Fast Non-Linear Projections using Graphics Hardware

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Fast Non-Linear Projections using Graphics Hardware

Jean-Dominique Gascuel, Nicolas Holzschuch, Gabriel Fournier, Bernard Péroche

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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.

Fast Non-Linear Projections using Graphics Hardware

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