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

CS 175 – Week 4 Mesh Decimation General Framework, Progressive Meshes. Overview. motivation general framework topological operators progressive meshes geomorphs parameterization. Motivation. problems with huge meshes storage transmission editing rendering. Motivation.

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

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  1. CS 175 – Week 4Mesh DecimationGeneral Framework, Progressive Meshes

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

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

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

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

  6. Motivation • objectives • intuitive control • few parameters • flexibility

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

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

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

  10. 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

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

  12. 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”

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

  14. 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

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

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

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