Balancing Rotation Minimizing Frames with Additional Objectives

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dc.contributor.authorMossman, Christopheren_US
dc.contributor.authorBartels, Richard H.en_US
dc.contributor.authorSamavati, Faramarz F.en_US
dc.contributor.editorChaine, Raphaëlleen_US
dc.contributor.editorDeng, Zhigangen_US
dc.contributor.editorKim, Min H.en_US
dc.date.accessioned2023-10-09T07:37:38Z
dc.date.available2023-10-09T07:37:38Z
dc.date.issued2023
dc.description.abstractWhen moving along 3D curves, one may require local coordinate frames for visited points, such as for animating virtual cameras, controlling robotic motion, or constructing sweep surfaces. Often, consecutive coordinate frames should be similar, avoiding sharp twists. Previous work achieved this goal by using various methods to approximate rotation minimizing frames (RMFs) with respect to a curve's tangent. In this work, we use Householder transformations to construct preliminary tangentaligned coordinate frames and then optimize these initial frames under the constraint that they remain tangent-aligned. This optimization minimizes the weighted sum of squared distances between selected vectors within the new frames and fixed vectors outside them (such as the axes of previous frames). By selecting different vectors for this objective function, we reproduce existing RMF approximation methods and modify them to consider additional objectives beyond rotation minimization. We also provide some example computer graphics use cases for this new frame tracking.en_US
dc.description.number7
dc.description.sectionheadersLearning and Image Processing
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14979
dc.identifier.issn1467-8659
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14979
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14979
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies -> Shape modeling; Procedural animation; Mathematics of computing -> Mathematical optimization
dc.subjectComputing methodologies
dc.subjectShape modeling
dc.subjectProcedural animation
dc.subjectMathematics of computing
dc.subjectMathematical optimization
dc.titleBalancing Rotation Minimizing Frames with Additional Objectivesen_US
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