Blending of Hyperbolic Closed Curves

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dc.contributor.authorIkemakhen, Azizen_US
dc.contributor.authorAhanchaou, Taoufiken_US
dc.contributor.editorDigne, Julie and Crane, Keenanen_US
dc.date.accessioned2021-07-10T07:46:16Z
dc.date.available2021-07-10T07:46:16Z
dc.date.issued2021
dc.description.abstractIn recent years, game developers are interested in developing games in the hyperbolic space. Shape blending is one of the fundamental techniques to produce animation and videos games. This paper presents two algorithms for blending between two closed curves in the hyperbolic plane in a manner that guarantees that the intermediate curves are closed. We deal with hyperbolic discrete curves on Poincaré disc which is a famous model of the hyperbolic plane. We use the linear interpolation approach of the geometric invariants of hyperbolic polygons namely hyperbolic side lengths, exterior angles and geodesic discrete curvature. We formulate the closing condition of a hyperbolic polygon in terms of its geodesic side lengths and exterior angles. This is to be able to generate closed intermediate curves. Finally, some experimental results are given to illustrate that the proposed methods generate aesthetic blending of closed hyperbolic curves.en_US
dc.description.number5
dc.description.sectionheadersShape Synthesis and Editing
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume40
dc.identifier.doi10.1111/cgf.14358
dc.identifier.issn1467-8659
dc.identifier.pages71-79
dc.identifier.urihttps://doi.org/10.1111/cgf.14358
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14358
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts
dc.subjectTheory of computation
dc.subjectComputational geometry
dc.subjectMathematics of computing
dc.subjectInterpolation
dc.subjectComputing methodologies
dc.subjectAnimation
dc.titleBlending of Hyperbolic Closed Curvesen_US
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