Since the mode of Pythagorean-Hodograph curve’s derivate is a polynomial, its involute should be a rational polynomial. We study the expression form of PH cubic’s involute, discovering that its control points and weights are all constructed by corresponding PH cubic’s geometry property. Moreover, we prove that cubic PH curves have neither cusp nor inflection; there are two points coincidence in...

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....

An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves γ. The task is to connect the points in V in the order in which they lie on γ. Giesen [Proceedings of the 15th Annual ACM Symposium on Computational Geometry (SCG ’99), 1999, pp. 207–216] showed recently that the traveling salesman tour of V solves the reconstruction problem for single cl...

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Introduction Re-gridding of data distributed in a spatially grid to finer or coarser resolution is a fundamental task in the field of data processing. The gridding process requires a re-distribution of the original dataset to a user requested grid according to a distribution function, which can be determined on the basis of the given data by interpolation methods. Commonly used interpolation me...

This paper examines clustering in datasets where each record is presented as a curve (trend). Our clustering approach is based on nonsmooth and nonconvex optimisation, namely the clustering problems have been formulated as mathematical programming problems and several optimisation methods from GANSO optimisation library have been applied to solve the problems. The least squares and uniform opti...

Pareto efficiency is a widely used property in solution concepts for cooperative and non–cooperative game–theoretic settings and, more generally, in multi–objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the literature focuses on computing concise representations to approximate the Pareto curve or on explo...

some numerical and experimental investigations are made on the performance of five different hyperelastic constitutive models (second order polynomial, yeoh, arruda-boyce, ogden and marlow) in tension and compressionmodes. first, the results of the tensile and compression tests on a rubber sample were used to determine the parameters of the models by curve fitting methods. next, by using an alg...

an analytical equation of state was applied to calculate the thermodynamic properties for argon.the equation of state is that of song and mason. it is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...