SCAF: Simplicial Complex Augmentation Framework for Bijective Maps - - PowerPoint PPT Presentation

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scaf simplicial complex augmentation framework for

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps - - PowerPoint PPT Presentation

Oct 26, 2022 37 likes •1.3k views

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps Zhongshi Jiang, New York University Scott Schaefer, Texas A&M University Daniele Panozzo, New York University Maps Simplicial Complex Augmentation Zhongshi Jiang 2

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SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Zhongshi Jiang, New York University Scott Schaefer, Texas A&M University Daniele Panozzo, New York University

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Maps

Simplicial Complex Augmentation Framework for Bijective Maps 2

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Zhongshi Jiang

Better Maps

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Distortion

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Distortion

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Distortion

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Overlap O v e r l a p p i n g Distortion

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Better Maps

Overlap O v e r l a p p i n g Distortion

Simplicial Complex Augmentation Framework for Bijective Maps 3

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Zhongshi Jiang

Overlapping

Simplicial Complex Augmentation Framework for Bijective Maps 4

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Zhongshi Jiang

Overlapping

Simplicial Complex Augmentation Framework for Bijective Maps 5

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Zhongshi Jiang

Overlapping

Simplicial Complex Augmentation Framework for Bijective Maps 6

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Zhongshi Jiang

Overlapping

Local Flip

Simplicial Complex Augmentation Framework for Bijective Maps 6

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Zhongshi Jiang

Overlapping

Local Flip

Simplicial Complex Augmentation Framework for Bijective Maps 6

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Zhongshi Jiang

Overlapping

Local Flip

Simplicial Complex Augmentation Framework for Bijective Maps 6

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Zhongshi Jiang

Overlapping

Local Flip

Simplicial Complex Augmentation Framework for Bijective Maps 7

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Zhongshi Jiang

Overlapping

Local Flip

Simplicial Complex Augmentation Framework for Bijective Maps 8

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Zhongshi Jiang

Overlapping

Local Flip

Global Overlap

Simplicial Complex Augmentation Framework for Bijective Maps 8

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 9

Locally Injective Maps Bijective Maps Results Comparisons

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 10

Locally Injective Maps Bijective Maps Results Comparisons

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Zhongshi Jiang

Bijective Condition: Local

Simplicial Complex Augmentation Framework for Bijective Maps 11

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Zhongshi Jiang

Symmetric Dirichlet Energy

Simplicial Complex Augmentation Framework for Bijective Maps 12

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Zhongshi Jiang

Symmetric Dirichlet Energy

Simplicial Complex Augmentation Framework for Bijective Maps 12

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Zhongshi Jiang

Symmetric Dirichlet Energy

Simplicial Complex Augmentation Framework for Bijective Maps 13

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Zhongshi Jiang

Symmetric Dirichlet Energy

Simplicial Complex Augmentation Framework for Bijective Maps 14

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

4

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

4

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Zhongshi Jiang

Symmetric Dirichlet Energy

Reference Triangle

Simplicial Complex Augmentation Framework for Bijective Maps 14

4

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Zhongshi Jiang

Locally Injective Mappings

Simplicial Complex Augmentation Framework for Bijective Maps 15 [ CM: Shtengel et al 2017] [SLIM: Rabinovich et al 2017] [AQP: Kovalsky et al 2016] [AKVP: Claci et al 2016] [LIM: Schueller et al 2013]

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Zhongshi Jiang

Scalable Locally Injective Mappings

Simplicial Complex Augmentation Framework for Bijective Maps 16

Rotation Invariance Energies [Rabinovich et al 2017]

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Zhongshi Jiang

Scalable Locally Injective Mappings

Simplicial Complex Augmentation Framework for Bijective Maps 16

Rotation Invariance Energies [Rabinovich et al 2017]

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Zhongshi Jiang

Scalable Locally Injective Mappings

Simplicial Complex Augmentation Framework for Bijective Maps 16

Rotation Invariance Energies [Rabinovich et al 2017]

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Zhongshi Jiang

Scalable Locally Injective Mappings

Simplicial Complex Augmentation Framework for Bijective Maps 16

Rotation Invariance Energies [Rabinovich et al 2017]

