A Sketch-Based Interface for Detail-Preserving Mesh EditingA Sketch-Based Interface for

Detail-Preserving Mesh Editing

Andrew NealenOlga SorkineMarc Alexa

Daniel Cohen-Or

Andrew NealenOlga SorkineMarc Alexa

Daniel Cohen-Or

• A sketch-based interface...

– Feature modification (object-space silhouettes)

– Feature creation (sharp features, ridges, ravines)

• ... For detail-preserving mesh editing

– Adjust remaining geometry around the modified/created feature such that shape characteristics are preserved

Ideas and Contributions Ideas and Contributions

• Silhouette sketching• Feature sketching• Sketching a shape can be interpreted as inverse Non-Photorealistic Rendering

• A sketch-based modeling interface which uses silhouettes and sketches as input, and produces contours, ridges and ravines

Ideas and Contributions Ideas and Contributions

Sketch-Based Interfaces and ModelingSketch-Based Interfaces and Modeling

• (Some) previous work

– SKETCH [Zeleznik et al. 96]

– Teddy [Igarashi et al. 99 and 03]

– Variational implicits [Karpenko et al. 02]

– Relief [Bourguignon et al. 04]

– Sketching mesh deformations [Kho and Garland 05]

– Parametrized objects [Yang et al. 05]

– Many, many more... and (hopefully) more to come!

Inspiration and MotivationInspiration and Motivation

• The (affine) handle metaphor

– Used in (almost) every editing tool

– Nice, but can be unintuitive for specific editing tasks

• Laplacian Mesh Editing

– Preserve local detail after imposing editing constraints

[Sorkine et al. 04]

[Sorkine et al. 04] [Zhou et al. 05]

[Botsch and Kobbelt 04]

Mesh Modeling FrameworkMesh Modeling Framework

• Discrete Laplacians

=L x

n

cotangent : wij = cot ij + cot ij

( , )( , )

1i i ij j

i j Eiji j E

ww

δ x x

Mesh Modeling FrameworkMesh Modeling Framework

• Surface reconstruction

=L x

L

L

y

z

x

z

y

xn

cotangent : wij = cot ij + cot ij

( , )( , )

1i i ij j

i j Eiji j E

ww

δ x x

Implicitly compute Ti transformations by comparing 1-rings of the deformed and

non-deformed mesh

For the details see:Laplacian Mesh Editing

[Sorkine et al. 04]

z

y

x

0

Mesh Modeling FrameworkMesh Modeling Framework

• Implicit transformations

y

z

xn

=

Ti (Rotation/Scale)

L

L

LL/Ti

L/Ti

L/Ti

Ti

Ti

Mesh Modeling FrameworkMesh Modeling Framework

• Surface reconstruction

y

z

xn

=

c1

fix

L/Ti

L/Ti

L/Ti

Ti

Ti

0

c1

Mesh Modeling FrameworkMesh Modeling Framework

• Editing operations

y

z

xn

=

fixedit

c2

L/Ti

L/Ti

L/Ti

Ti

Ti

0

z

y

x

0

c1

Mesh Modeling FrameworkMesh Modeling Framework

• Least-Squares solution

y

z

xn

=

fixw1 w1edit

c2

w2 w2

wLi wLi

L

L

LL/Ti

L/Ti

L/Ti

Ti

Ti

A x = bATA x = bAT

(ATA)-1x = bAT

Normal Equations

Silhouette SketchingSilhouette Sketching

• Using silhouettes as handles

– Detect object space silhouette

– Project to screen space and parametrize [0,1]

– Parametrize sketch [0,1]

– Find correspondences

Silhouette SketchingSilhouette Sketching

• Using silhouettes as handles

– Detect object space silhouette

– Project to screen space and parametrize [0,1]

– Parametrize sketch [0,1]

– Find correspondences

– Use as positional constraintswhile retaining depth value

Silhouette SketchingSilhouette Sketching

• What is a good silhouette?

