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  • Spatial Pythagorean hodograph (PH) curves, both in Euclidean and Minkowski 3-space, were originally introduced as polynomial curves with polynomial speed measured with respect to Euclidean or Minkowski norm, respectively. Recently, Kosinka and Lávička (2010) extended the notion of MPH curves also to the rational case by prescribing an associated planar rational PH curve and an additional rational function. At the same time, Farouki and Šír (2011) presented a method for constructing rational Euclidean PH curves in 3-space based on a field of rational unit tangent vectors. In this paper, we summarise known constructions and present a unifying idea for rational PH curves in Euclidean and Minkowski 3-space.
  • Spatial Pythagorean hodograph (PH) curves, both in Euclidean and Minkowski 3-space, were originally introduced as polynomial curves with polynomial speed measured with respect to Euclidean or Minkowski norm, respectively. Recently, Kosinka and Lávička (2010) extended the notion of MPH curves also to the rational case by prescribing an associated planar rational PH curve and an additional rational function. At the same time, Farouki and Šír (2011) presented a method for constructing rational Euclidean PH curves in 3-space based on a field of rational unit tangent vectors. In this paper, we summarise known constructions and present a unifying idea for rational PH curves in Euclidean and Minkowski 3-space. (en)
Title
  • From planar to spatial Euclidean and Minkowski Pythagorean hodograph curves
  • From planar to spatial Euclidean and Minkowski Pythagorean hodograph curves (en)
skos:prefLabel
  • From planar to spatial Euclidean and Minkowski Pythagorean hodograph curves
  • From planar to spatial Euclidean and Minkowski Pythagorean hodograph curves (en)
skos:notation
  • RIV/49777513:23520/11:43899235!RIV12-MSM-23520___
http://linked.open...avai/predkladatel
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  • Z(MSM4977751301)
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  • 16
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  • 200440
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  • RIV/49777513:23520/11:43899235
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  • Rational space curves, Euclidean and Minkowski Pythagorean hodograph curves, offsets, trimming (en)
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  • SK - Slovenská republika
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  • [BD4D1DE8A71B]
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  • G ? slovenský časopis pre geometriu a grafiku
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  • 8
http://linked.open...iv/tvurceVysledku
  • Kosinka, Jiří
  • Lávička, Miroslav
http://linked.open...n/vavai/riv/zamer
issn
  • 1336-524X
number of pages
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  • 23520
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