Abstract

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.