Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!mcvax!ukc!warwick!strgh From: strgh@daisy.warwick.ac.uk (J E H Shaw) Newsgroups: comp.graphics Subject: Re: Crookedness of space-curves Message-ID: <368@sol.warwick.ac.uk> Date: Wed, 24-Jun-87 13:49:18 EDT Article-I.D.: sol.368 Posted: Wed Jun 24 13:49:18 1987 Date-Received: Sat, 4-Jul-87 17:41:39 EDT References: <392@kuling.UUCP> Reply-To: strgh@sol.warwick.ac.uk () Distribution: world Organization: Computing Services, Warwick University, UK Lines: 21 (Tried to e-mail the following response to `coeff. of crookedness' question, but it just bounced back.) There were a couple of articles by McConalogue in the Computer Journal 1970 & 1971 that may be helpful (I don't have them to hand). However, it's seldom necessary to go beyond a cubic spline (or a more sophisticated low-order spline if the `curve' is rather angular - see, e.g. R.J.Renka, `Interpolatory tension splines with automatic selection of tension factors', SIAM J. Sci. Statist. Comput. 8:393-415 + references therein). If points are (x1,y1,z1,...), (x2,y2,z2,...), ..., I would just let ti = sqrt((xi+1 - xi)^2 + (yi+1 - yi)^2 + (zi+1 - zi)^2 + ...), Ti = sum_from_1_to_i-1 of ti, and fit splines independently to (ti,xi;i=1,2...), (ti,yi;i=1,2...), (ti,zi;i=1,2...) ... ^^^ if in >3 dimensions! -- Ewart Shaw -- J.E.H.Shaw Department of Statistics, University of Warwick, Coventry CV4 7AL $$\times\times\qquad\top\gamma\alpha\omega\exists\qquad{\odot\odot\atop\smile}$$