Fast and memory efficient polygonal simplification

Abstract

Conventional wisdom says that in order to produce high-quality simplified polygonal models, one must retain and use information about the original model during the simplification process. We demonstrate that excellent simplified models can be produced without the need to compare against information from the original geometry while performing local changes to the model. We use edge collapses to perform simplification, as do a number of other methods. We select the position of the new vertex so that the original volume of the model is maintained and we minimize the per-triangle change in volume of the tetrahedra swept out by those triangles that are moved. We also maintain surface area near boundaries and minimize the per-triangle area changes. Calculating the edge collapse priorities and the positions of the new vertices requires only the face connectivity and the the vertex locations in the intermediate model. This approach is memory efficient, allowing the simplification of very large polygonal models, and it is also fast. Moreover, simplified models created using this technique compare favorably to a number of other published simplification methods in terms of mean geometric error.

Tsallis Entropy for Geometry Simplification

“…Lindstrom and Turk [13,14] developed a purely geometric method that defines a memoryless quadric error metric to maintain the volume of the model and the surface area near the boundaries. However, this method does not distinguish between visible and hidden geometry.…”

“…Some methods attempt to measure the total deviation from the initial surface to the completely simplified surface, for example, by tracking an accumulated error while keeping a history of the simplification changes. Other methods attempt to measure only the cost of each individual edge collapse (the local deviation introduced by a single simplification step) and plan the entire process as a sequence of steps of increasing cost [4,10,11,13,14,17]. This iterative algorithm proceeds in two stages.…”

Efficient Simplification Methods for Generating High Quality LODs of 3D Meshes

“…The main drawbacks of this algorithm are memory overhead and the preservation of high-frequency features. Memoryless simplification [9] is a memoryless version of QSlim and generates high quality LODs, but its running time complexity is high. Many modifications [10−12] have been proposed that incorporate feature preserving potential into QSlim; these proposals increase the running time drastically.…”

Efficiently computing and updating triangle strips for real-time rendering

“…However, several other researchers have pointed out the advantage of creating new vertices during edge collapses. These new vertices could be created for accomplishing geomorphs [22] or for better placement of approximating vertices using sophisticated error metrics [17,25]. For incorporating such simplification metrics into the framework of Skip Strips we suggest storing multiple coordinate sets, once per approximating vertex, in the child pointer of the Skip Strip node.…”