view

er

Silhouette SketchingSilhouette Sketching

• What is a good silhouette?

view

er

Illustrating Smooth Surfaces[Hertzmann and Zorin 00]

c1

Silhouette SketchingSilhouette Sketching

• On edge constraints

y

z

xn

=

fixw1 w1edit

c2

w2 w2

wLi wLi

edit

xi + (1-) xj

c3w3 w3

L/Ti

L/Ti

L/Ti

Ti

Ti

0

Silhouette SketchingSilhouette Sketching

• Approximate sketching

– Balance weighting between detail and positional constraints

Silhouette SketchingSilhouette Sketching

• Approximate sketching

– Balance weighting between detail and positional constraints

• We wish to influence (discrete) differential properties of the mesh for arbitrary sketches

• Possible solution

– Cut existing polygons along the sketch and add new edges

• Our solution

– Adjust mesh geometry to lie under the sketch (as seen from the camera), while preserving mesh topology and ensuring well shaped triangles

Feature Sketching Feature Sketching

screen

v1

v2

n

Geometry AdjustmentGeometry Adjustment

• First: min cost edge path (close to sketch)

– Potentially jaggy appearance

sketch

vO

(orthographic) viewer

(schematic) cross-section

tangent plane

vOC

n

Geometry AdjustmentGeometry Adjustment

• Second: projection onto sketch

screensketchvSvSC

n

v1

v2

vO

(orthographic) viewer

tangent plane

vOC

n

Geometry AdjustmentGeometry Adjustment

• Second: projection onto sketch

– Approximates the sketch very well

– Can introduce badly shaped tri‘s

screensketchvSvSC

n

v1

v2

vO

(orthographic) viewer

vOC

n

Geometry AdjustmentGeometry Adjustment

• Third: local mesh regularization

– Ask uniformly weighted Laplacian to become cotangent weighted Laplacian, while fixing path vertices

v1

v2

screensketch

v´1

v´2

cotangent

umbrella

x = L

fix

=L x

vOC

n

Geometry AdjustmentGeometry Adjustment

• Third: local mesh regularization

– Well shaped triangles and nice piecewise linear approximation of the users sketch

screensketch

v´1

v´2

cotangent

x = L

fix

=L x

vOC

n

Feature EditFeature Edit

• Edit: scale (or add to) Laplacians

v´1

v´2

cotangent

Feature EditFeature Edit

• Edit: scale (or add to) Laplacians

v´1

v´2

cotangent

n

Feature EditFeature Edit

v´1

v´2

cotangent

n

c1

Laplacian ConstraintsLaplacian Constraints

• Scale (or add to) Laplacians

y

z

xn

=

fixw1 w1

wLi wLiL/Ti

L/Ti

L/Ti

Ti

Ti

0

z

y

x

ATA x = bAT

(ATA)-1x = bAT

Normal Equations

Contour EditContour Edit

n nv

nr

radial plane

nr

Contour EditContour Edit

n nv

nr

radial plane

nr

Contour EditContour Edit

radial curvature Inflection line

Contour EditContour Edit

Editing Session (1)Editing Session (1)

Editing Session (2)Editing Session (2)

Editing Session (3)Editing Session (3)

Editing Session (4)Editing Session (4)

Editing Session ResultEditing Session Result

Discussion…Discussion…

• The good...

– Intuitive, sketch-based User Interface for silhouette deformation and feature creation/modification

– Fast model updates after sketch (Iterative Modeling)

– Preserves surface detail as much as possible

• ... and the not so good

– Object-Space sil‘s useless in the presence of heavy noise

– Editing differential properties can take time to learn

Thank You!Thank You!

• Contact Information

Andrew Nealennealen@informatik.tu-darmstadt.de

Olga Sorkinesorkine@tau.ac.il

Marc Alexaalexa@informatik.tu-darmstadt.de

Daniel Cohen-Ordcor@post.tau.ac.il

Noisy Surface SilhouetteNoisy Surface Silhouette