Marching triangles: range image fusion for complex object modelling

Hilton, Adrian; Stoddart, Andrew J.; Illingworth, J.; Windeatt, Terry

doi:10.1109/icip.1996.560840

Cited by 105 publications

(64 citation statements)

References 8 publications

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“…The continuation methods [29][30][31] are of another category. These methods mesh the implicit surface by growing current polygonization's border through adding new vertices.…”

Section: Some Definitions and Meshing Methods For Molecular Surfacementioning

confidence: 99%

Advances in biomolecular surface meshing and its applications to mathematical modeling

Chen

2013

Chin. Sci. Bull.

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In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and simulation. Recently, with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation, providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure. In this review, we summarize recent works on this issue. First, various definitions of molecular surfaces and corresponding meshing methods are introduced. Second, our recent meshing tool, TMSmesh, and its performances are presented. Finally, we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM). molecular surface meshing, manifold mesh, mathematical modeling, TMSmeshCitation: Chen M X, Lu B Z. Advances in biomolecular surface meshing and its applications to mathematical modeling. Chin Sci Bull, 2013Bull, , 58: 1843Bull, -1849 10.1007/s11434-013-5829-8One main goal of computational structural biology/chemistry is to understand the functions and mechanisms of biomolecular systems and their relations to molecular structures with a wide range of computational approaches. To achieve this, proper and correct representation of the interface between biomolecule and solvent, molecular surface, is a primary task. In the field of implicit solvent modeling and continuum modeling, the molecular surface is used to model the dielectric interface which is the transition from the low-dielectric solute region to the high-dielectric solvent region. It is also important and useful in materials science and surface science [1]. Meshing molecular surface is a prerequisite for using boundary element method (BEM) and finite element method (FEM) in the implicit solvent models, and it is a more demanding task than for the only purposes of visualization and/or geometry analyses of molecular structure. So far, due to the highly complex and irregular shape of the molecular surface, *Corresponding author (email: bzlu@lsec.cc.ac.cn) efficient meshing of molecular surface for large real biomolecule with high quality remains a challenging problem. Actually, it was historically a great impediment to use BEM/FEM in continuum modeling of large molecular systems.The main purpose of this paper is to review the various definitions and meshing methods for molecular surface, including our recent work, and introduce their applications in implicit solvent modeling and simulation. Following this introduction section, in Section 1, various definitions of molecular surfaces and corresponding meshing methods are introduced. In Section 2, our recent algorithm and software, TMSmesh, are focused. We also made comparisons with some other methods. In Section 3, a closely related topic, volume me...

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“…The continuation methods [29][30][31] are of another category. These methods mesh the implicit surface by growing current polygonization's border through adding new vertices.…”

Section: Some Definitions and Meshing Methods For Molecular Surfacementioning

confidence: 99%

Advances in biomolecular surface meshing and its applications to mathematical modeling

Chen

2013

Chin. Sci. Bull.

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“…First, the insides of tubes are voxelized using a polyhedron filling algorithm [10]. Then, the boundary of the obtained discrete volume is triangulated by means of a Marching cube-like method [9]. In the future, a direct transformation from the set of cylindrical surfaces to the triangulated boudnary surface will be considered.…”

Section: Boundary Refinementmentioning

confidence: 99%

Deformable tree models for 2D and 3D branching structures extraction

Mille

Cohen

2009

2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops

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“…Contouring algorithms such as marching squares and marching triangles [23] are employed in computer graphics to generate zero level curves of bivariate functions. These contouring algorithms can be very efficient at solving (1.1), and until this paper the roots(f,g) command in Chebfun2 exclusively employed such a contouring approach [43].…”

Section: Contouring Algorithmsmentioning

confidence: 99%

Computing the common zeros of two bivariate functions via Bézout resultants

2014

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Abstract. The common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor Chebyshev basis. From here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and Bézout matrices with polynomial entries. Using techniques including domain subdivision, Bézoutian regularization and local refinement we are able to reliably and accurately compute the simple common zeros of two smooth functions with polynomial interpolants of very high degree (≥ 1000). We analyze the resultant method and its conditioning by noting that the Bézout matrices are matrix polynomials. Our robust algorithm is implemented in the roots command in Chebfun2, a software package written in object-oriented Matlab for computing with bivariate functions.

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Marching triangles: range image fusion for complex object modelling

Cited by 105 publications

References 8 publications

Advances in biomolecular surface meshing and its applications to mathematical modeling

Advances in biomolecular surface meshing and its applications to mathematical modeling

Deformable tree models for 2D and 3D branching structures extraction

Computing the common zeros of two bivariate functions via Bézout resultants

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