On control polygons of quartic Pythagorean-hodograph curves

DOI10.1016/j.cagd.2009.08.003zbMath1205.65109OpenAlexW2088538432WikidataQ114202380 ScholiaQ114202380MaRDI QIDQ625252

Lincong Fang, Guo-zhao Wang

Publication date: 15 February 2011

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2009.08.003

zbMATH Keywords

Bézier curvesHermite interpolationcontrol polygonPythagorean-hodograph

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (16)

Rectifying control polygon for planar Pythagorean hodograph curves ⋮ Construction of PH splines based on H-Bézier curves ⋮ A new method to construct polynomial minimal surfaces ⋮ A note on Pythagorean hodograph quartic spiral ⋮ Classification of polynomial minimal surfaces ⋮ Algebraic and geometric characterizations of a class of algebraic-hyperbolic Pythagorean-hodograph curves ⋮ Geometric characteristics of planar quintic Pythagorean-hodograph curves ⋮ Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets ⋮ Classification of planar Pythagorean hodograph curves ⋮ Interactive design of cubic IPH spline curves ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ New algebraic and geometric characterizations of planar quintic Pythagorean-hodograph curves ⋮ Unnamed Item ⋮ Pythagorean hodograph spline spirals that match \(G^3\) Hermite data from circles ⋮ Identification of two classes of planar septic Pythagorean hodograph curves ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon

Cites Work

• Unnamed Item
• A generalisation of the Pythagorean hodograph quintic spiral
• A control polygon scheme for design of planar \(C^2\) PH quintic spline curves
• \(C^1\)-Hermite interpolation with simple planar PH curves by speed reparametrization
• Absolute hodograph winding number and planar PH quintic splines
• Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• The conformal map \(z\to z^ 2\) of the hodograph plane
• The elastic bending energy of Pythagorean-hodograph curves
• Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves.
• \(G^{1}\) Hermite interpolation by Minkowski Pythagorean hodograph cubics
• Pythagorean Triples in Uniquef Factorization Domains
• Construction and shape analysis of PH quintic Hermite interpolants

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