An Algorithm for Continuous Resolution PolygonaIizations of a Discrete Surface

An algorithm for polygonalizing a discrete surface (height grid) is presented. A quad tree is used to create a bottom-up, irregular rectangular polygonalization of an input height grid by merging homogenous regions starting at the pixel level and working up the tree. A homogenous region is composed of any number of smaller regions that differ within a user specified error tolerance in gradient and that fit together to form a rectangular polygon. As rectangular polygons are merged, a polygon tree (poly tree) is built which describes the merge proce~s and can be used to rapidly locate neighboring polygons. The poly tree is used to describe the discrete surface at multiple levels of resolution. After all possible regions have been merged, the rectangular polygons are triangulated to eliminate gaps created by the irregular intersections of the rectangles . , This algorithm automatically preserves critical lines, even with coarse polygonal represent~tions. Continuous resolution can be achieved through the use of TIN morphing between the discrete levels of resolution computed by the algorithm. Additionally, parallel simulations indicate that this algorithm can achieve maximum speedups of O(,.Jn) to O(nllog n), where n is the number of nodes in the bottom level of the tree.