Problem: Computing path length on cubic spline?

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1 total messages Started by Sean Burke22 Wed, 27 Jan 1993 23:48

#1011

Author: Sean Burke22
Date: Wed, 27 Jan 1993 23:48

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Hi Netters,

  I've stumbled on what appears to be a surprisingly intractable
problem.  Let us say that you are using a set of cubic spline
functions to define a path through a set of points.  Now you
want to know the total length of this path.  Simple, right?
For each spline function,

	 y = A + Bx + Cx^2 + Dx^3
so
	dy = [b + 2cx + + 3Dx^2]

so the path length is described by a differential equation of the form

	dl = SQRoot[ dx^2 + dy^2] = SQRoot[Q + Rx + Sx^2 + Tx^3 + Ux^4]dx

  I have come to despair of finding an indefinite or definite 
closed-form solution to the integral of dl.  Is there no 
alternative to integrating these spline functions numerically? (Ouch!)
I thought that cubic splines were pretty straightforward, but 
suddenly I'm in over my head.  If anyone has encountered this
problem before, or cares to make a suggestion, I would be grateful.

Sean Burke
-- 

Sean Burke			sean@netcom.com

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