I haven't tested this, but it looks straightforward enough ... Using standard schoolroom stuff, curvature = dt / ds , where t = tangent angle, s = arc length; and tan t = sin t / cos t = dy / dx . Since your curvature is a polynomial function f(s) of arc length, integrating t = g(s) , where dg/ds = f ; integrating again (and quietly losing an irrelevant sign), x = sin g(s), y = cos g(s) . WFL On 1/11/10, Kerry Mitchell <lkmitch@gmail.com> wrote:
Hi all,
I came across polynomial spirals as generalizations of the Cornu spiral:
http://www.2dcurves.com/spiral/spiralps.html
At the bottom of this page are 4 examples where the curvature is a polynomial function of the arc length. How can one generate a pair of parameterized equations for x and y, given the fact that the curvature is a polynomial function of the arc length?
Thanks, Kerry
-- lkmitch@gmail.com www.kerrymitchellart.com http://spacefilling.blogspot.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun