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Re: Fierce and scary geometry algorithm for ‘ParallelPath’

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On Sunday, April 21, 2019 at 5:29:23 AM UTC-5, jdawisema...@gmail.com wrote:
> Good approach. 
> 
> But:
> • Circle is a particularly easy case. 
> • I dislike flattenpath, as it causes slight corners where curve meets a line or curve that ought to be continuous. 
> 
> Algorithm for latter. 
> ◊ For a Bézier cubic, calculate a straightness, which might the range of angles of tangents. 
> ◊ If that bigger than, say, 22½°, recurse. 
> ◊ Calculate end points of left hand, and partial derivatives wrt to the z of the curve long which walking, and double derivs.
> ◊ Have ApproximatingCurve make that into a Bézier cubic. https://groups.google.com/forum/#!topic/comp.lang.postscript/3RIq0Jnwrbo
> 
> There’s still a lot of awkwardness of sewing these pieces together. E.g., in a serif of a font, there might be many dozens of pieces to discard.

I had an emotional reaction to your response, but sat on it and studied
it, and with more distance I'm beginning to see what you're getting at.

Your sketch is more complicated but probably more correct. 
ISTM for parts of the image, we want something like a *morph* between
the inner curve and the outer curve. So, running along two curves
and producing a new curve place at a specified proportionate 
distance between the two, and comprising a shape that is a 
specified proportion of the shapes of the two source curves.

If one of the two source curves can be degenerate then that
gives: growing to infinity, shrinking to zero, interpolating
between curves. 

I think I should read up on 'upath' which I think handles some of the
gymnastics I've been doing with paths. Writing a function to take
two paths can't really work with the currentpath as naively as I've
grown used to doing.

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Fierce and scary geometry algorithm for ‘ParallelPath’ jdawiseman.bloomberg@gmail.com - 2019-04-17 13:37 -0700
  Re: Fierce and scary geometry algorithm for ‘ParallelPath’ edspikechapman@gmail.com - 2019-04-19 08:55 -0700
    Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdawiseman.bloomberg@gmail.com - 2019-04-20 02:44 -0700
      Re: Fierce and scary geometry algorithm for ‘ParallelPath’ Carlos <carlos@cvkm.cz> - 2019-04-29 02:41 +0200
        Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdaw1 <jdawiseman@gmail.com> - 2019-06-19 15:04 -0700
          Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-22 13:33 -0700
            Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-22 14:54 -0700
              Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-22 15:37 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-23 15:59 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-27 06:59 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-27 07:48 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-27 08:30 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-06-28 12:10 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-07-19 14:00 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-07-20 09:33 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-07-20 13:20 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdaw1 <jdawiseman@gmail.com> - 2021-03-14 10:25 -0700
  Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdawiseman.bloomberg@gmail.com - 2019-04-20 06:54 -0700
    Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-04-20 10:44 -0700
      Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdawiseman.bloomberg@gmail.com - 2019-04-20 11:01 -0700
        Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-04-20 11:33 -0700
          Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-04-20 11:50 -0700
            Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-04-20 13:01 -0700
              Re: Fierce and scary geometry algorithm for ‘ParallelPath’ jdawiseman.bloomberg@gmail.com - 2019-04-21 03:29 -0700
                Re: Fierce and scary geometry algorithm for ‘ParallelPath’ luser droog <luser.droog@gmail.com> - 2019-04-28 13:33 -0700

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