Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
An Algebraic Multilevel Multigraph Algorithm
SIAM Journal on Scientific Computing
Mesh Smoothing via Mean and Median Filtering Applied to Face Normals
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
ACM SIGGRAPH 2003 Papers
Analysis of triangle quality measures
Mathematics of Computation
SIAM Journal on Scientific Computing
A sharpness dependent filter for mesh smoothing
Computer Aided Geometric Design - Special issue: Geometry processing
Optimality of Multilevel Preconditioners for Local Mesh Refinement in Three Dimensions
SIAM Journal on Numerical Analysis
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Computational Approaches for Automatic Structural Analysis of Large Biomolecular Complexes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
2D FE quad mesh smoothing via angle-based optimization
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Feature-sensitive tetrahedral mesh generation with guaranteed quality
Computer-Aided Design
Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
Journal of Scientific Computing
Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation
Computer Aided Geometric Design
New software developments for quality mesh generation and optimization from biomedical imaging data
Computer Methods and Programs in Biomedicine
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We describe a combination of algorithms for high-fidelity geometric modeling and mesh generation. Although our methods and implementations are application-neutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Our software toolchain implementing these algorithms is general in the sense that it can take as input a molecule in PDB/PQR forms, a 3D scalar volume, or a user-defined triangular surface mesh that may have very low quality. The main goal of our work presented is to generate high quality and smooth surface triangulations from the aforementioned inputs, and to reduce the mesh sizes by mesh coarsening. Tetrahedral meshes are also generated for finite element analysis in biomedical applications. Experiments on a number of bio-structures are demonstrated, showing that our approach possesses several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). The availability of this software toolchain will give researchers in computational biomedicine and other modeling areas access to higher-fidelity geometric models.