Re: How to calculate two curves equidistant from a given curve?


Eric Gisse wrote:
> If you have a closed convex plane curve, which is also positively
> oriented [orientation doesn't matter beyond a sign change, though], the
> formula for a parallel curve that is always a fixed distance, r, away
> from the original curve, is given by this forumla:
>
> B(s) = A(s) - r*n(s)
>
> Where s is the parameter, r is the distance, and n(s) is the normal
> vector. B is called a parallel curve to A. It doesn't matter whether
> the parameterization is an arc length one or not.
>
> This was taken pretty much verbatim from DoCamro's "Differential
> Geometry of Curves and surfaces", page 47.

I see. So, in component notation it would be the formula given at
mathworld site. While this will work, the square root required for
normal vector's normalization hurts the performace of evaluating points
on such a curve.

Is there any 'reparametrization trick' that would get rid of the square
root?

Tony

.

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