A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects
| dc.contributor.author | Chang, Jumyung | |
| dc.contributor.author | Da, Fang | |
| dc.contributor.author | Grinspun, Eitan | |
| dc.contributor.author | Batty, Christopher | |
| dc.date.accessioned | 2020-02-18T16:40:42Z | |
| dc.date.available | 2020-02-18T16:40:42Z | |
| dc.date.issued | 2019-07 | |
| dc.description | Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. | en |
| dc.description.abstract | We present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models for elastic continua, we categorize and define a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. This palette consists of three categories: point connections, in which simplices meet at a single vertex around which they may twist and bend; curve connections in which simplices share an edge around which they may rotate (bend) relative to one another; and surface connections, in which a shell is embedded on or into a solid. To define elastic behaviors across non-manifold point connections, we adapt and apply parallel transport concepts from elastic rods. To address discontinuous forces that would otherwise arise when large accumulated relative rotations wrap around in the space of angles, we develop an incremental angle-update strategy. Our method provides a conceptually simple, flexible, and highly expressive framework for designing complex elastic objects, by modeling the geometry with a single simplicial mesh and decorating its elements with appropriate physical models (rod, shell, solid) and connection types (point, curve, surface). We demonstrate a diverse set of possible interactions achievable with our method, through technical and application examples, including scenes featuring complex aquatic creatures, children's toys, and umbrellas. | en |
| dc.description.sponsorship | This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014) | en |
| dc.identifier.uri | https://doi.org/10.1145/3340252 | |
| dc.identifier.uri | http://hdl.handle.net/10012/15651 | |
| dc.language.iso | en | en |
| dc.publisher | ACM | en |
| dc.subject | unified | en |
| dc.subject | mixed-dimensional | en |
| dc.subject | non-manifold | en |
| dc.subject | elastic | en |
| dc.title | A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Jumyung Chang, Fang Da, Eitan Grinspun, and Christopher Batty. 2019. A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects. Proc. ACM Comput. Graph. Interact. Tech. 2, 2, Article 11 (July 2019), 18 pages. https://doi.org/10.1145/3340252 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | David R. Cheriton School of Computer Science | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |