IBM Journal of Research and Development
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Adaptive subdivision and the length and energy of Be´zier curves
Computational Geometry: Theory and Applications
G2 curves composed of planar cubic and Pythagorean hodograph quintic spirals
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Rational Parametrization of Canal Surface by 4 Dimensional Minkowski Pythagorean Hodograph Curves
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
C1 Hermite interpolation using MPH quartic
Computer Aided Geometric Design
Computation of optimal composite re-parameterizations
Computer Aided Geometric Design
C1 Hermite interpolation with simple planar PH curves by speed reparametrization
Computer Aided Geometric Design
Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves
Computer Aided Geometric Design
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Starting with a given planar cubic curve [x(t), y(t)]T, we construct Pythagorean hodograph (PH) space curves of the form [x(t), y(t), z(t)]T in Euclidean and in Minkowski space, which interpolate the tangent vector at a given point. We prove the existence of these curves for any regular planar cubic and we express all solutions explicitly. It is shown that the constructed curves provide upper and lower polynomial bounds on the parametrical speed and the arc-length function of the given cubic. We analyze the approximation order and derive an explicit formula for the gap between the bounds. In addition, we discuss the approximation of the offset curves. Finally we define an invariant which measures the deviation of a given planar cubic from being a PH curve.