1

A Sketch-Based Interface for Detail-Preserving Mesh EditingAndrew Nealen / Olga Sorkine / Mark Alexa / Daniel Cohen-Or

SoHyeon Jeong2007/03/02

1AbstractIntuitive editing of surface meshesView-dependent sketchingVS handle-based deformation MethodBy silhouette selection and cropping By sketching directly onto the surfaceResultEdit new view-dependent handle positionIndirectly influencing differential properties along the sketch22ContentsIntroductionMesh modeling frameworkSilhouette sketchingFeature and contour sketchingGeometry adjustmentSharp featuresSmooth features and suggestive contoursDiscussion331. Introduction A Sketch-Based Interface Detail-Preserving4Sketch-based shape EditingEditing silhouette & suggestive contours

55Silhouette!The human visual system uses silhouettes as the first index into its memory of shapesWithout color, shading or texture But by their contours

Easily recognized silhouettes

[D.Hoffman et al.]66Sketch-based Shape Modeling Creating 3D shape by sketching its SilhouetteSKETCH : Zeleznik et al. 1996Teddy : Igarashi et al. 1999Karpenko et al. 2002Igarashi and Hughes 2003Bourguignon et al. 2004

[SKETCH][Teddy][Kerpenko et al.][Bourguignon et al.]

77Inverse NPRUser can sketch a curve which becomes feature lineContour or suggestive contours3D2DNPRSketch

[DeCarlo et al. 2003]

[Zeleznik et al. 1996]88Preserving FeaturesPreserving the global and local geometric features of a model during editingThe use of Laplacian/Poisson mesh modelsConstraints on the normals and the curvatureAllows constraint to be placed on virtual vertices

Users only suggest feature linesProperties of sketch can not always be accommodates exactly to preserve feature of the shape

992. Mesh Modeling FrameworkLaplacian with Least Squares Method10Least Squares MethodSolving an equationApproximating an equation

1111Least Squares MethodFinding the closest of given sampled data (constraint)Minimizing the distances

SolutionLinear : the zero of differentiation, closed-form solution

Non-linear : iterative method

The equation form that is approximated

1212Least Squares An ExampleFinding x which minimizes distances from sample data12, 3, 8, 5, 24Distances : Finding the zero of the differential equation

1313Laplacian Surface EditingLaplacian Relative coordinate of the center of neighbor-verticesContains local intrinsic features of a shape

Preserving local detail

[Sorkine et al. 04]

1414Modeling FrameworkLaplacian in the least squares [Alexa 2003; Lipman et al. 2004]Linear modeling constraintDifferential properties of the original geometry

Solving linear system of the form in least squares

According to normal equations

: The Laplace operator

: Vertices of original geometry: Constraint?: Deformed vertices1515Modeling FrameworkLaplacian of :

Weight : cotangent weight [Meyer et al. 2003] and

is proportional to the mean curvature around vertex i is the degree of vertex i

1616Laplacian in the form of a MatrixExample

v1v2v3v4v5v0

1717Laplacian in the form of a MatrixSolving

Pre-computed for each ROI(Factorized)18183. Silhouette Sketching19The ideaDefine a Region of Interest on the surfaceand a camera viewpoint

Select one of the resulting silhouette

Sketch a new shape for this silhouette

2020Computation of SilhouetteObject space silhouette+ switch between edge silhouettes and smooth surface silhouettes

Silhouette point on a edge its normal satisfy

2121Edge Detection [Hertzmann 1999]Normal

perpendicularview

2222Suggested new silhouette SegmentTransforming the silhouette in 3D to 2D screen space Mapping 2D silhouette with sketch [0,1] Transforming new position back to 3D (as position constraint)

23234. Feature and Contour Sketching Geometry adjustment Sharp features Smooth features and suggestive contours24Geometry AdjustmentAdjust the mesh geometry to accommodate such a feature directly under the sketch

Increase mesh complexityPreserve mesh topology

2525Finding Edge PathWeighted shortest path problem which minimizes distance from sketch

screenv1v2n

sketchvO(orthographic) viewer(schematic) cross-section2626Adjust the Geometry under SketchMove vertex along its tangent plane

tangent planevOCnscreensketchvSvSCnv1v2vO(orthographic) viewer2727Relax the Area around the SketchRemove badly shaped triangle

vOCnscreensketchv1v2dcotangentx=dLfix

2828

vOCnFeature EditEdit: scale (or add to) Laplaciansv1v2dcotangent29

Feature EditEdit: scale (or add to) Laplaciansv1v2dcotangentn

30

Feature Editv1v2dcotangentn

31

Contour Editnnvnrradial planenr3232

Contour Editnnvnrradial planenr

3333

Contour Editradial curvature Inflection line

3434Contour Edit

35355. Discussion36The Quality of shape editingTime required by systemUpdate time is a potential bottleneck To solve linear systems (P4/2.0 GHz)

How well the shape change This have improved

5.5K12K33KFactorization0.72.57.0Substitution0.0350.070.25(Second)3737