Hierarchical Deformation of Locally Rigid Meshes Josiah Manson and - - PowerPoint PPT Presentation

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Hierarchical Deformation of Locally Rigid Meshes Josiah Manson and - - PowerPoint PPT Presentation

Apr 03, 2023 236 likes •877 views

Hierarchical Deformation of Locally Rigid Meshes Josiah Manson and Scott Schaefer Motivation Simplified control of deformation Motivation Simplified control of deformation Motivation Simplified control of deformation No

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SLIDE 1

Hierarchical Deformation of Locally Rigid Meshes

Josiah Manson and Scott Schaefer

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Motivation

  • Simplified control of deformation
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SLIDE 3

Motivation

  • Simplified control of deformation
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SLIDE 4

Motivation

  • Simplified control of deformation
  • No auxiliary control structures
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Motivation

  • Simplified control of deformation
  • No auxiliary control structures
  • Arbitrary mesh connectivity
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SLIDE 6

Motivation

  • Simplified control of deformation
  • No auxiliary control structures
  • Arbitrary mesh connectivity
  • Fast feedback
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SLIDE 7

Auxiliary Controls

Skeletons

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SLIDE 8

Auxiliary Controls

[Sederberg and Parry 1986]

Grids

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Auxiliary Controls

[Ju et al. 2005] [Joshi et al. 2007]

Cages

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Intrinsic Controls

Subdivision control mesh

[Catmull and Clark 1978]

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SLIDE 11

Intrinsic Controls

[Sorkine and Alexa 2007] [Botsch et al. 2006]

Thin shell simulation

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SLIDE 12

Intrinsic Controls

Volumetric simulation

[Mezger et al. 2007]

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SLIDE 13

Intrinsic Controls

Vibrational modes

[Hildebrandt et al. 2012]

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SLIDE 14

Our Solution

  • Simplify the mesh
  • Perform physical simulation
  • Add details conforming to the simulation
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SLIDE 15
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Mesh Simplification

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Mesh Simplification

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Mesh Simplification

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Mesh Simplification

.9 .9 .4 .8 .6 .5 .7 .7 .1 .4 .3 .7 .5 .3 .1 .4 .5 .2 .7 .2 .3 .4 .7 .1 .6 .5 .8 .2 .6 .2 .5 .4 .7 .3 .7 .3 .7 .3

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Mesh Simplification

.9 .9 .4 .8 .6 .5 .7 .7 .1 .4 .3 .7 .5 .3 .1 .4 .5 .2 .7 .2 .3 .4 .7 .1 .6 .5 .8 .2 .6 .2 .5 .4 .7 .3 .7 .3 .7 .3

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Mesh Simplification

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Mesh Simplification

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SLIDE 23

Mesh Simplification

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Mesh Simplification

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Mesh Simplification

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Edge Collapse Metric

Distance to planes Distance to points

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SLIDE 27

Edge Collapse Metric

Distance to planes Distance to points

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SLIDE 28

Edge Collapse Metric

Distance to planes Distance to points

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As-rigid-as-possible Deformation

  • As-rigid-as-possible surface modeling

[Sorkine and Alexa 2007]

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As-rigid-as-possible Deformation

  • As-rigid-as-possible surface modeling

[Sorkine and Alexa 2007]

  • Added ability to satisfy constraints not at

mesh vertices

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SLIDE 31

As-rigid-as-possible Deformation

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As-rigid-as-possible Deformation

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SLIDE 33

As-rigid-as-possible Deformation

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SLIDE 34

Adding Details

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SLIDE 35

Adding Details

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SLIDE 36

Adding Details

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SLIDE 37

Adding Details

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SLIDE 38

Adding Details

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SLIDE 39

Adding Details

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Adding Details

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Adding Details

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Adding Details

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SLIDE 43

Adding Details

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Adding Details

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Adding Details

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Adding Details

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SLIDE 47

Adding Details

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Adding Details Constrained

  • Deform local neighborhood before expansion
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SLIDE 49

Adding Details Constrained

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Adding Details Constrained

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Results

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SLIDE 52

Results

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SLIDE 53

Convergence Time

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Benefits of Simplification

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Benefits of Simplification

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Benefits of Simplification

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Benefits of Simplification

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SLIDE 58
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Different Transforms

Rigid Similarity Stretch

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Conclusion

  • Calculate deformation at low resolution
  • Expand to high resolution

– As-rigid-as-possible, satisfy constraints – Use a local, symmetric expansion operation

  • Combine with other methods

– Different deformation of base mesh – As-similar-as-possible, tangential stretch

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SLIDE 61
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SLIDE 62

Multiresolution Signal Processing for Meshes

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SLIDE 63

Convergence Iterations