1. Level of Detail: Choosing and Generating LODs David Luebke University of Virginia

2. Recap: Generating LODs l Simplification operator: –Cell collapse –Vertex removal –Edge collapse n Full edge collapse n Half edge collapse n Vertex-pair merge a.k.a. “virtual edge collapse”

3. Generating LODs l Simplification algorithm –Outer optimization: where to simplify n No optimization n Ex: uniform grid cells n Greedy optimization n Ex: floating cell clustering n Ex: sort edge collapses by error, resort on collapse n Lazy optimization n Ex: sort edge collapses by error, dirty bit on collapse –Inner optimization: how to simplify n Ex: placement of new vertex, retriangulation

4. Basic Greedy Edge Collapse Algorithm Sort all edges (by some metric) repeat Collapse edge choose edge vertex (or compute optimal vertex) Fix-up topology until (no edges left)

5. Recap: Measuring Error l Most LOD algorithms measure error geometrically –What is the distance between the original and simplified surface? –What is the volume between the surfaces? –Etc l Really this is just an approximation to the actual visual error, which includes: –Color, normal, & texture distortion –Importance of silhouettes, background illumination, semantic importance, etc.

6. Measuring Visual Error l Measuring error –Image-based ideas n Lindstrom & Turk, SIGGRAPH 2000 –Perceptually-based ideas n Luebke & Hallen, EGRW 2001 n Williams, Luebke, Cohen, Kelley & Schubert, I3D 2003

7. Perceptually Driven LOD l Idea: measure local simplification operations against a perceptual model to predict whether the user can could see the effect of simplification l Model: contrast sensitivity function

8. Perception 101: Contrast Sensitivity Function l Contrast grating tests produce a contrast sensitivity function –Threshold contrast vs. spatial frequency –CSF predicts the minimum detectable static stimuli

9. Campbell-Robson Chart by Izumi Ohzawa Your Personal CSF

10. Perceptual Graphics: Where To Next? l Incorporate eccentricity, velocity (attention?) l Protect copyrighted media: imperceptible “watermarking” via mesh distortion l Interactive ray tracing…

11. Measuring Geometric Error l Measuring error –Hausdorff distance n One-sided: n Two-sided: –Common approximations: n Measure vertex-vertex distance, vertex-plane distance n METRO: Sample H(A,B) by sprinkling points on triangles n Quadric Error Metrics: a variation of vertex-plane distance that works well in practice

12. Edge Collapse Algorithm V1V1 V2V2 V2V2 Collapse

13. Edge Collapse Benefits l Edge collapse operation is simple l Supports non-manifold topology:

14. Edge Collapse vs. Vertex-Pair Merging l Even better: vertex-pair merging merges two vertices that: –Share an edge, or –Are within some threshold distance t l Q: What does vertex-pair merging enable over edge collapse?

15. Quadric Error Metric l Minimize distance to all planes at a vertex l Plane equation for each face: 0 :p  DCzByAx v           1 z y x DCBA T vp l Distance to vertex v :

16. Squared Distance At a Vertex    )( ))(( vplanesp TT vppv    )( )( v p TT vppv v v vplanesp TT            )(    )( 2 )()( v p T vpv

17. Quadric Derivation (cont’d) l pp T is simply the plane equation squared: l The pp T sum at a vertex v is a matrix, Q:  vQvv T  )(              2 2 2 2 DCDBDAD CDCBCAC BDBCBAB ADACABA pp T