Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
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منابع مشابه
Clifford Algebra, Spin Representation, and Rational Parameterization of Curves and Surfaces
The Pythagorean hodograph (PH) curves are characterized by certain Pythagorean n-tuple identities in the polynomial ring, involving the derivatives of the curve coordinate functions. Such curves have many advantageous properties in computer aided geometric design. Thus far, PH curves have been studied in 2or 3-dimensional Euclidean and Minkowski spaces. The characterization of PH curves in each...
متن کاملOn rational Minkowski Pythagorean hodograph curves
Minkowski Pythagorean hodograph curves are polynomial curves with polynomial speed, measured with respect to Minkowski norm. Curves of this special class are particularly well suited for representing medial axis transforms of planar domains. In the present paper we generalize this polynomial class to a rational class of curves in Minkowski 3-space. We show that any rational Minkowski Pythagorea...
متن کاملA geometric product formulation for spatial Pythagorean hodograph curves with applications to Hermite interpolation
A novel formulation for spatial Pythagorean–hodograph (PH) curves, based on the geometric product of vectors from Clifford algebra, is proposed. Compared to the established quaternion representation, in which a hodograph is generated by a continuous sequence of scalings/rotations of a fixed unit vector n̂ , the new representation corresponds to a sequence of scalings/reflections of n̂ . The two r...
متن کاملIdentification and "reverse engineering" of Pythagorean-hodograph curves
Methods are developed to identify whether or not a given polynomial curve, specified by Bézier control points, is a Pythagorean–hodograph (PH) curve — and, if so, to reconstruct the internal algebraic structure that allows one to exploit the advantageous properties of PH curves. Two approaches to identification of PH curves are proposed. The first is based on the satisfaction of a system of alg...
متن کاملEndpoint hermit interpolation with cubic ball PH curves
The Pythagorean hodograph (PH) curves are polynomial parametric curves whose hodograph (derivative) components satisfy the Pythagorean condition. Lots of research works had been done with PH curves relevant topics due that PH curves own many remarkable properties, e.g., its offset curves have exact rational representations. In this paper, ball curves with rational polynomial offset are studied....
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