Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings
The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical support and the analysis is complicated due to the full nonlinearity of the functional. In this paper, we provide a theor...
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| creator | Yueh, Mei-Heng |
| description | The stretch energy is a fully nonlinear energy functional that has been
applied to the numerical computation of area-preserving mappings. However, this
approach lacks theoretical support and the analysis is complicated due to the
full nonlinearity of the functional. In this paper, we provide a theoretical
foundation of the stretch energy minimization for the computation of
area-preserving mappings, including a neat formulation of the gradient of the
functional, and the proof of the minimizers of the functional being
area-preserving mappings. In addition, the geometric interpretation of the
stretch energy is also provided to better understand this energy functional.
Furthermore, numerical experiments are demonstrated to validate the
effectiveness and accuracy of the stretch energy minimization for the
computation of square-shaped area-preserving mappings of simplicial surfaces. |
| doi_str_mv | 10.48550/arxiv.2205.14414 |
| format | Article |
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applied to the numerical computation of area-preserving mappings. However, this
approach lacks theoretical support and the analysis is complicated due to the
full nonlinearity of the functional. In this paper, we provide a theoretical
foundation of the stretch energy minimization for the computation of
area-preserving mappings, including a neat formulation of the gradient of the
functional, and the proof of the minimizers of the functional being
area-preserving mappings. In addition, the geometric interpretation of the
stretch energy is also provided to better understand this energy functional.
Furthermore, numerical experiments are demonstrated to validate the
effectiveness and accuracy of the stretch energy minimization for the
computation of square-shaped area-preserving mappings of simplicial surfaces.</description><identifier>DOI: 10.48550/arxiv.2205.14414</identifier><language>eng</language><subject>Computer Science - Computational Geometry ; Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2022-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2205.14414$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2205.14414$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Yueh, Mei-Heng</creatorcontrib><title>Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings</title><description>The stretch energy is a fully nonlinear energy functional that has been
applied to the numerical computation of area-preserving mappings. However, this
approach lacks theoretical support and the analysis is complicated due to the
full nonlinearity of the functional. In this paper, we provide a theoretical
foundation of the stretch energy minimization for the computation of
area-preserving mappings, including a neat formulation of the gradient of the
functional, and the proof of the minimizers of the functional being
area-preserving mappings. In addition, the geometric interpretation of the
stretch energy is also provided to better understand this energy functional.
Furthermore, numerical experiments are demonstrated to validate the
effectiveness and accuracy of the stretch energy minimization for the
computation of square-shaped area-preserving mappings of simplicial surfaces.</description><subject>Computer Science - Computational Geometry</subject><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb0woMIHMOEfSLBjO7bHqmqhUiuQiFijl_i5sdTGkRMqyte3tExnuFdHOoQ8cZZLoxR7gfQTjnlRMJVzKbm8J19VhzHhFFrY01X87h1MIfY0ejp1SD-ny9Z2dNlj2p3oNvThEH5vFx8TnSeE7CPhiOkY-h3dwjBcOD6QOw_7ER__OSPValkt3rLN--t6Md9kUGqZOW8MmKIssJHeMIXcMIFaMa1t47gRzlrLm4KXjXCgoLRcMmYbrUvmWi3EjDzftNewekjhAOlU_wXW10BxBmd3Sz8</recordid><startdate>20220528</startdate><enddate>20220528</enddate><creator>Yueh, Mei-Heng</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220528</creationdate><title>Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings</title><author>Yueh, Mei-Heng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-df88a8262eb4f805e1803e750779bd183d9991b216b3da5a6914009b7760dc733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Computational Geometry</topic><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Yueh, Mei-Heng</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yueh, Mei-Heng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings</atitle><date>2022-05-28</date><risdate>2022</risdate><abstract>The stretch energy is a fully nonlinear energy functional that has been
applied to the numerical computation of area-preserving mappings. However, this
approach lacks theoretical support and the analysis is complicated due to the
full nonlinearity of the functional. In this paper, we provide a theoretical
foundation of the stretch energy minimization for the computation of
area-preserving mappings, including a neat formulation of the gradient of the
functional, and the proof of the minimizers of the functional being
area-preserving mappings. In addition, the geometric interpretation of the
stretch energy is also provided to better understand this energy functional.
Furthermore, numerical experiments are demonstrated to validate the
effectiveness and accuracy of the stretch energy minimization for the
computation of square-shaped area-preserving mappings of simplicial surfaces.</abstract><doi>10.48550/arxiv.2205.14414</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Geometry Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings |
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