Decimating Meshes

Two methods are available in Dragonfly to reduce the number of vertices, edges, and triangles in a mesh — Pro decimation and Quadric decimation. These methods work by the iterative elimination of components identified through local geometric optimality criteria. You should note that both methods will attempt to preserve the overall shape, volume, and boundaries of the original mesh as much as possible.

Pro decimation… With this simplification method, each vertex in the mesh is classified and inserted into a priority queue. The priority is based on the error to delete the vertex and re-triangulate the hole. Vertices that cannot be deleted or triangulated (at this point in the algorithm) are skipped. Then, each vertex in the priority queue is processed (i.e., deleted followed by hole triangulation using edge collapse). This continues until the priority queue is empty. Next, all remaining vertices are processed, and the mesh is split into separate pieces along sharp edges or at non-manifold attachment points and reinserted into the priority queue. Again, the priority queue is processed until empty. If the desired reduction is still not achieved, the remaining vertices are split as necessary (in a recursive fashion) so that it is possible to eliminate every triangle as necessary.

Reference: https://www.vtk.org/doc/nightly/html/classvtkDecimatePro.html#details.

Quadric decimation… Is based on repeated edge collapses until the requested mesh reduction is achieved. Edges are placed in a priority queue based on the “cost” to delete the edge. The cost is an approximate measure of error (distance to the original surface) — described by the so-called quadric error measure. The quadric error measure is associated with each vertex of the mesh and represents a matrix of planes incident on that vertex. The distance of the planes to the vertex is the error in the position of the vertex (originally the vertex error is zero). As edges are deleted, the quadric error measure associated with the two end points of the edge are summed (this combines the plane equations) and an optimal collapse point can be computed. Edges connected to the collapse point are then reinserted into the queue after computing the new cost to delete them. The process continues until the desired reduction level is reached or topological constraints prevent further reduction. Note that this basic algorithm can be extended to higher dimensions by taking into account variation in attributes (i.e., scalars, vectors, and so on).

Reference: https://www.vtk.org/doc/nightly/html/classvtkQuadricDecimation.html#details.