Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
On the shape of tetrahedra from bisection
Mathematics of Computation
Cutting cubes—visualizing implicit surfaces by adaptive polygonization
The Visual Computer: International Journal of Computer Graphics
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
Automatic unstructured grid generators
Finite Elements in Analysis and Design
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
An approach to modeling multi-material objects
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Volumetric multi-texturing for functionally gradient material representation
Proceedings of the sixth ACM symposium on Solid modeling and applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Automatic Mesh Generation: Applications to Finite Element Methods
Automatic Mesh Generation: Applications to Finite Element Methods
Dual/Primal mesh optimization for polygonized implicit surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Cellular-functional modeling of heterogeneous objects
Proceedings of the seventh ACM symposium on Solid modeling and applications
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
Constructive hypervolume modeling
Graphical Models - Volume modeling
Dynamic Meshes for Accurate Polygonization of Implicit Surfaces with Sharp Features
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
Duplicate-skins for compatible mesh modelling
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Heterogeneous object modeling: A review
Computer-Aided Design
Technical Section: Variational implicit surface meshing
Computers and Graphics
Modeling complex heterogeneous objects with non-manifold heterogeneous cells
Computer-Aided Design
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The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.