Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Extended free-form deformation: a sculpturing tool for 3D geometric modeling
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Sculpting: an interactive volumetric modeling technique
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Feature-based image metamorphosis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Computer graphics techniques
Simple constrained deformations for geometric modeling and interactive design
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
A generalized de Casteljau approach to 3D free-form deformation
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Feature-based volume metamorphosis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Free-form deformations with lattices of arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A haptic interaction method for volume visualization
Proceedings of the 7th conference on Visualization '96
An approach to modeling multi-material objects
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Wires: a geometric deformation technique
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Localized-hierarchy surface splines (LeSS)
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
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
Constructive modeling of FRep solids using spline volumes
Proceedings of the sixth ACM symposium on Solid modeling and applications
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
A system for sculpting 3-D data
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Shape-driven deformations of functionally defined heterogeneous volumetric objects
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Constructive hypervolume modeling
Graphical Models - Volume modeling
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
General Constrained Deformations based on Generalized Metaballs
PG '98 Proceedings of the 6th Pacific Conference on Computer Graphics and Applications
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In this paper, we propose a framework for modeling and deforming heterogeneous volumetric objects defined as point sets with attributes. We propose to use constructive hypervolume objects, where the function representation (FRep) is used as the basic model for both object geometry and attributes represented independently using real-valued scalar functions of point coordinates. While FRep directly defines object geometry, for an attribute it specifies space partitions used to define the attribute functions. In this model, an extended space mapping is applied in a geometric space extended by a functional coordinate to transform volumetric objects. We describe in this chapter three different applications of this mapping. First we propose an approach to constructive modeling of 3D solids defined by real-valued functions using B-spline volumes as primitives. A 4D uniform rational cubic B-spline volume is employed to define a 3D solid, which can serve as object geometry or as a space partition for defining volumetric attributes. Second application of the extended space mapping is deformation of an existing object. We propose to define a new node in the FRep tree based on shape-driven deformations. These deformations can be controlled by additional shapes (points, curves, surfaces, or solids) and can be applied to object geometry and attributes during any modeling step. The last application is a new operation for a locally controlled metamorphosis between two functionally defined shapes. To implement this operation, a set of non-overlapping space partitions is introduced, where the metamorphosis occurs locally. The sequence of local metamorphosis processes is controlled by a specific time schedule. The definitions of the partitions, of the time schedule, and finally of the local metamorphosis operation, are described and illustrated by examples.