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 17

Locally Injective Maps Bijective Maps Results Comparisons

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Zhongshi Jiang

Bijective Condition: Global

Simplicial Complex Augmentation Framework for Bijective Maps 18

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Zhongshi Jiang

Bijective Maps: Smith and Schaefer 2015

Collision Detection on

Boundary

Local Support Energy

Simplicial Complex Augmentation Framework for Bijective Maps 19

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Zhongshi Jiang

Scaffold: Natural Collision Detector

Simplicial Complex Augmentation Framework for Bijective Maps 20

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Zhongshi Jiang

Scaffold: Natural Collision Detector

Simplicial Complex Augmentation Framework for Bijective Maps

Ground

21

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Zhongshi Jiang

Scaffold Pipeline

Simplicial Complex Augmentation Framework for Bijective Maps 22

[Zhang et al 2005]

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Zhongshi Jiang

Scaffold Pipeline

Simplicial Complex Augmentation Framework for Bijective Maps 22

[Zhang et al 2005] [Tutte 1963]

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Zhongshi Jiang

Scaffold Pipeline

Simplicial Complex Augmentation Framework for Bijective Maps 22

[Zhang et al 2005] [Tutte 1963]

Build Scaffold

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Zhongshi Jiang

Scaffold Pipeline

Simplicial Complex Augmentation Framework for Bijective Maps 22

[Zhang et al 2005]

Tutte Embedding

[Tutte 1963]

Build Scaffold
Valid Interior Deformation

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 23

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 23

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 23

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 24

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 25

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 25

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 25

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Zhongshi Jiang

Scaffold Restricts

Simplicial Complex Augmentation Framework for Bijective Maps 25

local

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

Start from Identity

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

Start from Identity
Deform Arbitrarily

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

Start from Identity
Deform Arbitrarily
Bounce Back

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

Start from Identity
Deform Arbitrarily
Bounce Back

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Zhongshi Jiang

More Progressive

[Müller et al 2015]

Simplicial Complex Augmentation Framework for Bijective Maps 26

Start from Identity
Deform Arbitrarily
Bounce Back

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Zhongshi Jiang

Scaffold

Simplicial Complex Augmentation Framework for Bijective Maps 27

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Zhongshi Jiang

Scaffold Helps

Simplicial Complex Augmentation Framework for Bijective Maps 28

global

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Zhongshi Jiang

Scaffold Helps

Simplicial Complex Augmentation Framework for Bijective Maps 29

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SCAF Helps

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SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Simplicial Complex Augmentation Framework for Bijective Maps 31

Previous
Local Knowledge
Collision Detection

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 32

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 33

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 34

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Zhongshi Jiang

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

Scaffold Optimization
Global Knowledge
Collision Resolution

Simplicial Complex Augmentation Framework for Bijective Maps 34

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Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 35

coordinates

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Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 35

coordinates

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Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 35

coordinates

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Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 35

coordinates

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Zhongshi Jiang

Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 36

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Zhongshi Jiang

Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 36

[Rabinovich et al 2017]

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Zhongshi Jiang

Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 37

[Rabinovich et al 2017]

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Zhongshi Jiang

Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 37

[Rabinovich et al 2017]

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Zhongshi Jiang

Formulation

Simplicial Complex Augmentation Framework for Bijective Maps 37

[Rabinovich et al 2017]

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Zhongshi Jiang

Triangulation

Local Update
Edge Flip

Simplicial Complex Augmentation Framework for Bijective Maps 38

[Müller et al 2015] [Zhang et al 2005]

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Zhongshi Jiang

Triangulation

Local Update
Edge Flip

Simplicial Complex Augmentation Framework for Bijective Maps 38

[Müller et al 2015] [Zhang et al 2005]

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Zhongshi Jiang

Triangulation

Local Update
Edge Flip

Simplicial Complex Augmentation Framework for Bijective Maps 39

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Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 40

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 40

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 40

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 40

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 41

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 41

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 42

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 43

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Zhongshi Jiang

Triangulation

Direct reconstruct
Coarse

Simplicial Complex Augmentation Framework for Bijective Maps 44

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 45

Locally Injective Maps Bijective Maps Results Comparisons

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Result

Simplicial Complex Augmentation Framework for Bijective Maps 46

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Zhongshi Jiang

Robustness

Global Parameterization

Dataset [Myles et al 2014]

119 meshes cut by [Bommes et al.

