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ACM Transactions on Graphics (TOG)
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SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
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SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
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
Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
Set Models and Boolean Operations for Solids and Assemblies
IEEE Computer Graphics and Applications
Constructive hypervolume modeling
Graphical Models - Volume modeling
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
VG'01 Proceedings of the 2001 Eurographics conference on Volume Graphics
Discretization of functionally based heterogeneous objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Representation of porous artifacts for bio-medical applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Rendering trimmed implicit surfaces and curves
AFRIGRAPH '04 Proceedings of the 3rd international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Web-Based Shape Modeling with Hyperfun
IEEE Computer Graphics and Applications
Bilateral Recovering of Sharp Edges on Feature-Insensitive Sampled Meshes
IEEE Transactions on Visualization and Computer Graphics
Modelling with implicit complexes
SIGGRAPH '05 ACM SIGGRAPH 2005 Sketches
Direct extraction of surface meshes from implicitly represented heterogeneous volumes
Computer-Aided Design
Heterogeneous object modeling: A review
Computer-Aided Design
Modeling complex heterogeneous objects with non-manifold heterogeneous cells
Computer-Aided Design
Incremental reconstruction of sharp edges on mesh surfaces
Computer-Aided Design
Heterogeneous object design: an integrated CAX perspective
Heterogeneous objects modelling and applications
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The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using real-valued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling - a multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with time-dependent adaptive mesh generation where function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.