Approximate CatmullClark Patches. Scott Schaefer Charles Loop


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1 Approximate CatmullClark Patches Scott Schaefer Charles Loop
2 Approximate CatmullClark Patches Scott Schaefer Charles Loop CatmullClark Surface ACCPatches
3 Polygon Models Prevalent in game industry Very fast to render Not smooth (faceted) Complicated LOD management Highresolution models require lots of bandwidth and computational resources
4 Goal: Fast Smooth Surfaces Eliminate faceting artifacts Animate lowres representation Let GPU worry about LOD Current Future
5 DirectX Pipeline Input Assembler Vertex Buffer Index Buffer Vertex Shader Texture Geometry Hull Shader Rasterizer/ Tessellator Interpolator Texture Stream Output Domain Pixel Shader Texture Output Merger Depth/Stencil Render Target
6 Tessellator Unit Tessellator
7 Tessellator Unit Tessellator
8 Domain Shader Tessellation factor per edge Called for each vertex of the sample pattern Early form in the XBox 360 DS_OUT DS(float2 uv : BARYCENTRIC, int patchind : INDEX) { DS_OUT Out = (DS_OUT)0; // fetch data for patch #patchind // evaluate patch at uv } return Out;
9 Subdivision Surfaces Used in movie and game industries Supported by most 3D modeling software Toy Story Disney / Pixar Geri s Game Pixar Animation Studios
10 Subdivision Surfaces Set of rules S that recursively act on a shape p 0 p k+1 = S p k Arbitrary topology surfaces Smooth everywhere 0 p 1 p k p
11 CatmullClark Surfaces 6 ) 3( u u u 6 3 u u u 6 ) (1 3 u 6 ) (1 3 v v v 6 ) 3( v v v 6 3 v
12 CatmullClark Surfaces
13 CatmullClark Surfaces
14 CatmullClark Surfaces
15 CatmullClark Surfaces
16 CatmullClark Surfaces
17 CatmullClark Surfaces
18 CatmullClark Surfaces
19 Stam s Exact Evaluation Algorithm Subdivide until x is in ordinary region S i P x
20 Stam s Exact Evaluation Algorithm Subdivide until x is in ordinary region S i P x
21 Stam s Exact Evaluation Algorithm Subdivide until x is in ordinary region S i P x
22 Stam s Exact Evaluation Algorithm Subdivide until x is in ordinary region S i P Extract Bspline control points and evaluate at x x
23 Stam s Exact Evaluation Algorithm Subdivide until x is in ordinary region V i V 1 P Extract Bspline control points and evaluate at x x
24 Performance Issues Limits # extraordinary verts
25 Performance Issues Limits # extraordinary verts
26 Performance Issues Limits # extraordinary verts Lots of shader constants V i ( V 1 P ) Valence Constants
27 Solution: Polynomial Patches Replace extraordinary patches with polynomials Geometry patch (degree 3x3) 2 Tangent patches (degree 3x2) Based on conversion from Bspline to Bezier form
28 Solution: Polynomial Patches Replace extraordinary patches with polynomials Geometry patch (degree 3x3) 2 Tangent patches (degree 3x2) Based on conversion from Bspline to Bezier form b03 b13 b23 b33 b02 b12 b22 b32 b01 b11 b21 b31 b00 b10 b20 b30
29 Solution: Polynomial Patches Replace extraordinary patches with polynomials Geometry patch (degree 3x3) 2 Tangent patches (degree 3x2) Based on conversion from Bspline to Bezier form u03 u u u02 u u u01 u11 u21 u00 u u 10 20
30 Solution: Polynomial Patches Replace extraordinary patches with polynomials Geometry patch (degree 3x3) 2 Tangent patches (degree 3x2) Based on conversion from Bspline to Bezier form v02 v12 v22 v32 v01 v11 v21 v31 v00 v10 v20 v30
31 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use limit masks
32 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use limit masks
33 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use n limit masks n 5 2 n n 5 n 5
34 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use n limit masks n n 5 2( n 5) 2 n n 5 2( n 5)
35 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use n( n 5) limit masks n 4 n n( n 5) n( n 5) n( n 5) n( n 5) 4 n( n 5) n( n 5) 1 n( n 5) 4 n( n 5) 1 n( n 5) 4 1 n ( n 5) n( n 5)
36 ACC Geometry Patches Use knotinsertion rules from ordinary case At corners, use limit masks Smooth everywhere except edges touching extraordinary vertices 1 n( n 5) 4 n( n 5) 1 n( n 5) 4 n( n 5) 1 n( n 5) 1 n( n 5) 4 n( n 5) 4 n( n 5) n n 5 1 n( n 5) 4 n( n 5) 4 1 n ( n 5) n( n 5)
37 ACC Tangent Patches Continuous normal field needed for displacement mapping Create two tangent patches (u/v) for each position patch
38 ACC Tangent Patches Continuous normal field needed for displacement mapping Create two tangent patches (u/v) for each position patch
39 ACC Tangent Patches Continuous normal field needed for displacement mapping Create two tangent patches (u/v) for each position patch v
40 ACC Tangent Patches Continuous normal field needed for displacement mapping Create two tangent patches (u/v) for each position patch v
41 ACC Tangent Patches Continuous normal field needed for displacement mapping Create two tangent patches (u/v) for each position patch v
42 ACC Tangent Patches v10 v00 v 20 v 30 u u u 20 ˆv 10 ˆv 20 ˆv 00 ˆv 30 v( t) u( t) vˆ( t) u( t) v
43 ACC Tangent Patches v10 v00 v 20 v 30 u u u 20 v v ˆv 10 ˆv 20 ˆv ci c c 0 0 u u cos 2 n i c u 1 c u 1 ˆv v
44 Examples
45 Examples ACC Geometry Patches
46 Examples ACC Geo/Tan Patches
47 Examples CatmullClark Surface
48 Examples
49 Examples ACC Geometry Patches
50 Examples ACC Geo/Tan Patches
51 Examples CatmullClark Surface
52 Examples
53 Examples ACC Geometry Patches
54 Examples ACC Geo/Tan Patches
55 Examples CatmullClark Surface
56 Examples ACC Geo/Tan CatmullClark
57 Examples
58 Examples ACC Geometry Patches
59 Examples ACC Geo/Tan Patches
60 Examples CatmullClark Surface
61 Comparison Better Worse
62 Comparison Better Worse
63 Comparison Better Worse
64 Comparison Better Worse
65 Conclusions Creates visually smooth surfaces Suitable for displacement/normal mapping Handles any number of extraordinary vertices Simple to evaluate Demo part of DirectX March 2008 SDK
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