# Constructive Volumetric Sculpting Using Trivariate B-splines

a b c

(a) A teapot-like object is modeled using a single cubic B-spline primitive.

(b) Heterogeneous object modeling. Several primitives and operations, including the proposed B-spline primitive, are used to build the constructive trees for the geometry and the attributes.

© Several trivariate B-spline primitives are used for interactive modeling of space partitions for texturing a BRep object.

B. Schmitt, Pasko A., C. Schlick, “Constructive sculpting of heterogeneous volumetric objects using trivariate B-splines”, The Visual Computer, 2004, vol. 20, Nos. 2-3, 2004, pp. 130 - 148.

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## Abstract

This paper deals with modeling heterogeneous volumetric objects as point sets with attributes using trivariate B-splines. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of variable attributes assigned at each point. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.). Our approach is based on the constructive hypervolume model. We propose a volume sculpting scheme with multiresolution capability based on trivariate B-spline functions to define both object geometry and its attributes. A new trivariate B-spline primitive is proposed and can be used as a leaf in a FRep constructive tree. An interactive volume modeler based on trivariate B-splines and other simple primitives is described, with a real time re-polygonization of the surface during modeling. We illustrate that the space partition obtained in the modeling process can be applied to define attributes for the objects with an arbitrary geometry model such as B-rep or homogeneous volume models.