By mapping the volumes of objects, rather than their surfaces, a new technique could yield solutions to computer graphics problems in animation and CAD. In computer graphics and computer-aided design (CAD), 3D objects are often represented by the contours of their outer surfaces. Computers store these shapes as “thin shells,” which model the contours of the skin of an animated character but not the flesh underneath. This modeling decision makes it efficient to store and manipulate 3D shapes, but it can lead to unexpected artifacts. An animated character’s hand, for example, might crumple when bending its fingers. These differences are particularly problematic when developing mapping algorithms, which automatically find relationships between different shapes. 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. Because it incorporates volumetric information, the researchers’ technique is better able to model fine parts of an object, avoiding the twisting and inversion typical of surface-based mapping.
