Using Langevin-Type Stochastic-Dynamical Particles for Sampling and Rendering Implicit Surfaces

Satoshi TANAKA; Yasushi FUKUDA; Akio MORISAKI; Satoru NAKATA

Using Langevin-Type Stochastic-Dynamical Particles for Sampling and Rendering Implicit Surfaces

Satoshi TANAKA, Yasushi FUKUDA, Akio MORISAKI, Satoru NAKATA

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We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.

Publication: IEICE TRANSACTIONS on Information Vol.E83-D No.2 pp.265-274

Publication Date: 2000/02/25

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Type of Manuscript: PAPER

Category: Computer Graphics

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Satoshi TANAKA, Yasushi FUKUDA, Akio MORISAKI, Satoru NAKATA, "Using Langevin-Type Stochastic-Dynamical Particles for Sampling and Rendering Implicit Surfaces" in IEICE TRANSACTIONS on Information, vol. E83-D, no. 2, pp. 265-274, February 2000, doi: .
Abstract: We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.
URL: https://global.ieice.org/en_transactions/information/10.1587/e83-d_2_265/_p

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@ARTICLE{e83-d_2_265,
author={Satoshi TANAKA, Yasushi FUKUDA, Akio MORISAKI, Satoru NAKATA, },
journal={IEICE TRANSACTIONS on Information},
title={Using Langevin-Type Stochastic-Dynamical Particles for Sampling and Rendering Implicit Surfaces},
year={2000},
volume={E83-D},
number={2},
pages={265-274},
abstract={We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Using Langevin-Type Stochastic-Dynamical Particles for Sampling and Rendering Implicit Surfaces
T2 - IEICE TRANSACTIONS on Information
SP - 265
EP - 274
AU - Satoshi TANAKA
AU - Yasushi FUKUDA
AU - Akio MORISAKI
AU - Satoru NAKATA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E83-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2000
AB - We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.
ER -