Shining a light on material appearance

Abstract

This research proposes a new algorithm for mapping Normal Distribution Functions to Heightfields in order to answer its research question: ”Given an NDF, how can we generate a corresponding Heightfield using simple optimization algorithms?”. This research is important, as it helps us to gain a better understanding of how limited statistics-based representations of 3D surfaces are. To this end, we have produced an algorithm using the Simulated Annealing optimization technique, a technique that randomly explores possible solutions of a problem until it finds the optimal solution. The algorithm begins with a flat Heightfield (a 2D representation of a surface that shows the relative altitude of a discrete plane of points), iteratively changes points on the Heightfield and compares its measured NDF (Normal Distribution Function, a function to denote the area distribution along a given direction in a Heightfield) to the target NDF that we want to map. Once the target NDF is reached, or once the pre-determined number of iterations has been reached, the algorithm concludes and the NDF-to-Heightfield mapping has been completed. Three different variations are tried, one na¨ıve implementation which changes points on the Heightfield completely at random, another where the angle of the normal vector of a random surrounding facet of a chosen point is used as guidance for randomization, and finally one where this angle is guided using the relative position of the chosen point to the centre of the Heightfield. The conclusion the proposed algorithm provides is that, while possible, the process of mapping NDFs to Heightfields is a costly and complex operation, and leaves a lot of room for ambiguity. While the research cannot provide a case of an exact match of a target NDF and measured NDF of a Heightfield created through the algorithm, we do show it is without a doubt possible given time.