On mapping Bezier curve and surface subdivision algorithms into a hypercube with geometric adjacency constraint

The authors discuss the Bezier curve and surface generation algorithms on a hypercube computer. They show that the computation structures of Bezier curve and surface generation based on subdivision method can be modeled as binomial trees and extended binomial trees respectively. Properties of binomial trees and extended binomial trees are explored and mappings from these tree structures to hypercubes are discussed. As the spatial coherence plays an important role in computer graphics and geometric algorithms, the authors imposed the geometric adjacency on these mappings and proved that there exist adjacency preserving mappings. Moreover, they show that their mappings are optimal with respect to expansion, dilation and congestion