Convex object based volume visualization: a formal proof and example

In this paper, we provide formal definitions for object space, space subdivision and ray tracing. We also introduce concept models such as ordered space subdivisions and ordered visualization. From these works, we can evaluate the correctness and performance of our space subdivision scheme for volume visualization. With these definitions, we also analyze some established space subdivision approaches such as uniform space subdivision and octree based space subdivision. In this paper, we suggest a new subdivision strategy, the convex object based subdivision scheme, which can be more efficient in generating the convex objects for ordered visualization.