Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Design of C2 spatial pythagorean-hodograph quintic spline curves by control polygons
Proceedings of the 7th international conference on Curves and Surfaces
Reconstruction of quasi developable surfaces from ribbon curves
Numerical Algorithms
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In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C^2 Pythagorean-hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed constraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation of derivatives only (without spatial localization). The special structure of PH curves allows the arc-length conditions to be expressed as algebraic constraints on the curve coefficients. The C^2 PH quintic splines are thus defined through minimization of a quadratic function subject to quadratic constraints, and a close starting approximation to the desired solution is identified in order to facilitate efficient construction by iterative methods. The C^2 PH spline constructions are illustrated by several computed examples.