Absolute hodograph winding number and planar PH quintic splines
References (9)
The conformal map of the hodograph plane
Comput. Aided Geom. Design
(1994)The elastic bending energy of Pythagorean-hodograph curves
Comput. Aided Geom. Design
(1996)- et al.
Construction and shape analysis of PH quintic Hermite interpolants
Comput. Aided Geom. Design
(2001) - et al.
Construction of Pythagorean-hodograph interpolating splines by the homotopy method
Adv. Comput. Math.
(1996)
Cited by (11)
Shape analysis of planar PH curves with the Gauss–Legendre control polygons
2020, Computer Aided Geometric DesignA new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants
2020, Computer Aided Geometric DesignGauss–Lobatto polygon of Pythagorean hodograph curves
2019, Computer Aided Geometric DesignCitation Excerpt :The polynomial speed functions furnish the PH curves with many nice properties such as exact arc length evaluation, rational offset curves, rational unit tangent vectors. To utilize these properties, many algorithms for PH curve construction on various conditions have been developed (Choi et al., 2008; Choi and Kwon, 2008; Farouki et al., 2002, 2008; Farouki and Neff, 1995; Huard et al., 2014; Jüttler, 2001; Moon et al., 2001; Šír and Jüttler, 2007). Especially, the PH curve construction problems under the arc length constraint have been addressed recently (Farouki, 2016, 2019).
Deformation of spatial septic Pythagorean hodograph curves using Gauss–Legendre polygon
2019, Computer Aided Geometric DesignCitation Excerpt :Because of the square map in the PH condition, the Hermite interpolation problems are expressed as systems of quadratic equations, so the solution might not be unique. The Hermite interpolation problems for planar PH curves usually have multiple solutions, and several selection schemes of the best solution have been reported (Choi et al., 2008; Choi and Kwon, 2008; Farouki and Neff, 1995; Moon et al., 2001). On the other hand, the Hermite interpolation problems for spatial PH curves have infinitely many solutions (Farouki et al., 2002, 2008; Kwon, 2010), which also require the selection schemes for the optimal solution.
Rectifying control polygon for planar Pythagorean hodograph curves
2017, Computer Aided Geometric DesignC<sup>1</sup> Hermite interpolation with PH curves by boundary data modification
2013, Journal of Computational and Applied MathematicsCitation Excerpt :In particular, boundary modification would appear to offer a lot of promise as an effective tool for constructing a better curve than several produced by PH spline interpolation [25].
- 1
The first author also holds joint appointment in the Research Institute of Mathematics, Seoul National University.
- 2
This work was supported by the BK21 project of the Ministry of Education, Korea.