Constrained Strip Generation and Management for Efficient Interactive 3D Rendering

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Constrained Strip Generation and Management
forEfficient Interactive 3D Rendering

• Pablo Diaz-Gutierrez, Anusheel Bhushan,
• M. Gopi and Renato Pajarola
• Computer Graphics Lab
• University of California, Irvine

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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Results and conclusion

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Triangle Strips Traditionally

• Improve rendering performance
• Render T triangles
• Using GL_TRIANGLES send 3T vertices.
• S strips 2ST vertices.
• Not negligible init time per strip.
• Alternating vs. generalized strips.
• Incremental vs. global algorithms

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Triangle Strips Recent work samples

• Hoppe 99 Optimization of mesh locality for
  transparent vertex caching.
• Strip arrangement depends on cache size
  (typically 16-32 verts.).
• Mitani and Suzuki 04 Making papercraft toys
  from meshes using strip-based approximate
  unfolding.
• Rossignac 99 Edgebreaker Connectivity
  Compression for Triangle Meshes.
• Isenburg 00 Triangle Strip Compression.
• Stewart 01 Tunneling for triangle strips in
  continuous level-of-detail meshes
• El Sana, Azanli, Varshney 99 Skip Strips
  Maintaining Triangle Strips for View-dependent
  Rendering

Images courtesy of paper authors
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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Results and conclusion

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Single-strips

• A single-strip is a Hamiltonian path in the dual
  graph of a triangle mesh.
• Calculating a Hamiltonian path is NP-complete
  Introduce some vertices to simplify problem.
• We use single-loops First and last triangles are
  adjacent.

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Why single-strips?

• Pure performance doesnt justify single-strips
• With long strips, one extra vertex is negligible.
• Single-strips have more advantages
• Some topological properties can be derived.
• Use linearity to compress connectivity.
• Easy to keep long strips during simplification.
• Simpler data structures and algorithms.
• Reduce overhead (proportional to number of
  strips).

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Single-strip creation

• We use Gopi and Eppstein 04 single-strip
  algorithm.
• A perfect graph matching matches every vertex to
  exactly one of its neighbors.
• Exists for a 3-regular, 3-connected graph
  (Petersens theorem).
• Such as the dual graph of a triangulated
  manifold.
• Perfect matching
• Matches every triangle to exactly one of its
  neighbors
• Disjoint triangle loops formed by unmatched
  neighbors
• Then merge loops to form a single strip loop.

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Single-strip creation merging loops

• Nodal vertex processing

Insufficient to merge all disjoint loops in the
mesh. Need another operation.
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Single-strip creation merging loops

• Edge split Identify separating matched edge.

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Single-strip creation merging loops

• Edge split Split matched triangles adding
  Steiner vertex.

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Single-strip creation merging loops

• Edge split Nodal vertex processing at the
  Steiner vertex.

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Single-strip creation merging loops

• Edge split Two loops merged into one.

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Single-strip creation Strip control

• No control over resulting single-strip.
• By control we mean
• Deciding the direction of growth
• Making it follow patterns
• Space-filling curves
• Bounding it to a region of the mesh
• Restrict it to grow in planar regions
• Why dont we have it?
• Strip control is fine grain (local decisions)
• This is a global, coarse grain approach Input a
  mesh, output a single-strip.

?
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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Results and conclusion

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Our contribution

• We present an algorithm that provides certain
  control over the single-strip.
• Made to follow preferred strip directions

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Constrained Single-strips

• How to control a single-strip?
• Advice (assign weights) the matching algorithm to
  choose certain edges of the dual graph over
  others.
• Application-dependent
• Higher weight
• Desired matched edge
• Non-desired strip edge
• Weighing scheme is independent of stripification
  algorithm
• Use Weighted Perfect Matching

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Constrained Single-strips

• How to control a single-strip?
• Advice (assign weights) the matching algorithm to
  choose certain edges of the dual graph over
  others.
• Application-dependent
• Higher weight
• Desired matched edge
• Non-desired strip edge
• Weighing scheme is independent of stripification
  algorithm
• Use Weighted Perfect Matching

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Constrained Single-strips

• How to control a single-strip?
• Advice (assign weights) the matching algorithm to
  choose certain edges of the dual graph over
  others.
• Application-dependent
• Higher weight
• Desired matched edge
• Non-desired strip edge
• Weighing scheme is independent of stripification
  algorithm
• Use Weighted Perfect Matching

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Constrained Single-strips Efficiency

• Original single-strip algorithm O(N2)
• N Number of triangles
• Dominated by matching algorithm
• Constrained single-strip O(N2 log N)
• Performance penalty for weighted matching

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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Back-face culling
• Improvement of vertex cache usage
• Results and conclusion

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Back-face culling with single-strips

• Back-face culling to avoid rendering non visible
  faces due to orientation.
• More useful if many faces are tested together
• Force the strip to form planar clusters
• Test long segments of the strip at same time

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Back-face culling with single-strips

• Weight calculation
• Variational Shape Approximation Cohen-Steiner et
  al. 04 to find planar clusters of triangles and
  assign
• High weight in edges across region borders
• Low (zero) weight everywhere else
• Resulting disjoint loops remain within planar
  regions

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Back-face culling with single-strips

• Efficient visibility testing
• Construct segment tree
• Associate view-cone to each segment
• Test root segment first
• Front-facing Render segment
• Back-facing Skip segment
• Partially front-facing Traverse down the
  hierarchy
• Long strips after culling

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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Back-face culling
• Improvement of vertex cache usage
• Results and conclusion

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Improving vertex cache usage

• Target maximizing vertex cache hit ratio
• Strip reuses recent vertices
• Just like a space-filling curve
• Duality Space-filling curve and its medial axis
• Equivalently Single-strip and edge spanning tree

Sierpinski space-filling curve and its medial axis
Our high-locality single-strip
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Improving vertex cache usage

• Weight calculation
• Calculate breadth-first edge tree
• Weight 1 for edges in the tree
• Weight 0 for edges NOT in the tree
• Cache oblivious strip layout
• Cache-hit ratio around 90 of other cache-aware
  layouts for any specific cache-size Hoppe 99,
  Bar-Yehuda et al. 96

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Talk Outline

• Triangle strips Discussion
• Single-strips
• Constrained single-strips
• Applications of constrained single-strips
• Results and conclusion

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Results
Frames per second for real-time rendering of
single-strips on 4 models with different
constraints. Values measured during a 360 degree
walk-around of the model.
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Contributions

• Added control to single-stripification
• Demonstrated two applications
• Back-face culling while maintaining long strips
• Cache-oblivious strip optimization

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Current and future work

• Handle manifolds with boundaries (done)
• Patch-based single-stripification.
• Specialized perfect matching algorithms (for
  3-regular graphs).
• Use approximate (non-perfect) matching.
• Test different space-filling curves.
• Find other applications of single-strips.

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Thank you.

• Questions, comments and corrections are welcome