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If a researcher tries to apply them bidirectionally to create a symmetric map, the energies no longer behave as expected. The typical energies used in shape alignment are only designed to map in one direction. “If you choose the right energy for your algorithm, it can give you maps that are more realizable,” Abulnaga explains. This effect is even more pronounced in the volumetric case.Ībulnaga documented how most mapping algorithms don’t use symmetric energies. But for many mapping algorithms, choosing the wrong shape to be the source or target leads to worse results. For example, mapping a horse onto a giraffe should produce the same matchings as mapping a giraffe onto a horse. In the new work, a symmetric method doesn’t care which order the shapes come in as input there is no distinction between a “source” and “target” for the map. His team realized one reason for this failure is that many physical energies - and most mapping algorithms - lack symmetry. These energies are often borrowed from physics, which uses similar equations to model the motion of elastic materials like gelatin.Įven when Abulnaga improved the energy in his mapping algorithm to better model volume physics, the method didn’t produce useful matchings. Most mapping algorithms work by trying to minimize an “energy,” which quantifies how much a shape deforms when it is displaced, stretched, squashed, and sheared into another shape. The team quickly realized that new mathematics and algorithms were needed to tackle volume mapping. The research will be presented at the ACM SIGGRAPH conference.Ībulnaga began this project by extending surface-based algorithms so they could map shapes volumetrically, but each attempt failed or produced implausible maps.

Joining Abulnaga on the paper are Oded Stein, a former MIT postdoc who is now on the faculty at the University of Southern California Polina Golland, a Sunlin and Priscilla Chou Professor of EECS, a principal investigator in the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL), and the leader of the Medical Vision Group and Justin Solomon, an associate professor of EECS and the leader of the CSAIL Geometric Data Processing Group. The same algorithm can transfer textures, annotations, and physical properties from one 3D shape to another, with applications not just in visual computing but also for computational manufacturing and engineering. For instance, it could be used to transfer the motions of a previously animated 3D character onto a new 3D model or scan.

The technique could be useful in a number of graphics applications. 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. 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. Our method brings geometric mapping closer to physical reality,” says Mazdak Abulnaga, an electrical engineering and computer science (EECS) graduate student who is lead author of the paper on this mapping technique. “Switching from surfaces to volumes stretches the rubber glove over the whole hand.

#Tetrix 3d models how to#

Their algorithm determines how to move and stretch the corners of tetrahedra in a source shape so it aligns with a target shape.īecause 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. Their technique represents shapes as tetrahedral meshes that include the mass inside a 3D object. 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. These differences are particularly problematic when developing mapping algorithms, which automatically find relationships between different shapes.

An animated character’s hand, for example, might crumple when bending its fingers - a motion that resembles how an empty rubber glove deforms rather than the motion of a hand filled with bones, tendons, and muscle. This modeling decision makes it efficient to store and manipulate 3D shapes, but it can lead to unexpected artifacts.

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Computers store these shapes as “thin shells,” which model the contours of the skin of an animated character but not the flesh underneath. In computer graphics and computer-aided design (CAD), 3D objects are often represented by the contours of their outer surfaces.