3D Modeling for EveryoneHsueh-Ti Derek Liu
University of Toronto
3D modeling
Spectral geometry
SIGGRAPH Asia 2018 ICLR 2019 SIGGRAPH Asia 2019 SIGGRAPH 2020
SGP 2017 SIGGRAPH 2019 Eurographics 2019 SIGGRAPH Asia 2020
Image Editing
3D scanning
medium.com
Macworld.com
OmniVirt.com
3D display
Advances in 3D Technology
3D Modeling
3D Modeling is Hard
2D Analogue
Make 3D modeling available for everyone
3D modeling is a long-standing problem
blender cloud - springVaxman et al. 2018
wikimedia autodesk
Classic 3D Modeling
primitive shape Today
?
Acquiring 3D data is easy nowadays
3D scanning
medium.com
3D datasets
Thingi10K
Future 3D Modeling
primitive shape complex shape
?novelperspectives
Geometric filtering 3D Stylization Data-driven subdivision
appearancenormal
prior
Geometric FilteringHsueh-Ti Derek Liu, Michael Tao, Alec Jacobson, “Paparazzi: Surface Editing by way of Multi-View Image Processing ”, SIGGRAPH Asia 2018
Image Filters
Geometric Filters
Complex Filters?
[Gatys et al. 2016]
?
Appearance-driven Editing
Hsueh-Ti Derek Liu, Michael Tao, Alec Jacobson, “Paparazzi: Surface Editing by way of Multi-View Image Processing ”, SIGGRAPH Asia 2018
Appearance-driven EditingV
R(V)
rendering
differentiable renderer ∂R∂V
image
filteri
ng
R′ (V)
Rendering Means to an End
… ?
A Simple Differentiable Renderer
Lambertian material
Flat shading orthographic camera
directional lights
orthographic projection
A Simple Differentiable Renderer
Lambertian material
Flat shading
directional lights DifferentiableSimple
Fast
Rendering as a tool for visualization Rendering as a tool for 3D modeling
3D StylizationHsueh-Ti Derek Liu, Alec Jacobson, “Cubic Stylization”, SIGGRAPH Asia 2019
Stylization3D 2D
non-photorealistic rendering [Hertzmann, Zorin 2000]
image stylization [Gatys et al. 2016]
2D 2D 3D 3D
3D stylization
?
Cubic Stylization
Chichén Itzá
source: wikimedia.org Feathered Serpent
source: wikimedia.org Block Statue
Egypt
United Kingdom
Draped Seated Woman by Henry Moore
© puffin11k
Taiwan
Taichi by Ju Ming source: wikimedia.org
© Art Poskanzer
!e Kiss by Constantin Brâncus
Romania
Chichén Itzá
source: wikimedia.org Feathered Serpent
source: wikimedia.org Block Statue
Egypt
United Kingdom
Draped Seated Woman by Henry Moore
© puffin11k
Taiwan
Taichi by Ju Ming source: wikimedia.org
© Art Poskanzer
!e Kiss by Constantin Brâncus
Romania
Chichén Itzá
source: wikimedia.org Feathered Serpent
source: wikimedia.org Block Statue
Egypt
United Kingdom
Taiwan
Taichi by Ju Ming source: wikimedia.org
© Art Poskanzer
!e Kiss by Constantin Brâncus
Romania
Draped Seated Woman by Henry Moore
© puffin11k
How to characterize a cube?
How to characterize a cube? 266664001
377775
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266664010
377775
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
266664100
377775
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
“cubic geometry has axis-aligned surface normals”Hsueh-Ti Derek Liu, Alec Jacobson, “Cubic Stylization”, SIGGRAPH Asia 2019
k k1 = | x | + | � |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
axis-aligned unit vector
non axis-aligned unit vectork
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
kAAADV3icfVJRjxIxEO6CnrjqCfroSyPBmBgJKLnTRMxFX3zg4UyOOxJ2Jd0yQHPd7l47q5Blf4d/wb90v0a7C5zARSdp83Xm+6aTmQliKQy2WtdOqXzn7sG9yn33wcNHh4+rtSfnJko0hz6PZKQHATMghYI+CpQwiDWwMJBwEVx+zuMX30EbEakzXMTgh2yqxERwhtY1qv5qvPCW1EOYY8rmwrxmUkwVjGmiBFIV6ZDJjHrLUZt+oJ5HXcu/ukrYmN7IVKTo/6Vu4y85K3J16XLzHs2X9NXWc7GkK/7mG0t37V2tt5qtwuht0F6DOlnb6ajm/PTGEU9CUMglM2bYbsXop0yj4BIy10sMxIxfsikMLVQsBOOnRUsz2rCeMZ1E2h6FtPBuK1IWGrMIA8sMGc7Mfix3/iuWZzQZ3SlAigBsYQr8VMEPnBd624ctZSGLgWf7+QKz2M2WFt+uqAYwZELl4mFPTBkmGkz3DAZ+2hMqmdNPIrLLk4QbLs5y7jrY25S11y6cvPNToeIEQfFVtyaJpBjRfMnoWGjgKBcWMK6FbTjlM6YZR7uKbjHK97kd3QzuNjh/02y/bXa+duon39ZDrZBn5Dl5SdrkmJyQL+SU9Al3Dp2O03U+lq5Lv8sH5cqKWnLWmqdkx8q1P9I/FK0=
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
“surface normals of the output mesh”
L1-norm on Surface Normals
Earap + ∥n( )∥1?“as-rigid-as-possible”
“surface normals of the output mesh”
L1-norm on Surface Normals
Earap + ∥n( )∥1?Non-line
ar“as-rigid-as-possible”
“rotated surface normals of the input mesh”
Rotated Input Normals
Earap + ∥R × n( )∥1
“rotated surface normals of the input mesh”
Rotated Input Normals
Earap + ∥R × n( )∥1Linear
Different “Cubeness”
Orientation Dependent
Polygonal Boxes Stylization
Characterizing a shape using surface vertices Characterizing a shape using surface normals
Data-Driven SubdivisionHsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri, Noam Aigerman, Alec Jacobson, “Neural Subdivision”, SIGGRAPH 2020
Subdivision Surfaces
Classic Subdivision[Loop 1987] ’
wi i
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
i
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
Classic Subdivision[Loop 1987] ’
wi i
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
i
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
……
Smoothness prior
Kovacs et al. 2010
Neural Subdivisionsmoothness
priordata-driven prior
Hsueh-Ti Derek Liu, Vladimir G. Kim, Siddhartha Chaudhuri, Noam Aigerman, Alec Jacobson, “Neural Subdivision”, SIGGRAPH 2020
[Loop 1987]
i
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
Subdivision Network
How to train subdivision networks
Loss function
� (
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
)
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
,
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
Training data
Network design
Machine Learning on Regular Grid
…
flaps of undirected edges [Hanocka et al. 2019]
fixed input dim. no ordering
flaps of half-edges
fixed input dim. canonical ordering
1
2
3
4
vertex rings
no fixed input dim. no ordering
Handling Irregular Mesh
rigid mo
tion
Rigid Motion Invariant
rigid mo
tion
rigid motioninvariant
Rigid Motion Invariant
Generalize when trained on single shape
training data
Generalize when trained on single shape
training data
Stylized Subdivision
Data-Driven prior
Smoothness prior Data-driven prior
Different Perspectives appearancenormal
data-driven priorPossibilities
3D Modeling for EveryoneHsueh-Ti Derek Liu
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