Optimal mapping with topology change for animation and geometry problems
department or school: Science, Faculty of
department or school: Computer Science, Department of
data provider: DSpace
degree campus: UBCV
creator: Zhu, Yufeng
issued: 2018-12-19T17:44:22Z
issued: 2018
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: This thesis investigates several aspects of the optimal mapping problem, finding a bijective function between two shapes which minimizes some metric, and its many applications in computer graphics such as finding planar embeddings of curved surface meshes, image warping, mesh deformation, elastoplastic simulation, and more. We highlight in particular problems where differences in topology between the shapes—which necessitate discontinuities in the mapping—play a crucial role, e.g. due to animation decisions or physical fracture. Our first project presents an approach to extend discrete variational shape interpolation to create keyframe animation involving extreme deformation, topology change and dynamics. To construct correspondence between keyframe shapes as well as satisfying feature matching constraints, we introduce a consistent multimesh structure that is able to resolve topological in-equivalence between shapes and a Comesh Optimization algorithm that optimizes our multimesh for both intra and inter-mesh quality. To further speed up the total solving time, we then develop three new improvements to the state of the art nonlinear optimization techniques that are frequently used in this field, including a barrier-aware line-search filter that cures blocked descent steps due to element barrier terms; an energy proxy model that adaptively blends the Sobolev gradient and L-BFGS descent to gain the advantages of both; and a characteristic gradient norm providing a robust and largely mesh- and energy independent convergence criterion. Finally, we demonstrate another related interesting graphics application, brittle fracture simulation. In particular, we investigate whether we can sidestep the volumetric optimal mapping problem for solving elastic deformation and instead use a boundary element discretization which only requires a surface mesh. We will show how the computational cost of such problems can be alleviated using a boundary integral formulation and kernel-ind…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/68102
note: Optimal Mapping with Topology Change for Animationand Geometry ProblemsbyYufeng ZhuB. Sc, Shanghai Jiaotong University, 2010M. Sc, University of Southern California, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Computer Science)The University of British Columbia(Vancouver)December 2018c© Yufeng Zhu, 2018The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Optimal Mapping with Topology Change for Animation and GeometryProblemssubmitted by Yufeng Zhu in partial fulfillment of the requirements for the degreeof Doctor of Philosophy in Computer Science.Examining Committee:Robert Bridson, Computer ScienceSupervisorChen Greif, Computer ScienceCo-supervisorAlla Sheffer, Computer ScienceUniversity ExaminerCarl Ollivier-Gooch, Mechanical EngineeringUniversity ExaminerPaul Kry, Computer Science, McGill UniversityExternal ExamineriiAbstractThis thesis investigates several aspects of the optimal mapping problem, finding abijective function between two shapes which minimizes some metric, and its manyapplications in computer graphics such as finding planar embeddings of curvedsurface meshes, image warping, mesh deformation, elastoplastic simulation, andmore. We highlight in particular problems where differences in topology betweenthe shapes—which necessitate discontinuities in the mapping—play a crucial role,e.g. due to animation decisions or physical fracture.Our first project presents an approach to extend discrete variational shape in-terpolation to create keyframe animation involving extreme deformation, topologychange and dynamics. To construct correspondence between keyframe shapes aswell as satisfying feature matching constraints, we introduce a consistent multi-mesh structure that is able to resolve topological in-equivalence between shapesand a Comesh Optimization…
has type: Thesis/Dissertation
date issued: 2019-02
is shown at: 10.14288/1.0375785
language: eng
degree discipline: Computer Science
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/68102