Fast Non-Linear Projections using Graphics Hardware

1
Fast Non-Linear Projections using Graphics
Hardware

• Jean-Dominique Gascuel, Nicolas Holzschuch,
  Gabriel Fournier, Bernard Péroche
• I3D 2008

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Non-linear projections What Why ?
wiki.panotools.org, Ben Kreunen
lensmateonline.com
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Motivations
Heidrich Seidel,1998Introduced Parabola
envmaps
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Previous work

• Kautz 2004 CPU rasterization
• Close papers
• Fournier 2005 Indirect illumination
• Loyd 2006 Logarithmic shadow maps
• Hou 2006 Multi perspective reflections
• Liu 2007 Non linear beam tracing
• GPU based, same rendering pipeline FS

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Our contributions

• Targeted to a specific class of non-linear
  projections
• Single center of projection
• Convex, C1, and invertible
• Each triangle maps to one simple shape.
• Simple equations for projected edges.
• Fast
• ? x2 to x4 times faster than cubemaps or
  hemicubes.
• Everything is done on the GPU

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Plan

• Introduction
• Case studies
• Sphere projection
• Parabola projection
• Other projections
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Sphere projection 1/5
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Sphere projection 2/5
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Sphere projection 3/5
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Sphere projection 4/5
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Sphere projection 5/5
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Triangles made of known ellipses

• Looking at the2D screen

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Plan

• Introduction
• Case studies
• Sphere projection
• Parabola projection
• Other projections
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Parabola projection 1/3
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Parabola projection 2/3
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Parabola projection 3/3
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Parabola 3D line ? 2D circle 1/2
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Triangles made of arcs 2/2
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Plan

• Introduction
• Case studies
• Sphere projection
• Parabola projection
• Other projections
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Other projections

• Fisheyes
• arcs with
• single minimum in normal direction,
• possible maximumat extremities.

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Application-driven choice

• Sphere
• lighting ? solid angle x cos
• Parabola
• envmaps ? less distortions
• Lambert
• ambient occlusion ? equal area
• Fish eye 2
• Ideal photographic fish-eye

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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Rendering strategy
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FS Ray-casting

• FS discards pixels outside original 3D triangle
• unproject 2D fragment coordinates ? 3D ray
  direction
• ray/triangle intersection

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FS Interpolations

• Mimic linear interpolation inside the 3D triangle
• ? Non-linear interpolation in 2D screen
• For all vertex varying attributes normals,
  colors, texture coordinates, etc.
• Ray-intersect gives barycentric coordinates a, ß
• ? dot product (1, a, ß) . (C0, C1-C0, C2-C0)

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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Basic Triangle
• Near plane Clipping
• Concave Covering Triangle
• Quad Based Bounding
• Demo Results
• Conclusion

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Bounding triangle 1/2
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Bounding Triangle 2/2
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Triangle Covering
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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Basic Triangle
• Near plane Clipping
• Concave Covering Triangle
• Quad Based Bounding
• Demo Results
• Conclusion

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Bellow horizon
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Camera Plane Clipping 1/3
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Camera Plane Clipping 2/3
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Camera Plane Clipping 3/3
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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Basic Triangle
• Near plane Clipping
• Concave Covering Triangle
• Quad Based Bounding
• Demo Results
• Conclusion

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Concave Covering Triangle 1/2
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Concave Covering Triangle 2/2

• 1 input triangle ? 1 to 4 bounding triangles

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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Needed because

1. We dont have easy tangents for Fisheyes
   projections
2. G80 geometry shader take worst case timing4
   output triangles in some rare case ? x4 slowdown
   everywhere in GS

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Oriented Bounding Box

• Easy for a single ellipse.

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Quad coverage scheme

• Merge extremal points into a single aaBB

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Parabola projection

• Bent triangles are made of circles
• Any axis will work.
• ? optimal axis aligned bounding box

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Generic bounding scheme
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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Example scenes

• Lemmings

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Triangles

• 37 overdraw

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Aligned bbox
107 overdraw But FASTER on G80
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Test scene 2/4

• Cubemaps/hemicube

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Test scene 3/4

• Columns Thin triangles,
• With large deformations

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Test scenes 4/4

• Sphere 560K triangles
•  Real life 

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Inside the OpenGL pipeline

• Facades

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Cubemap vs. Parabola-map

• Better quality than cubemaps
• Heidrich, Laine, Osman
• Lower memory footprint
• Low triangle scenes x2 to x4 speedups (better
  on hi res)

Color(ms) Depth (ms) Coverage(ms)
6 x 512x512 cubemaps2x 512x512 parabola 2590716 548 157 490 121
6 x 16x16 cubemaps2 x 16x16 parabola 8.83.4 5.2 2.6 4.8 2.2
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Hemicube vs non-linear projection
Color(ms) Depth (ms) Coverage(ms)
5 512 512 hemicube 1 512 512 parabola 1 512 512 sphere map 1 512 512 Lambert 1500 375 433 396 375 79 71 80 320 61 61 67
5 16 16 hemicube 1 16 16 parabola 7.1 2.5 4.3 1.9 4.0 1.6

• Low triangle scenes
• x2.5 to x5 speedups (better on hi res)

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Plan

• Introduction
• Case studies
• Rendering Pipeline
• Triangle Based Bounding
• Quad Based Bounding
• Demo Results
• Conclusion

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Conclusion

• Implemented Non-linear projections on GPU
• Specific class of projections, useful for many
  applications
• Tight bounding shapes
• Faster than cubemaps
• Projections
• Parabola optimal BB ? fast overall computations
• Sphere sub-optimal BB, still fast
• Other (Lambert/Fisheye) generic BB, lots of
  overdraw
• Full sources at http//artis.inrialpes.fr/Publicat
  ions

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Future Directions

• Better quad bounding for Lambert fisheye
• Should be Sphere projection
• Improve GS bottleneck
• Faster, not worst case based (NVidias job)
• Multi pass triangle bounding
• Multiple layers rendering (all faces at once)
• Deferred shading
• Benchmark within a local/global lighting
  framework.