CS 175 – Week 4 Mesh Decimation General Framework, Progressive Meshes

CS 175 – Week 4Mesh DecimationGeneral Framework, Progressive Meshes

Overview • motivation • general framework • topological operators • progressive meshes • geomorphs • parameterization

Motivation • problems with huge meshes • storage • transmission • editing • rendering

Motivation • redundant information • many triangles in planar region • triangle smaller than a pixel • reduce size • remove vertices, edges, triangles • preserve shape (geometry)

Motivation • non-manifold simplification • vertex clustering • topology may change • manifold simplification • mesh decimation • incremental operation

Motivation • objectives • intuitive control • few parameters • flexibility

Mesh Decimation • general framework • topological operator • local simplification • fairness criterion • cost of local simplification • iteratively apply cheapest simplification

Mesh Decimation • basic algorithm • compute cost of all simplifications • sort into priority queue • while queue not empty • perform cheapest simplification • update queue

Topological Operators • vertex removal • re-triangulate hole • edge collapse • choose new point position • half-edge collapse • purely topological operator

Progressive Meshes • edge collapse c(i,j,r,l) • remove vj and (I,j,l), (j,I,r) • reconnect neighbours of vj with vi • inverse vertex split s(i,j,r,l) • insert vj and (i,j,l), (j,I,r) • reconnect neighbours of vi with vj

Progressive Meshes • store • base mesh M0 • sequence of vertex splits • properties • full sequence of hierarchies • more compact than shared vertex

Geomorphs • interpolate between Mk0 and Mk1 • build correspondence betweenremoved and remaining vertices • vertices in Mk1 have corresponding vertex in Mk0 • linearly interpolate vertex positions • avoids “snapping”

Parameterization • correspondence between removed vertices and remaining triangles • index plus barycentric coordinates • build progressively • exponential map around vj • gives parametric distances

Related Issues • feature lines • collapse vertices to neighbouring feature vertices only • selective refinement • apply vertex splits only in areas that are visible from the viewpoint • e.g. flight simulator

Related Issues • mesh compression • connectivity • 2 bits per vertex • geometry • linear predictors • difference vectors • regular remeshing

Next Session • fairness criteria • Hausdorff distance • first and second order fairness • error quadrics

CS 175 – Week 4 Mesh Decimation General Framework, Progressive Meshes