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Mesh optimization (1993)

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by Tony Derose , Tom Duchampy , John Mcdonaldz , Werner Stuetzlez
Citations:319 - 9 self
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@TECHREPORT{Derose93meshoptimization,
    author = {Tony Derose and Tom Duchampy and John Mcdonaldz and Werner Stuetzlez},
    title = {Mesh optimization},
    institution = {},
    year = {1993}
}

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Abstract

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).

Citations

1524 Matrix Computations - Golub, Loan - 1983
613 Algebraic topology - Spanier - 1981
538 Surface reconstruction from unorganized points. SIGGRAPH Computer Graphics 26(2):71–78 Hornung A, Wurm KM, Bennewitz M (2010) Humanoid robot localization in complex indoor environments - Hoppe, DeRose, et al. - 1992
518 Decimation of Triangle Meshes - Schroeder, Zarge, et al.
358 Re-Tiling Polygonal Surfaces - Turk
255 B.: Data structures for soft objects - Wyvill, McPheeters, et al. - 1986
154 Introduction to piecewise-linear topology - Rourke, Sanderson - 1972
100 Geometrically deformed models: A method for extracting closed geometric models from volume data - Miller, Breen, et al. - 1991
97 On three-dimensional surface reconstruction methods - Bolle, Vemuri - 1991
59 Generalized implicit functions for computer graphics - Sclaroff, Pentland - 1991
50 WYVILL B.: Data structure for soft objects. The visual computer - WYVILL, MCPHEETERS - 1986
29 Discrete smooth interpolation in geometric modeling - Mallet - 1992
12 Towards an anatomical model of heart motion as seen in 4-d cardiac ultrasound data - Schudy, Ballard - 1979
11 Geometric Topology in Dimensions 2 and 3, volume 47 of Graduate Texts in Mathematics - Moise - 1977
8 Fitting of surfaces to scattered data - DeRose, Hoppe, et al.
6 Surface reconstruction from scattered measurements - Goshtasby - 1992
6 Model detection of cardiac chambers in ultrasound images - Schudy, Ballard - 1978
3 Parametric approximation of data using ODR splines - Marin, Smith - 1990
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