Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Simplex splines support surprisingly strong symmetric structures and subdivision
Proceedings of the international conference on Curves and surfaces in geometric design
Multiresolution modeling and visualization of volume data based on simplicial complexes
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Triangular NURBS and their dynamic generalizations
Computer Aided Geometric Design
Three dimensional freeform sculpting via zero sets of scalar trivariate functions
Proceedings of the fifth ACM symposium on Solid modeling and applications
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
Proceedings of the conference on Visualization '00
Proceedings of the sixth ACM symposium on Solid modeling and applications
Constructive modeling of FRep solids using spline volumes
Proceedings of the sixth ACM symposium on Solid modeling and applications
Haptics-based volumetric modeling using dynamic spline-based implicit functions
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
Simplification of Tetrahedral Meshes with Error Bounds
IEEE Transactions on Visualization and Computer Graphics
Interactive Direct Rendering of Trivariate B-Spline Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Modeling with Triangular B-Splines
IEEE Computer Graphics and Applications
Tetrahedral Mesh Modeling of Density Data for Anatomical Atlases and Intensity-Based Registration
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Feature preserved volume simplification
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Haptic Sculpting of Volumetric Implicit Functions
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Delaunay refinement mesh generation
Delaunay refinement mesh generation
Surface Reconstruction with Triangular B-splines
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Heterogeneous object modeling: A review
Computer-Aided Design
Dynamic spherical volumetric simplex splins with application in biomedical simulation
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Modeling complex heterogeneous objects with non-manifold heterogeneous cells
Computer-Aided Design
Heterogeneous object design: an integrated CAX perspective
Heterogeneous objects modelling and applications
Conformal solid T-spline construction from boundary T-spline representations
Computational Mechanics
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This paper presents a new and powerful heterogeneous solid modeling paradigm for representing, modeling, and rendering of multi-dimensional, physical attributes across any volumetric objects. The modeled solid can be of complicated geometry and arbitrary topology. It is formulated using a trivariate simplex spline defined over a tetrahedral decomposition of any 3D domain. Heterogeneous material attributes associated with solid geometry can be modeled and edited by manipulating the control vectors and/or associated knots of trivariate simplex splines easily. The multiresolution capability is achieved by interactively subdividing any regions of interest and allocating more knots and control vectors accordingly. We also develop a feature-sensitive fitting algorithm that can reconstruct a more compact, continuous trivariate simplex spline from structured or unstructured volumetric grids. This multiresolution representation results from the adaptive and progressive tetrahedralization of the 3D domain. In addition, based on the simplex spline theory, we derive several theoretical formula and propose a fast direct rendering algorithm for interactive data analysis and visualization of the simplex spline volumes. Our experiments demonstrate that the proposed paradigm augments the current modeling and visualization techniques with the new and unique advantages.