By mapping the volumes of objects, rather than their surfaces, a new technique could yield solutions to computer graphics problems in animation and CAD. MIT scientists have improved 3D shape alignment in computer graphics by developing a method that maps volumes, not just surfaces. This results i
This image shows how the algorithm the researchers’ developed can align two shapes by mapping the volume of one shape, in this case a horse, onto another shape, a cow. Their system represents each shape as a tetrahedral mesh and then the algorithm determines how to move and stretch the corners of tetrahedra so they align. Credit: Courtesy of the researchers
To address these shortcomings, researchers at MIT have developed an approach that aligns 3D shapes by mapping volumes to volumes, rather than surfaces to surfaces. Their technique represents shapes as tetrahedral meshes that include the mass inside a 3D object. Their algorithm determines how to move and stretch the corners of tetrahedra in a source shape so it aligns with a target shape.
The approach Abulnaga and his collaborators developed was able to align shapes more effectively than baseline methods, leading to high-quality shape maps with less distortion than competing alternatives. Their algorithm was especially well-suited for challenging mapping problems where the input shapes are geometrically distinct, such as mapping a smooth rabbit to LEGO-style rabbit made of cubes.
Even when Abulnaga improved the energy in his mapping algorithm to better model volume physics, the method didn’t produce useful matchings. His team realized one reason for this failure is that many physical energies — and most mapping algorithms — lack symmetry.
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