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Level Of Detail Management for 3D Games

Level Of Detail Management for 3D Games. Generating LODs. Amitabh Varshney Graphics and Visual Informatics Laboratory Department of Computer Science University of Maryland at College Park http://www.cs.umd.edu/gvil. Geometry & Topology Simplifications. Geometry Simplification

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Level Of Detail Management for 3D Games

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  1. Level Of Detail Management for 3D Games

  2. Generating LODs Amitabh Varshney Graphics and Visual Informatics Laboratory Department of Computer Science University of Maryland at College Park http://www.cs.umd.edu/gvil

  3. Geometry & Topology Simplifications • Geometry Simplification • Reducing the number of geometric primitives (vertices, edges, triangles) • Topology Simplification • Reducing the number of holes, tunnels, cavities • Geometry + Topology Simplification • Aggressive simplifications

  4. Outline • Local Simplification Operators • Geometry and Topology Simplifications • Global Simplification Operators • Variable-Precision Rendering

  5. Outline • Local Simplification Operators • Geometry and Topology Simplifications • Global Simplification Operators • Variable Precision Rendering

  6. Local Simplification Operators • Edge Collapse • Vertex-Pair Collapse • Triangle Collapse • Cell Collapse • Vertex Removal • General Geometric Replacement

  7. Edge Collapse va Edge Collapse vnew vb VertexSplit Hoppe, SIGGRAPH 96; Xia et al.,Visualization 96; Hoppe, SIGGRAPH 97; Bajaj et al., Visualization 99; Gueziec et al., CG&A 99; …

  8. Half-Edge Collapse va Half-Edge Collapse va vb VertexSplit

  9. Implementation: Watch for Mesh Foldovers va Edge Collapse vc vd vnew vb vd vc

  10. Implementation: Watch for Identical / Non-Manifold Tris Edge Collapse va vnew vb

  11. Vertex-Pair Collapse va Vertex Pair Collapse vnew vb VertexSplit Schroeder, Visualization 97; Garland & Heckbert, SIGGRAPH 97; Popovic & Hoppe, SIGGRAPH 97; El-Sana & Varshney, Eurographics 99; …

  12. Triangle Collapse Triangle Collapse va vc vnew vb Hamann, CAGD 94; Gieng et al., IEEE TVCG 98

  13. Cell Collapse Grid based: Rossignac & Borrel, Modeling in Computer Graphics 93 Octree-based: Luebke & Erikson, SIGGRAPH 98

  14. va Vertex Removal Vertex Removal Triangulation va Schroeder et al., SIGGRAPH 92; Klein & Kramer, Spring Conf. On Comp. Graphics 97

  15. General Geometric Replacement • Replace a subset of adjacent triangles by a simplified set with same boundary • Proposed as Multi-triangulation by DeFloriani et al.Visualization 97, Visualization 98 • Fairly general: can encode edge collapses, vertex removals, and edge flips

  16. Discussion / Comparison • Edge Collapse and Triangle Collapse: • Simplest to implement • Support geometric morphing across levels of detail. • Full-edge vs. Half-edge collapses: • Full edge represents better simplifications • Half-edge is more efficient in incremental encoding • Cell Collapse: • Simple, Robust • Varies with rotation/translation of grid • Vertex Removal vs Edge Collapse • Hole retriangulation is not as simple as edge collapse • Smaller number of triangles affected in vertex removal

  17. Outline • Local Simplification Operators • Geometry and Topology Simplifications • Global Simplification Operators • Variable Precision Rendering

  18. Simplification of Geometry vs Topology

  19. Local Topology Simplifying Algorithms • Collapsing vertex pairs / virtual edges • Schroeder, Visualization 97 • Popovic and Hoppe, SIGGRAPH 97 • Garland and Heckbert, SIGGRAPH 97 • Collapsing primitives in a cell • Rossignac and Borrel, Modeling in Comp. Graphics 93 • Luebke and Erikson, SIGGRAPH 97

  20. Simplifying Genus • Allow virtual edge collapses • Limit potentially O(n2) virtual edges • Typical constraints: • Delaunay edges • Edges that span neighboring cells in a spatial subdivision: octree, grids, etc. • Maximum edge length

  21. Outline • Local Simplification Operators • Geometry and Topology Simplifications • Global Simplification Operators • Variable Precision Rendering

  22. Global Simplification Operators • Usually simplify topology • Volume Processing Operators • Low Pass Filtering • Morphological Processing

