| This dissertation begins with a camera calibration system, Caliber, which solves pose estimation problems consisting of two types of constraints: relative pose constraints, resulting from measurements, such as found in SLAM and motion estimation problems; and rigidity constraints, the notion of objects that are rigidly attached to each other so that their relative pose is fixed over time even if that pose is not known a priori. We show that this problem is NP-hard, but demonstrate an algorithm that works well in practice. Applications include calibrating goniometers for accurate measurement of light reflection.;We then proceed further down the pipeline from measurement of light reflection to the modeling of the appearance of surfaces. Specifically, we examine the appearance of wood. While suitable BRDF models exist, the texture parameter maps for these wood BRDFs are difficult to author---good results have been shown with elaborate measurements for small flat samples, but these models are not much used in practice. Furthermore, mapping 2D image textures onto 3D objects leads to distortion and inconsistencies. Procedural volumetric textures solve these geometric problems, but existing methods produce much lower quality than image textures. This chapter aims to bring the best of all these techniques together: we present a comprehensive volumetric simulation of wood appearance, including growth rings, color variation, pores, rays, and growth distortions. The fiber directions required for anisotropic specular figure follow naturally from the distortions.;The final piece of the dissertation is another application of numerical optimization, this time in games, both in the sense of entertainment and in the sense of game theory. A key challenge in game design is achieving balance between the strategies available to the players. We model the balancing problem as modifying a zero-sum game, using one variable per strategy, so that every strategy has an incentive to be employed. We begin with a special case where these variables affect player payoffs multiplicatively, and show that the simple Sinkhorn-Knopp algorithm can be used to balance the game. We then proceed to analyze the more general case where the variables have a monotonic effect on payoffs, and show that it is amenable to standard optimization methods. |
