Shape-driven deformations of functionally defined heterogeneous volumetric objects

ABSTRACT

In this paper, we propose a framework for deforming heterogeneous volumetric objects defined as point sets with attributes. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of attributes assigned at each point. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical etc.). It is not necessary for an attribute to be described by a continuous function.In our approach, 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 a space partition used to define the attribute function.Deformation of an existing object is usually considered as the final step of the modelling process. In this paper, 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 at any modelling step.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

Keywords:
constructive hypervolumes, deformation, function representation, heterogeneous objects, implicit surface