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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

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3D 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

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Overview

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3D model Model Polygons(triangles) vertices Other parameters (normals, textures)

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Multiplanar Representation ht Convert model vertices from (x,y,z) to (ht, theta, radius) space. Scan convert each triangle. Axis “Radius” Images (brighter = farther darker = closer to axis darker = closer to axis black = no point on object) black = no point on object) 3D model (Axis = green) theta r1,r2 r1 r2 ht theta

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corrected Scan-converted 3D to multiplanar representation Usingseparationofplanes(seed-algo) a2b 1a1b 3 1a1b 2a2b

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2D morphing between the planes For e.g. using Beier & Neely’s technique (1992)

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Reconstruction -ve plane +ve plane Form triangles using adjacent pixels, take advantage of continuity at boundaries Multiplane rep. To model space Original torus Reconstructed torus Multiplanes

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Different Scenarios E.g. No correspondence for one plane No correspondence for two planes (a) Hole in the object (b) An extruded object Corresponding planes present

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Results 1/2 way there

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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.

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Boundaries between multiplanes 1. 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 need to match boundaries exactly. need to match boundaries exactly. 3. The boundaries of the surfaces which are connected originally must move connected originally must move together in the morphing => use related together in the morphing => use related lines in related images. lines in related images. Poor morphing + reconstruction

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