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

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

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

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’?

Pipeline

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)

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

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

Pipeline

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.

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

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?

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

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

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

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

Results Slides