Quickly bounding diagonal edge lengths in tessellated bilinear patches.

ABSTRACTWe present QuickBound, an algorithm for quickly determining whether a uniformly tessellated grid derived from a bilinear patch satisfies a maximum edge length threshold. Our approach generalizes the well-known technique of bounding the length of all horizontal and vertical edges in the uniformly tessellated grid by checking only a small, constant number of edges. We generalize this technique to apply to all diagonal edges. Our approach, called Quick-Bound, reduces the time complexity of determining whether an (m face x n face) grid satisfies the edge length threshold from O(mxn) to O(1). We provide a proof of correctness for QuickBound and also measure its effectiveness in a real-time bilinear patch visualizer.