Existence of Pythagorean-hodograph quintic interpolants to spatial G1 Hermite data with prescribed arc lengths. (November 2019)

• Record Type: Journal Article
• Authors: Farouki, Rida T.
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 202
• Page End: 216
• Publication Date: 2019-11
• Subjects: Geometric Hermite interpolation -- Pythagorean–hodograph curves -- Arc length constraints -- Existence conditions -- Shape optimization -- Polynomial roots; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A unique feature of polynomial Pythagorean–hodograph (PH) curves is the ability to interpolate G 1 Hermite data (end points and tangents) with a specified total arc length. Since their construction involves the solution of a set of non–linear equations with coefficients dependent on the specified data, the existence of such interpolants in all instances is non–obvious. A comprehensive analysis of the existence of solutions in the case of spatial PH quintics with end derivatives of equal magnitude is presented, establishing that a two–parameter family of interpolants exists for any prescribed end points, end tangents, and total arc length. The two free parameters may be exploited to optimize a suitable shape measure of the interpolants, such as the elastic bending energy.