Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An approach to modeling multi-material objects
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Subdivision surfaces in character animation
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Hypervolume visualization: a challenge in simplicity
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
A mathematical model for boundary representations of n-dimensional geometric objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Constructive modeling of FRep solids using spline volumes
Proceedings of the sixth ACM symposium on Solid modeling and applications
Texturing and Modeling
Fast Visualization, Manipulation, and Analysis of Binary Volumetric Objects
IEEE Computer Graphics and Applications
Distance Field Manipulation of Surface Models
IEEE Computer Graphics and Applications
Computer
Constructive hypervolume modeling
Graphical Models - Volume modeling
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
The Visual Computer: International Journal of Computer Graphics
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
Trimming for subdivision surfaces
Computer Aided Geometric Design
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The implicit complex model allows for the representation of heterogeneous objects as multidimensional point sets with multiple attributes, where elements of different dimensions and with attributes of different nature are combined together in a topological structure. In this chapter, we present in detail the underlying function-based model for a certain class of cells to be used among several others in the implicit complex model. Each cell is dimensionally homogeneous and defined by a real vector-function. We provide a brief survey of different modelling techniques related to point sets with attributes. It spans such different areas as solid modelling, scalar fields, volume models, and material modelling. Then, on the basis of this survey we formulate requirements to a more general model. In the presented generalizing constructive hypervolume model, point set geometry and attributes are represented independently using real-valued scalar functions with their underlying tree data structures. While 3D and higher dimensional entities have been widely studied, we present function-based definitions of lower dimensional entities, such as surface patches and curve segments, with a corresponding trimming technique. A high level language supporting modelling function-based cells and attributes is described and illustrative examples are provided.