Solving geometric constraint problems through Monte Carlo optimization

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Title Solving geometric constraint problems through Monte Carlo optimization
Publication Type thesis
School or College College of Engineering
Department Computing
Author Perry, Daniel James
Date 2008-08
Description Geometric constraint problems appear in many situations, including CAD systems, robotics, and computational biology. The complexity of these problems inspires the search for efficient solutions. We have developed a method to solve geometric constraint problems in the areas of geometric computation and robot path planning using configuration space subdivision. In this approach the configuration space, or parameter space, is subdivided and conservatively tested to find collision-free regions, which are then numerically searched for specific path solutions. This thesis presents a new more general approach to this last solution search step, using Monte Carlo optimization. In this new search approach, within a single subdivided area of configuration space, space is randomly sampled and then iteratively resampled based on importance weighting, until convergence to a solution with an acceptable error. We show that by using Monte Carlo optimization to extend configuration space subdivision we can solve higher dimensional problems more efficiently than configuration space subdivision by itself.
Type Text
Publisher University of Utah
Subject Computer graphics; Geometric programming; Monte Carlo method
Dissertation Institution University of Utah
Dissertation Name MS
Language eng
Relation is Version of Digital reproduction of "Solving geometric constraint problems through Monte Carlo optimization" J. Willard Marriott Library Special Collections, T7.5 2008 .P47
Rights Management © Daniel James Perry
Format application/pdf
Format Medium application/pdf
Format Extent 112,770 bytes
Identifier us-etd2,31464
Source Original: University of Utah J. Willard Marriott Library Special Collections
ARK ark:/87278/s6959z1g
Setname ir_etd
ID 192307
Reference URL https://collections.lib.utah.edu/ark:/87278/s6959z1g
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