Using Special-Purpose Computing to Examine Chaotic Behavior in Nonlinear Mappings

Studying chaotic behavior in nonlinear systems requires numerous computations in order to simulate the behavior of such systems. The Standard Map Machine was designed and implemented as a special computer for performing these intensive computations with high-speed and high-precision. Its impressive performance is due to its simple architecture specialized to the numerical computations required of nonlinear systems. This report discusses the design and implementation of the Standard Map Machine and its use in the study of nonlinear mappings; in particular, the study of the standard map.

Principles, Opportunism and Seeing in Design: A Computational Approach

This thesis introduces elements of a theory of design activity and a computational framework for developing design systems. The theory stresses the opportunistic nature of designing and the complementary roles of focus and distraction, the interdependence of evaluation and generation, the multiplicity of ways of seeing over the history of a design session versus the exclusivity of a given way of seeing over an arbitrarily short period, and the incommensurability of criteria used to evaluate a design. The thesis argues for a principle based rather than rule based approach to designing documents. The Discursive Generator is presented as a computational framework for implementing specific design systems, and a simple system for arranging blocks according to a set of formal principles is developed by way of illustration. Both shape grammars and constraint based systems are used to contrast current trends in design automation with the discursive approach advocated in the thesis. The Discursive Generator is shown to have some important properties lacking in other types of systems, such as dynamism, robustness and the ability to deal with partial designs. When studied in terms of a search metaphor, the Discursive Generator is shown to exhibit behavior which is radically different from some traditional search techniques, and to avoid some of the well-known difficulties associated with them.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.