Spatial transfer functions: a unified approach to specifying deformation in volume modeling and animation

In this paper, we introduce the concept of spatial transfer functions as a unified approach to volume modeling and animation. A spatial transfer function is a function that defines the geometrical transformation of a scalar field in space, and is a generalization and abstraction of a variety of deformation methods. It facilitates a field based representation, and can thus be embedded into a volumetric scene graph under the algebraic framework of constructive volume geometry. We show that when spatial transfer functions are treated as spatial objects, constructive operations and conventional transfer functions can be applied to such spatial objects. We demonstrate spatial transfer functions in action with the aid of a collection of examples in volume visualization, sweeping, deformation and animation. In association with these examples, we describe methods for modeling and realizing spatial transfer functions, including simple procedural functions, operational decomposition of complex functions, large scale domain decomposition and temporal spatial transfer functions. We also discuss the implementation of spatial transfer functions in the vlib API and our efforts in deploying the technique in volume animation.