  23. Low Pass Filtering in Volumetric Domain • Convert the polygonal mesh to a volumetric grid (voxelization) • Apply low-pass filters of increasing support Triangle counts(a) 334K, (b) 181K, (c) 76K (d) 17K, (e) 3K, (f) 568 [He et al. IEEE TVCG 96]

  24. Morphological Processing • Convert polygonal mesh to a volume grid • Build a distance field • Associate each voxel with smallest distance to the object • Dilation(T) • Any voxel with distance < T is reclassified as being inside; expands the object • Erosion • Complement of dilation; shrinks object • Dilation followed by Erosion simplifies topology • Proposed by Nooruddin & Turk, IEEE TVCG 02

  25. Morphological Operators of Erosion & Dilation Original (140K faces) Topology Simplified (5K faces) Simplified by QSlim (3.3 K faces) Nooruddin & Turk IEEE TVCG 2002 Simplified by QSlim (3.3K faces)

  26. Outline • Local Simplification Operators • Geometry and Topology Simplifications • Global Simplification Operators • Variable-Precision Rendering

  27. Defining Level of Detail • Number of Primitives • Precision of primitives • Colors (Heckbert 82, Xiang 97) • Normals (Deering 95, Zhang & Hoff 97) • Vertex coordinates (King & Rossignac 99)

  28. Variable-Precision Rendering • Reduce the precision of graphics primitives • Relate the number of bits of input precision for a given display accuracy • Speedup 3D transformation and lighting by taking advantage of SIMD parallelism • Explore spatio-temporal coherence

  29. Related Work Sugihara 89 Taubin & Rossignac 98 Milenkovic & Nackman 90 Taubin et al. 98 Rossignac & Borrel 93 Li & Kuo 98 Deering 95 Cohen-Or et al. 99 Fortune & Van Wyk 96 Bajaj et al. 99 Chow 97 King & Rossignac 99 Luebke & Erikson 97 Bajaj et al. 2000 Fortune 98 Pajarola & Rossignac 2000

  30. Variable-Precision vs. Multiresolution Original Multiresolution Variable Precision

  31. Assumptions • Minimum-sized cube covering the object • x, y, z normalized to range [-1.0, 1.0] • N-bit fixed-point representation of operands • Rounding to the nearest integer • Worst-case study

  32. Results from Error Analysis

  33. Variable-Precision Transformation • Construct bounding volume hierarchy • Find the projected size of the object • Determine the nearest visible vertex accuracy

  34. Variable-PrecisionTransformation Accuracy needed for each vertex: Compute by using bounding volume hierarchy

  35. Spatio-temporal Coherence • Spatial coherence • Using differences in neighboring vertices • Mx’ = M (x + x) = M x + M x • Top-down octree traversal • Temporal Coherence • Frame-to-frame • M’x = (M + M) x = M x + M x • Can be combined with spatial coherence

  36. Transformation Result Floating Point (32 bits/vertex coordinate) Variable Precision (7.9 bits/vertex coordinate)

  37. Variable-Precision Lighting (OpenGL Lighting Model)

  38. Illumination Error Analysis • Specular (least accurate) decides the overall accuracy • Lose 1 bit for normalization, 1~2 bits for dot product, 6 bits for exponentiation • Total loss of accuracy: 8 ~ 9 bits • Overall: m = n+8 or n+9 (n = output accuracy, m = input accuracy)

  39. Implementation Notes • Vertices processed in groups as a tradeoff between • L2 cache size • Expensive cost of resetting MMX register flag between changes in operand types • Avoid error buildup • Matrix setup and composition per frame is full precision • Transformations are variable precision • Computation cost is negligible

  40. Results: Venus Floating Point Variable Precision

  41. Results: Venus Floating Point Variable Precision

  42. Results Auxiliary Machine Room Variable Precision Close-up Floating Point Close-up

  43. Conclusions • • More efficient transformation and lighting • • Complementary to multiresolution approaches • • For the datasets we tested • Using PII 400MHz PC with 128M RAM • Voodoo3 3500 graphics card and Glide API • Provides a factor of 4 or more speedup

  44. Variable-Precision Rendering Software http://www.cs.umd.edu/gvil/vpr.html Download free for non-commercial use

  45. What We Discussed • Geometry and Topology Simplifications • Local Simplification Operators • Global Simplification Operators • Variable Precision Transformation and Lighting

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