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Transcript
Decimation Of Triangle Meshes Avneesh Sud Special Topics in Computer Graphics What Is Decimation ? Reduction in the number of triangles in a triangle mesh, maintaining the original topology, as well as its overall appearance determined by discrete and scalar attributes. Decimation Advanced Topics in Graphics The Basic Mesh • The Mesh is a collection of triangles in 3space, given by ( V,T(V) ), where V is the list of vertices, and T(V) the list of triangle definitions Decimation Advanced Topics in Graphics Requirements for a Good Decimation • The original topology of the mesh must be preserved • The decimated mesh must be a good approximation to the original • Optional : Vertices of the decimated mesh be a subset of original set. This allows to preserve the appearance attributes Decimation Advanced Topics in Graphics The algorithm • Characterize the local vertex geometry and topology • Evaluate decimation criteria • Triangulate the resulting holes. Decimation Advanced Topics in Graphics Characterizing Local Geometry • Determines the vertices which are possible candidates for deletion. • All vertices except complex vertices are candidates for deletion. Decimation Advanced Topics in Graphics Characterizing Local Geometry Simple Corner Edge Boundary Complex Decimation Advanced Topics in Graphics Interior Edge Evaluating Decimation Criteria • Simple Vertices : Distance to average plane Decimation Advanced Topics in Graphics Evaluating Decimation Criteria • Boundary and Feature Edges : Distance to edge Decimation Advanced Topics in Graphics Triangulation • If a vertex is eliminated, the loop created by removing the vertex is re-triangulated. • Every loop is star shaped : recursive loop splitting triangulation schemes are used. • If a loop cannot be retriangulated, the vertex generating the loop is not removed. Decimation Advanced Topics in Graphics Recursive Splitting Triangulation • A split plane orthogonal to average plane is determined. • If two loops do not overlap the split plane is acceptable Decimation Advanced Topics in Graphics Recursive Splitting Triangulation • Best splitting plane is determined using an aspect ratio Min. distance of loop vertices from split line Aspect Ratio Split line length • Maximum aspect ratio gives best splitting plane Decimation Advanced Topics in Graphics Special Cases • Modification of topology of a closed structure • Topological ‘holes’ in the mesh These are checked by triangulation to ensure duplicate triangles or edges are not created Decimation Advanced Topics in Graphics Results Decimation Advanced Topics in Graphics Results Decimation Advanced Topics in Graphics
