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Higher Order SurfacesHigher Order SurfacesHenry Moreton
Why surfaces?Higher order primitives
Animation
Level of Detail
Bandwidth
Filtering
The “Surfaces” RoadmapPolynomial Surfaces
B-Spline, BézierTensor product, Triangle
Subdivision SurfacesCatmull-Clark, Loop
Displacement Mapping
Massive Levels of Geometric Detail
Geo
met
ricCo
mpl
exity
CPU
CPU
Graphics Processor
Graphics Processor
PreviousGeneration
1 Frame(1/60 sec)
1 Frame(1/60 sec)
AI,Physics,Game Play
Transform& Lighting Rendering
T&L Created A Major Content Shift...
Current Generation
A New Band of Computation
CPU Graphics Processor
AI,Physics,Game Play
Transform& Lighting RenderingGeometry
Processing
...Another Order of Magnitude
❋image courtesy of Pixar Animation Studios
The GeForce3 Graphics Pipelinecurved
surfaces
vertexshaders
setuprasterizer
tex-addrops
textureblending
frame-bufferantialiasing
shadowtextures
per-vertex geometry & shading programs
per-pixel shading
Historical Solution e.g. OpenGL Evaluators
Square - tensor product patches
Grid - just specify rows and columns
Integer - number of segments
Share - use T&L hardware
10
20
Triangular Patches are Necessary
3DStudioMax
Patch outlines
Hardware emulation
SquareGridIntegerShare
Four Independent Tessellation Factors
4
6 5
9
4
9
56
SquareGridIntegerShare
Generalized Tessellation isImportant
SquareGridIntegerShare
Fractional Number of Segments
6.0
6.25
6.5
6.75
7.0
SquareGridIntegerShare
LOD Morphing Suppresses Visual Artifacts
SquareGridIntegerShare
Multiple Tessellation StylesOptimal TessellationMorphing Tessellation
SquareGridIntegerShare
Dedicated Hardware
Doesn’t slow down transform
Performance matched pipeline
Most efficient way to draw triangles
Bandwidth
CPU – light weight animation
Transform & Lighting – great vertex reuse
SquareGridIntegerShare
Setting Tessellation Factorsedge based – (patch soup)
Crack preventionTessellation factors must be specified consistently for shared edges.Data structures or -Tessellation factors must be based on shared information, patch edges.
CriteriaCurvatureScreen space
Transform the control hull edge (Bézier)Silhouettes
Shared surface normals
How to Get Started?
ModelingPolynomial Patches – quadrilateral and triangular
DX8Bézier, B-spline, & Catmull-Rom spline patches
OpenGL Bézier patches – rational
NO Trimmed NURBSUse exporters -
Maya, 3DStudio
DX8 InterfaceSurface representation
Bézier
B-spline
Catmull-Rom
Shape (domains)
Quadrilateral
Triangular
Constraints
Uniform degree
Bézier Catmull-Rom
B-spline
DX8 Entry Points
DrawRectPatch & DrawTriPatch Specify and draw triangular/rectangular patches
DeletePatchFree cached patches
SetRenderState D3DPATCHEDGESTYLE
Discrete - integerContinuous – fractional
CAPSD3DDEVCAPS_RTPATCHES D3DDEVCAPS_QUINTICRTPATCHES
OpenGL Interface
Surface representation
Bézier
Shape (domains)
Quadrilateral
Triangular
OpenGL Entry Points
MapControlPointsNVEVAL_2D_NV or EVAL_TRIANGULAR_2D_NV
Specify the control points for the vertex component
MapParameterivNV & MapParameterfvNVMAP_TESSELLATION_NV
Specify the tessellation factors for the patch
EvalMapsNVTessellate (render) the patch, sending vertices, forming triangles to T&L
Tips & TechniquesDos & Don’ts
Level of detail calculationMemory footprintPerformanceMixing with meshesContinuityTangents, normals & bi-normalsSkinning and blending
Level of Detail Calculationscreen space edge length
By patch – significant foreshorteningTransform to screen spaceCompute control hull lengthDivide by desired edge length
By object – little foreshorteningBeforehand
Compute boundary lengths in model spaceEach frame (or so)
Transform Bbox or proxy to screen spaceCompute sizeScale relative lengths computed off-line
Variable vs. Fixed LOD by Object
24,794 triangles6,326 triangles
Memory Footprint
With tessellation factors A,B,C,Dmin(max(A,C), max(B,D))××××order + 3××××order + slopRoughly 2x for fractional tessellation
Equivalent triangle meshmax(A,C) ×××× max(B,D) + min(A,C) + min(B,D) + 1
Comparison – bi-cubicAssume A=B=C=D4A + 16 vs. A^2 + 2A + 1
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9
patchestriangles
Performance - Hardware
One “clock” per degreeBi-cubic position 3
Two partial derivatives 5
Two linearly varying textures 2
total 10 clocks
Performance – SoftwareChange nothing
time to transfer data
Change tessellation (LOD)order^3 multiplies (matrix mult) + order ×××× (order-1) adds
Change geometry+ order^3 multiplies (matrix mult)
Similar to your costs…
Integer tessellationUse tessellation factor of oneUse patch normal
Fractional tessellationAlways splits once…Use tessellation factor of twoCalculate boundary mid point using subdivisionUse patch normal
Mixing with Meshes
Tangents, Normals & Bi-Normals
Autonormal – Standard T&LDriver does the work for you…Only use with standard T&L
Manual – Vertex ShaderCompute tangents (partial derivatives)Compute normal (cross product) in Shader
Partials are simple!Subtract rows and/or columns of control pointsTriangles too
Partial Derivatives
Skinning & Blending
Modify control points on the CPUSimpleRecalculate patch every change (frame?)
Activate union of matricesFor each patch take union of matricesInterpolate weights using a patch or patches
Continuity
Affected regionControl points neighboring boundary
ComplicationsSome control points are incident to two boundaries
SolutionProject onto a plane at the corner
Demos - Animation
Demos – LOD morphing
Examples!
Examples…
Questions, comments, feedback
• www.nvidia.com/developer
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