Optimization on Inverse Reflector Design

List of Figures1.1 Overall scheme of this thesis. The orange boxes are the problemsto solve, and the yellow boxes are the solutions. Theboxes with text in bold are the developed solutions in thisthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1 Goniophotometer system description, as is shown in [Ash93] . 92.2 Lumigraph description. Each ray is represented by a 4D parameterizationof a pair of cells in two parallel planes. In theexample, the ray is represented by (u i , v j , s p , t q ), where u i ,v jand s p ,t q are the cell coordinates for first and second planesrespectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Light ray tracing description. . . . . . . . . . . . . . . . . . . 122.4 Photon Map (left) and Caustic Map (right) creation. Thesphere (bottom) is used as density estimator over the KD-Treethat contains the maps . . . . . . . . . . . . . . . . . . . . . . 142.5 Bounding Volume Hierarchy example. . . . . . . . . . . . . . . 162.6 Full screen quad technique. A quad is rendered on the fullviewport. The viewport has the same size than the desiredoutput texture. Then, each pixel becomes a fragment that isprocessed by a GPU fragment shader. . . . . . . . . . . . . . . 182.7 Binary Search algorithm . . . . . . . . . . . . . . . . . . . . . 202.8 Sphere Tracing algorithm . . . . . . . . . . . . . . . . . . . . . 212.9 Relief Mapping algorithm. . . . . . . . . . . . . . . . . . . . . 222.10 Quadtree Relief Mapping algorithm. . . . . . . . . . . . . . . . 232.11 Example of Hooke & Jeeves optimization method for a functionof two parameters (P 1 , P 2 ). The node numbers show theoptimization progression. The gray squares are the point shiftingsalong the axis. Note that in nodes 4 and 6 no new pointproduces better results, thus the shift jump size is reduced andthe process starts again at the same point. . . . . . . . . . . . 25v