Controlled Topology Simplification (Voxel Based Object Simplification)

1. Controlled Topology Simplification(Voxel Based Object Simplification) T. He, L. Hong, A. Varshney, S. Wang Udeepta Bordoloi

2. Why Simplification? • Levels of Detail • High frame rate • Removal of high frequencies (anti-aliasing) • Moire patterns

3. Conceptually… • Simplification can be in two areas: • Geometry • Reduce the number of geometry primitives • Topology • Reduce the number of holes, tunnels etc.

4. The factor of Topology • Simplifying • Will change the topology!!! • Preserving • Will limit the amount of simplification possible • Will keep certain high frequencies • Can we take the ‘middle path’?

5. Pipeline

6. Sampling • Input models • Polygonal • Range scanned • Volume • Mathematical function • Sample the 3-d space • Get a 3-d signal (volume as we know in sci-viz)

7. Controlled(?) Filtering • Use low-pass filtering to create frequency-limited versions of the sampled volume • To create a series of LOD volumes, use a series of low-pass filters. • End result: volume pyramid • Can easily get interpolated volumes for in-between levels

8. Compare this volume hierarchy with - • Locality based clustering of geometry • Mip-maps (which use averaging, also a kind of low-pass filtering)

9. Pipeline

10. Reconstruction • Volume reconstruction • Surface reconstruction • Iso-surface • Too many faces • Can output high frequency patterns • Need to preserve topology of the iso-surface while simplifying • Method of choice: improved Splitting Box Algo.

11. Splitting Box • Vertices above/equal iso-value : black • Vertices below iso-value : white • Edge is MC if • Color changes at most once along the sequence of its vertices • Face is MC if all 4 edges are MC • Box is MC if all 6 faces are MC

12. Splitting Box • Start with the whole grid as a single box • Recursive division of the box along its longest edge until • 2x2x2 box • MC box B with satisfactory approximation • What is a satisfactory approximation?

13. Satisfactory approximation • Sub-boxes of B, B1 and B2, are MC • Approximation triangles intersect the common face of B1 and B2 in between grid points where there is a color change • Triangle chain of B geometrically coincident with that of B1 and B2 (?) • Thus, approximate surface cannot be more than one sampling distance in error

14. Adaptive Marching Cubes • Edge is AMC if • Color changes at most once along the sequence of its vertices • Face is AMC if all 4 edges are AMC • Box is AMC if all possible grid lines in the encompassed 3d space are AMC

15. How is AMC different from Splitting Box? • Splitting Box can have unnecessary splits • E.g., non-MC box can get split along an MC edge, thus sub-boxes would still be non-MC • Non-AMC splits are done by finding the axes which have non-AMC edges • Different approximation checking • Within a user-specified distance from the true (MC) surface

16. Multi-layered surface rendering • Render multiple surfaces at different opacities • Visibility order determination a problem

17. Results • Slides