2009] [Myles et al. 2014]

Simplicial Complex Augmentation Framework for Bijective Maps 47

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Robustness

Global Parameterization

Dataset [Myles et al 2014]

119 meshes cut by [Bommes et al.

2009] [Myles et al. 2014]

Simplicial Complex Augmentation Framework for Bijective Maps 47

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Robustness

Simplicial Complex Augmentation Framework for Bijective Maps 48

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Zhongshi Jiang

Robustness

Simplicial Complex Augmentation Framework for Bijective Maps 48

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Robustness

Simplicial Complex Augmentation Framework for Bijective Maps 48

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Same Formulation
Different Tessellation
TetGen [Si 2015]
Local Operations [Klinger 2009]

Volume

Simplicial Complex Augmentation Framework for Bijective Maps 49

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Zhongshi Jiang

Same Formulation
Different Tessellation
TetGen [Si 2015]
Local Operations [Klinger 2009]

Volume

Simplicial Complex Augmentation Framework for Bijective Maps 49

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Zhongshi Jiang

Same Formulation
Different Tessellation
TetGen [Si 2015]
Local Operations [Klinger 2009]

Volume

Simplicial Complex Augmentation Framework for Bijective Maps 49

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 50

Locally Injective Maps Bijective Maps Results Comparisons

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Zhongshi Jiang

Quality

Simplicial Complex Augmentation Framework for Bijective Maps 51

[Smith and Schaefer 2015]

Ours

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Zhongshi Jiang

Quality

9K faces

Simplicial Complex Augmentation Framework for Bijective Maps 52

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Zhongshi Jiang

Quality

9K faces

Simplicial Complex Augmentation Framework for Bijective Maps 52

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Zhongshi Jiang

Quality

[Smith and Schaefer 2015]: 2 hour 20 min 9K faces

Simplicial Complex Augmentation Framework for Bijective Maps 52

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Zhongshi Jiang

Quality

[Smith and Schaefer 2015]: 2 hour 20 min < 2 min 9K faces

Simplicial Complex Augmentation Framework for Bijective Maps 52

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Zhongshi Jiang

Efficiency

80K faces

Simplicial Complex Augmentation Framework for Bijective Maps 53

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Zhongshi Jiang

Efficiency

80K faces

Simplicial Complex Augmentation Framework for Bijective Maps 53

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Zhongshi Jiang

Efficiency

80K faces < 40 min

Simplicial Complex Augmentation Framework for Bijective Maps 53

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Zhongshi Jiang

Efficiency

Over 5 days!

80K faces < 40 min

Simplicial Complex Augmentation Framework for Bijective Maps 53

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Zhongshi Jiang

Efficiency

Over 5 days!

80K faces < 40 min

Simplicial Complex Augmentation Framework for Bijective Maps 53

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Zhongshi Jiang

Scalability

Inherited from SLIM [Rabinovich et al. 2017]

Simplicial Complex Augmentation Framework for Bijective Maps 54

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Limitations

Local Minimum
Valid Initialization
Easy in 2D
Hard in 3D
Implementation in 3D
Less Efficient
More Involved

Simplicial Complex Augmentation Framework for Bijective Maps 55

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Zhongshi Jiang Simplicial Complex Augmentation Framework for Bijective Maps 56

Efficient Scalable Robust

SCAF: Simplicial Complex Augmentation Framework for Bijective Maps

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Zhongshi Jiang

The authors acknowledge funding from the NSF CAREER awards IIS-1652515 and IIS- 1148976, and a gift from Adobe. We would like to thank Michael Rabinovich and Roi Poranne for providing the source code and Lucy models for [Rabinovich et al. 2017], Leonardo Sacht for providing the source code and Leg model for [Sacht et al. 2013], and the anonymous reviewers for their insightful comments and suggestions.

Thank You!

https://github.com/jiangzhongshi/scaffold-map

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