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Re: Topography contours

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Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> If you have a topology in continuous space that you can sample to
> arbitrary resolution, both in space and in height, what is the best
> way of producing isomers (contour lines of equal height).

I've never heard of the called that before.  If you are searching, I
think contour lines will be more successful

There must be established algorithm for this and if you find one, please
post a link.

If you can assume your function is continuous and smooth, I thought you
could use partial derivatives to find the tangent of the contour at a
given point.  You could the move some small step in that direction and
try again.  But to stop errors piling up, you'd have to a search in the
neighbourhood of the end point for a close match to the starting value.

Given that, maybe just a search at each step is the best bet.  If the
function is smooth in relation to the step size you want to take, you
might get away with a binary search of the points on a circle of radius
r (the step size) away from the previous point, with the angles ranging
from -pi to +pi and 0 being "ahead" -- the direction of the last line
segment in the contour.  (It would be easier to describe with a
diagram!)

And you could, of course, make the step size dependent on how smooth
the function is in an particular neighbourhood.

-- 
Ben.

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Topography contours Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2020-11-11 09:26 -0800
  Re: Topography contours Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-11-12 15:57 +0000
    Re: Topography contours Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2020-11-12 08:24 -0800
      Re: Topography contours Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-11-12 17:44 +0000
        Re: Topography contours Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2020-11-13 05:22 -0800

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