Feature-based Surface Feature-based Surface Decomposition for Decomposition for

Correspondence and Morphing Correspondence and Morphing between Polyhedrabetween Polyhedra

Arthur D GregoryAndrei State, Ming C Lin, Dinesh Manocha, Mark A Livingston

University of North Carolina at Chapel Hill

http://www.cs.unc.edu/~geom/3Dmorphing{gregory,andrei,lin,dm,livingst}@cs.unc.edu

HighlightsHighlights

Empower animators to create a visually pleasing morph

Simple user interfaceGeneral

Previous WorkPrevious Work

Kanai et al. [1997] DeCarlo and Gallier [1996]Galin and Akkouche [1996] Lazarus and Verroust [1994]Kent, Carlson, and Parent [1992]Kaul and Rossignac [1991]Wyvill [1990]

OverviewOverview

Two Input Polyhedra

Edit trajectories

User

Interpolatetrajectories

Morphing sequence

SpecifyCorrespondence

Compute mergedpolyhedron

Correspondence Correspondence SpecificationSpecification

Correspondence Correspondence ComputationComputationFeature-Nets decompose input polyhedra into

morphing patchesFor each corresponding Morphing Patch pair:

– map both onto a 2D polygon– merge the vertex-edge graphs– reconstruct the facets

Correspondence Correspondence ComputationComputation

A (Igloo) B (House)

Correspondence Correspondence ComputationComputation

Extremal Vertices

Patch A Patch B

MappingMapping

Patch A Patch B

Mapping Mapping DesiderataDesiderata

MergingMerging

Patch A Patch B

ReconstructionReconstruction

Completed Completed CorrespondenceCorrespondence

Morphing Trajectory Morphing Trajectory SpecificationSpecification

AnalysisAnalysis

Computation time = O(K*[m+n])

K = max{log Q,Q} m = vertices in A n = vertices in B

ImplementationImplementation

Implemented in C++ Uses OpenGL and Tcl/Tk libraries for

display and user interface.Interactive user interface on SGI and PC

systems

PerformancePerformance

Models Igloo-House Triceratops-Human Human Heads Donut-Cup

Triangles 82 40 5,660 17,528 3,426 4,020 4,096 8,452

OutputTriangles

MorphingPatches

UserTime

Time toComputeMerged Polyhedron

214 97,900 32,520 61,701

10 86 67 50

~5min ~6 hours ~3 hours ~4 hours

<1sec 2.5min 30 sec 1 min

Ongoing EffortsOngoing Efforts

Remove restriction that the chains of the feature net must lie on edges of the models

Do not require the user to specify a connected feature net

Provide better control of the model’s shape during the morph

Ongoing EffortsOngoing Efforts

Remove restriction that models must be homeomorphic– models can change topology during the

morphExtend to include textured objects

– currently interpolate only normals and vertex color

System System Architecture Architecture

ConclusionConclusion

Empower animators to create a visually pleasing morph

Simple user interfaceCompute correspondence through surface

decompositionGeneral