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Computational geometry
About: Computational geometry is a research topic. Over the lifetime, 5110 publications have been published within this topic receiving 220642 citations.
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30 Jun 2009
TL;DR: Algorithm of finding cases where floating-point computation causes incorrect results is proposed and calculations with calculation error exclusion as a way of such errors elimination are proposed.
Abstract: Calculation errors while using floating-point computation are considered as a source of computational geometry algorithms incorrect results. Methods of decreasing such errors influence on the algorithm are discussed. Computations with calculation error exclusion as a way of such errors elimination are proposed. Computations with calculation error exclusion defined as a kind of computation where results of certain arithmetic operations could be represented exactly (computations in rational numbers, for example). Algorithm of finding cases where floating-point computation causes incorrect results is proposed.
01 Nov 2006
TL;DR: The algorithm in this paper aims at remeshing not only disk-like objects without holes but also closed objects, which using the concept of virtual boundary is proved practical and efficient in the prototype system.
Abstract: In order to solve the problems that complex mesh needs a huge storage and high transmission price, and is difficult to be edited, simple algorithms are often required to obtain a series of object simulations In this paper, three different parameterization algorithms are adopted to analyze their different effects on mesh quality after remeshing Based on the parameterized mesh over a planar domain, subdivision algorithm is used to transform the mesh with arbitrary structure to a regular triangular or quadrilateral mesh The algorithm in this paper aims at remeshing not only disk-like objects without holes but also closed objects, which using the concept of virtual boundary The algorithm is proved practical and efficient in our prototype system
TL;DR: The approach uses symbolic execution to analyze the specification in order to extract a set of constraints which model the problem, which are leveraged to compute probability distributions relating search steps to predicates about an unknown target.
Abstract: We present a method of automatically synthesizing steps to solve search problems. Given a specification of a search problem, our approach uses symbolic execution to analyze the specification in order to extract a set of constraints which model the problem. These constraints are used in a process called model counting, which is leveraged to compute probability distributions relating search steps to predicates about an unknown target. The probability distribution functions determine an information gain objective function based on Shannon entropy, which, when maximized, yields the next optimal step of the search. We prove that our algorithm converges to a correct solution, and discuss computational complexity issues. We implemented a domain specific language in which to write search problem specifications, enabling our static analysis phase. Our experiments demonstrate the effectiveness of our approach on a set of search problem case studies inspired by the domains of software security, computational geometry, AI for games, and user preference ranking.
TL;DR: A computational geometric model is developed that explains why distortion might take place in stereo, both in stereo and motion, and how functions of the distorted space exhibiting some sort of invariance, produce desirable representations for biological and artificial systems.
Abstract: The encounter of perception and action happens at the intermediate representations of space-time. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters causes distortion of the computed depth of the scene. The unified framework introduced here describes this distortion in computational terms. We characterize the space of distortions by its level sets, that is, we characterize the systematic distortion via a family of iso-distortion surfaces which describes the locus over which depths are distorted by some multiplicative factor. Clearly, functions of the distorted space exhibiting some sort of invariance, produce desirable representations for biological and artificial systems [13]. Given that humans' estimation of egomotion or estimation of the extrinsic parameters of the stereo apparatus is likely to be imprecise, the framework is used to explain a number of psychophysical experiments on the perception of depth from motion or stereo.
TL;DR: A remarkable theorem is described: "It is possible to tile the plane with non-overlapping squares using exactly one square of each integral dimension" and one can "square the plane".
Abstract: A remarkable theorem is described: "It is possible to tile the plane with non-overlapping squares using exactly one square of each integral dimension". Thus, one can "square the plane".