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 Topology
Reduce the number of geometry primitives
Topology
Reduce the number of holes, tunnels etc.

4. The factor of Topology Simplifying Preserving
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 Sample the 3-d space 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