Pythagorean hodograph quintic transition between two circles with shape control
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Cited by (59)
Approximation of monotone clothoid segments by degree 7 Pythagorean–hodograph curves
2021, Journal of Computational and Applied MathematicsCitation Excerpt :We do not discuss here the application of translation/rotation/scaling transformations to canonical-form clothoid segments to suit the requirements of specific applications, since this is addressed elsewhere[7,8,16–18]. A number of related studies [23–29] have been concerned with designing “transition” curves between elementary (linear/circular) path segments. However, the focus in these studies has been on the smoothness or curvature monotonicity of the transition curve, without explicitly attempting to achieve a linear dependence of curvature on arc length.
Optimization of Corner Blending Curves
2019, CAD Computer Aided DesignCitation Excerpt :An analogous concern occurs in the layout of highways or railways, wherein precise control of the curvature of transition curves is required to guarantee compatibility with prescribed safe vehicle traversal speeds [11–14]. For blend curves that connect segments of disparate curvature (e.g., linear and circular segments, or two circle segments with different radii), monotone curvature variation is preferred, and such “spiral” blend segments have been extensively studied [15–28]. For blend curves connecting two linear segments, however, a symmetric unimodal curvature profile that yields the desired change of direction (or turning angle) is desired [29,30].
Geometric interpolation by PH curves with quadratic or quartic rational normals
2019, CAD Computer Aided DesignCitation Excerpt :The control polygon based techniques can even be used to define PH spline curves or for recognizing PH curves from Bézier curves [19,20]. Interpolation of Hermite data by single or multi-connected PH curves is an efficient way for approximating general smooth curves or fitting discrete data and it has been used in various applications [21–26]. Besides interpolating the boundary data, a PH curve may also have a prescribed arc length [27].
A novel speed model for safety evaluation of freeway alignment in Euclidean 3D space
2019, Traffic Injury PreventionGeometric characteristics of planar quintic Pythagorean-hodograph curves
2018, Journal of Computational and Applied MathematicsConstruction of G<sup>1</sup> planar Hermite interpolants with prescribed arc lengths
2016, Computer Aided Geometric Design