Dynamic Skin Triangulation

Cheng, Harry H.; Dey, Tamal K.; Edelsbrunner, Herbert; Sullivan, John M.

doi:10.1007/s00454-001-0007-1

Cited by 74 publications

(64 citation statements)

References 14 publications

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“…Cheng et. al [9] maintained an approximating triangulation of a deforming skin surface. Simplex subdivision schemes are used to generate tetrahedral meshes for molecular structures in solving the Poisson-Boltzmann equation [22].…”

Section: Molecular Surface Approximationmentioning

confidence: 99%

“…We obtain the unit sphere triangulation from [45]. For each vertex q on the triangulated atom surface M N , is computed using the point projection algorithm, where n(q) is the spherical normal at q. for each triangle vertex q ∈ S N ∩S N 0 do { • compute P M N 1 (q, n(q)), and then compute - (9) • } Table 2 shows the minimal error of our level one surface for a residue and a chain from Ribosome 30S, where e(M) is defined as . It can be observed that the error decreases as p increases.…”

Section: Minimal Error Of Levelmentioning

confidence: 99%

“…It can be observed that the error decreases as p increases. The algorithm for computing minimal error can also be used to compute the maximal error by changing the min to max in (9). Maximal errors for Ribosome 30s are also listed in Table 2 for different p 1 (see the second row).…”

Section: Minimal Error Of Levelmentioning

confidence: 99%

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Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gaussian isotropic kernel functions and a two-level clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flow techniques are used to improve the surface and volume mesh quality. Several examples are presented, including generated meshes for biomolecules that have been successfully used in finite element simulations involving solvation energetics and binding rate constants.

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Section: Molecular Surface Approximationmentioning

confidence: 99%

Section: Minimal Error Of Levelmentioning

confidence: 99%

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Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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“…The skin surface is the envelope of families of an infinite number of evolving spheres [37]. It satisfies many desirable mathematical properties.…”

Section: Visualizing Biomolecular Surfacesmentioning

confidence: 99%

Visual Analysis of Biomolecular Surfaces

Natarajan

Koehl

Wang

et al. 2008

Mathematics and Visualization

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Summary. Surface models of biomolecules have become crucially important for the study and understanding of interaction between biomolecules and their environment. We argue for the need for a detailed understanding of biomolecular surfaces by describing several applications in computational and structural biology. We review methods used to model, represent, characterize, and visualize biomolecular surfaces focusing on the role that geometry and topology play in identifying features on the surface. These methods enable the development of efficient computational and visualization tools for studying the function of biomolecules.

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“…The skin surface is not C 2 -continuous, but its maximum normal curvature, κ, is continuous. This property is exploited by Cheng et al [1], who describe an algorithm that constructs a triangular mesh representing the skin surface. In this mesh, the sizes of edges and triangles are inversely proportional to the maximum normal curvature.…”

Section: Introductionmentioning

confidence: 99%