Constructive Hypervolume Textures

Abstract

The concept of solid texturing is extended in two directions: constructive modeling of space partitions for texturing and modeling of multidimensional textured objects called hypervolumes. A hypervolume is considered as a point set with attributes of both physical (density, temperature, etc.) and photometric (color, transparency, diffuse and specular reflections, etc.) nature. The point set geometry and attributes are modeled independently using real-valued scalar functions of several variables. Each real-valued function defining geometry or an attribute is evaluated in the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This approach provides a framework for modeling, texturing and visualization of 3D solids, time- dependent and multidimensional objects in a completely uniform manner. We introduced a special modeling language and implemented software tools supporting the proposed approach. The concept of constructive hypervolume textures is independent of the geometry representation. We provide examples of textured Frep and BRep objects as illustrations.