Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolants

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dc.contributor.authorLiska, Richard
dc.contributor.authorShashkov, Mikhail
dc.contributor.authorSwartz, Blair
dc.date.accessioned2016-12-09T08:15:58Z
dc.date.available2016-12-09T08:15:58Z
dc.date.issued2002
dc.description.abstractG-smooth curves and surfaces are developed to span a given logically cuboid distribution of nodes. Given appropriate data, they locally reconstruct the curves and surfaces of spherical or cylindrical coordinates. Thus, if a set of nodes consists of a contiguous subset of a tensor product grid of points associated with a (possibly non-uniform) set of coordinate values of some rectangular, cylindrical, or spherical coordinate system; then the appropriate coordinate curves (linear or circular segments) and coordinate surfaces (segments of planes, cylinders, spheres and cones) that interpolate the subset are reconstructed exactly. The underlying construction uses four successive nodes to define a curve spanning the middle pair as follows: One interpolates each of the two successive triples of nodes with the segment of a circle or straight line going through these three points. Then one blends the two segments continuously between the middle pair of nodes. The blend is relatively linear in terms of arc-length along each segment. The union of such successive curve-sections forms a G curve. Wire-frames of such curves define cell edges. Similar intermediate curvilinear interpolation of the wires defines cell faces, and their union defines G coordinate-like surfaces. The surface generated depends on the direction one interpolates the wires. If the nodes are a tensor product grid associated with a sufficiently smooth reference coordinate system, then the cell edges (and probably also the cell faces) are third-order accurate.en_US
dc.identifier.citationLiska, R., Shashkov, M., Swartz, B. (2002). Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolants. Selcuk Journal of Applied Mathematics, 3 (2), 81-98.en_US
dc.identifier.endpage98
dc.identifier.issn1302-7980en_US
dc.identifier.startpage81
dc.identifier.urihttps://hdl.handle.net/20.500.12395/3460
dc.identifier.volume3
dc.language.isoenen_US
dc.publisherSelcuk University Research Center of Applied Mathematicsen_US
dc.relation.ispartofSelcuk Journal of Applied Mathematicsen_US
dc.relation.publicationcategoryMakale - Kategori Belirleneceken_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.subjectEnterpolasyonen_US
dc.subjectInterpolationen_US
dc.subjectConeen_US
dc.subjectKonien_US
dc.subjectCylinderen_US
dc.subjectSilindiren_US
dc.subjectSphereen_US
dc.subjectKüreen_US
dc.subjectCircleen_US
dc.subjectDaireen_US
dc.subjectSmooth reconstructionen_US
dc.subjectDüzgün yeniden yapımen_US
dc.titleLocally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolantsen_US
dc.typeArticleen_US

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