Spherical Parameterization and Remeshing Emil Praun, University of Emil Praun, University of Utah Utah Hugues Hoppe, Microsoft Hugues Hoppe, Microsoft Research Research
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Spherical Parameterization and Remeshing Emil Praun, University of Utah Hugues Hoppe, Microsoft Research.
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Slide 1
Spherical Parameterization and Remeshing Emil Praun, University
of Utah Hugues Hoppe, Microsoft Research
Slide 2
Motivation: Geometry Images [Gu et al. 02] 3D geometry
completely regular sampling geometry image 257 x 257; 12
bits/channel
Slide 3
Geometry Images [Gu et al. 02] No connectivity to store No
connectivity to store Render without memory gather operations
Render without memory gather operations No vertex indices No
texture coordinates Regularity allows use of image processing tools
Regularity allows use of image processing tools Motivation:
Geometry Images
Slide 4
Spherical Parametrization geometry image 257 x 257; 12
bits/channel Genus-0 models: no a priori cuts
Slide 5
Contribution Our method: genus-0 no constraining cuts Less
distortion in map; better compression New applications: morphing
morphing GPU splines GPU splines DSP DSP
Spherical Parametrization Goals: robustness robustness good
sampling good sampling sphere S mesh M [Sander et al. 2001]
[Hormann et al. 1999] [Sander et al. 2002] [Hoppe 1996]
coarse-to-fine stretch metric coarse-to-fine stretch metric [Kent
et al. 92] [Haker et al. 2000] [Alexa 2002] [Grimm 2002] [Sheffer
et al. 2003] [Gotsman et al. 2003]
Before Vsplit: No degenerate/flipped No degenerate/flipped
1-ring kernel Apply Vsplit: No flips if V inside kernel V
Coarse-to-Fine Algorithm
Slide 11
Before Vsplit: No degenerate/flipped No degenerate/flipped
1-ring kernel Apply Vsplit: No flips if V inside kernel Optimize
stretch: No degenerate (they have stretch) V Coarse-to-Fine
Algorithm
Slide 12
Traditional Conformal Metric Preserve angles but area
compression Bad for sampling using regular grids
Slide 13
Stretch Metric [Sander et al. 2001] [Sander et al. 2002]
Penalizes undersampling Better samples the surface
Slide 14
Regularized Stretch Stretch alone is unstable Add small
fraction of inverse stretch withoutwith
Timing Results Model # faces Time Cow23,216 7 min. 7 min.
David60,000 8 min. Bunny69,630 10 min. Horse96,948 15 min.
Gargoyle200,000 23 min. Tyrannosaurus200,000 25 min. Pentium IV,
3GHz, initial code
Slide 28
Timing Results Model # faces Time Cow23,216 65 sec. David60,000
80 sec. Bunny69,630 1.5 min. Horse96,948 2.5 min. Gargoyle200,000 4
min. Tyrannosaurus200,000 Pentium IV, 3GHz, optimized code
Slide 29
Rendering interpret domain render tessellation
Slide 30
Level-of-Detail Control n=1 n=2 n=4 n=8 n=16 n=32 n=64
Smooth Geometry Images 33x33 geometry image C 1 surface GPU
3.17 ms [Losasso et al. 2003] ordinary uniform bicubic
B-spline
Slide 36
Summary original spherical parametrization geometry image
remesh
Slide 37
Conclusions Spherical parametrization Guaranteed one-to-one
Guaranteed one-to-one New construction for geometry images
Specialized to genus-0 Specialized to genus-0 No a priori cuts
better performance No a priori cuts better performance New boundary
extension rules New boundary extension rules Effective compression,
DSP, GPU splines,
Slide 38
Future Work Explore DSP on unfolded octahedron 4 singular
points at image edge midpoints 4 singular points at image edge
midpoints Fine-to-coarse integrated metric tensors Faster
parametrization; signal-specialized map Faster parametrization;
signal-specialized map Direct D S M optimization Consistent
inter-model parametrization