3D Morphing using Multiplanar Representation

3D Morphing using Multiplanar Representation

Anurag Mittal

Mahesh Ramasubramanian

Computer Science Department & Program of Computer Graphics

Cornell University

Anurag Mittal

Mahesh Ramasubramanian

Computer Science Department & Program of Computer Graphics

Cornell University

3D morphing3D morphing

• What is 3D morphing ?– A 3D model of the object is transformed from one shape into another.

• Why 3D morphing ?– Morphs are independent of viewing and lighting parameters.

– View-dependent effects possible e.g., shadows, highlights, camera can be animated during the morph.

– Traditional 2D morphs are inherently “flat” looking.

• Features of a Good 3D morphing algorithm– Conceptually Simple

– Minimal topological restrictions.

– Easy to use user-control

• What is 3D morphing ?– A 3D model of the object is transformed from one shape into another.

• Why 3D morphing ?– Morphs are independent of viewing and lighting parameters.

– View-dependent effects possible e.g., shadows, highlights, camera can be animated during the morph.

– Traditional 2D morphs are inherently “flat” looking.

• Features of a Good 3D morphing algorithm– Conceptually Simple

– Minimal topological restrictions.

– Easy to use user-control

OverviewOverview

3D model3D model

Model Model PolygonsPolygons(triangles)(triangles)

verticesverticesOther parametersOther parameters

(normals, textures)(normals, textures)

Multiplanar RepresentationMultiplanar Representation

htht

Convert model vertices from (x,y,z)Convert model vertices from (x,y,z)to (ht, theta, radius) space.to (ht, theta, radius) space.Scan convert each triangle.Scan convert each triangle.

Axis Axis

““Radius” ImagesRadius” Images(brighter = farther(brighter = farther darker = closer to axisdarker = closer to axis black = no point on object)black = no point on object)

3D model3D model(Axis = green)(Axis = green)

thetatheta

r1,r2r1,r2

r1r1r2r2

htht

thetatheta

correctedcorrectedScan-Scan-convertedconverted

3D to multiplanar 3D to multiplanar representationrepresentation

UsingUsingseparationseparation

ofofplanesplanes(seed-(seed-algo)algo)

33 3333

33 33

2a2a 2b2b

1a1a 1b1b 33

1a1a 1b1b

2a2a 2b2b

2D morphing between the planes2D morphing between the planes

For e.g. using Beier & Neely’s technique (1992)For e.g. using Beier & Neely’s technique (1992)

ReconstructionReconstruction

-ve plane-ve plane

+ve plane+ve plane

Form triangles using adjacent pixels, Form triangles using adjacent pixels, take advantage of continuity at boundariestake advantage of continuity at boundaries

Multiplane rep. To model spaceMultiplane rep. To model space

Original torusOriginal torus

Reconstructed torusReconstructed torusMultiplanesMultiplanes

Different ScenariosDifferent Scenarios

• E.g. E.g.

•

No correspondence for one planeNo correspondence for one plane

•

No correspondence for two planesNo correspondence for two planes(a) Hole in the object (a) Hole in the object

(b) An extruded object (b) An extruded object

Corresponding planes presentCorresponding planes present

ResultsResults

1/2 way there1/2 way there

Conclusion Conclusion

• All the advantages of 3D over 2D morphing are inherited.

• Complexity of 3D morphing is not there!• Works for different topologies, as opposed to some

existing methods.• All other parameters (textures, normals, colors,...) can

be morphed similarly.

• All the advantages of 3D over 2D morphing are inherited.

• Complexity of 3D morphing is not there!• Works for different topologies, as opposed to some

existing methods.• All other parameters (textures, normals, colors,...) can

be morphed similarly.

anim20_256bowltorus.gifanim20_256cansoc256.gif anim20_256funbeeth.gif anim20_256funb.gif

Boundaries between

multiplanes

Boundaries between

multiplanes

1. Intermediate object points must have1. Intermediate object points must have contribution from both the objects contribution from both the objects during dissolving.during dissolving. (you can’t use 0 as one of the values !!!)(you can’t use 0 as one of the values !!!)2. Consequence of the above is that you 2. Consequence of the above is that you need to match boundaries exactly.need to match boundaries exactly.3. The boundaries of the surfaces which are3. The boundaries of the surfaces which are connected originally must move connected originally must move together in the morphing => use relatedtogether in the morphing => use related lines in related images.lines in related images.

Poor morphing + reconstructionPoor morphing + reconstruction