I3D 20081 Fast Non-Linear Projections using Graphics Hardware Jean-Dominique Gascuel, Nicolas Holzschuch, Gabriel Fournier, Bernard Péroche I3D 2008.

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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 ?

[lensmateonline.com][wiki.panotools.org, Ben Kreunen]

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Motivations

[Kautz et al., 2004]Cosine sphere for local shadows

[Heidrich & Seidel,1998]Introduced Parabola envmaps

[Osman et al., 2006]Dual parabola shadowmaps

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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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Triangles made of known ellipses

Looking at the2D screen:

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Plan

• Introduction• Case studies



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Parabola projection 1/3

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Parabola: 3D line 2D circle1/2

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Triangles made of arcs 2/2

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Plan




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Other projections…

Fisheyesarcs with: • single minimum in

normal direction,• possible maximum

at extremities.

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Application-driven choice

• Spherelighting solid angle x cos

• Parabolaenvmaps less distortions

• Lambertambient occlusion equal area

• Fish eye 2Ideal 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 α, β

dot product: (1, α, β) . (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 Triangle2/2

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Triangle Covering

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Plan




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Camera Plane Clipping 1/3

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Plan




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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


• Rendering Pipeline



• Demo & Results

• Conclusion

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Needed because

1. We don’t have easy tangents for Fisheyes projections

2. G80 geometry shader take worst case timing:

4 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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Plan

• Introduction

• Case studies




• Demo & Results

• Conclusion

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Example scenes

Lemmings

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Triangles

37% overdraw

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Aligned bbox

107% overdrawBut FASTER on G80

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Test scene2/4

Cubemaps/hemicube

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Test scene3/4

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

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

• Better quality than cubemaps

Heidrich, Laine, Osman• Lower memory footprint

• Low triangle scenes:~ x2 to x4 speedups (better on hi res)

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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




• 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/Publications

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Future Directions

• Better quad bounding for Lambert & fisheyeShould be ~ Sphere projection

• Improve GS bottleneck– Faster, not worst case based (NVidia’s job)– Multi pass triangle bounding

• Multiple layers rendering (all faces at once)

• Deferred shading

• Benchmark within a local/global lighting framework.

I3D 20081 Fast Non-Linear Projections using Graphics Hardware Jean-Dominique Gascuel, Nicolas Holzschuch, Gabriel Fournier, Bernard Péroche I3D 2008.

Documents

gpu slide

rendering strategy slide

rendering pipeline fs

dual parabola shadowmaps

bernard proche i3d

ben kreunen slide

pipeline triangle

bounding quad