Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Solid shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
Simple and efficient polygonization of implicit surfaces
Journal of Graphics Tools
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Dynamic Meshes for Accurate Polygonization of Implicit Surfaces with Sharp Features
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Quadric-based polygonal surface simplification
Quadric-based polygonal surface simplification
Surface reconstruction of freeform objects based on multiresolution volumetric method
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Discretization of functionally based heterogeneous objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Edge-sharpener: recovering sharp features in triangulations of non-adaptively re-meshed surfaces
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SHIC: A View-Dependent Rendering Framework for Isosurfaces
VV '04 Proceedings of the 2004 IEEE Symposium on Volume Visualization and Graphics
IEEE Transactions on Visualization and Computer Graphics
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
3D scattered data interpolation and approximation with multilevel compactly supported RBFs
Graphical Models - Special issue on SMI 2003
Duplicate-skins for compatible mesh modelling
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Bilateral Recovering of Sharp Edges on Feature-Insensitive Sampled Meshes
IEEE Transactions on Visualization and Computer Graphics
Multi-level partition of unity implicits
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Efficient Method for Point-Based Rendering on GPUs
Edutainment '08 Proceedings of the 3rd international conference on Technologies for E-Learning and Digital Entertainment
Technical Section: Variational implicit surface meshing
Computers and Graphics
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Incremental reconstruction of sharp edges on mesh surfaces
Computer-Aided Design
Journal of Computational Physics
Optimized surface discretization of functionally defined multi-material objects
Advances in Engineering Software
Non-manifold mesh extraction from time-varying segmented volumes used for modeling a human heart
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
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A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard marching cubes mesh Lorensen(in our experiments we use VTK marching cubes VTK). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that "double dual" mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.