactly is an NP (Non-Polynomial)-hard problem, whereas B out is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.
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