# things often done in geometrical applications

From: David Dailey <ddailey@zoominternet.net>
Date: Fri, 28 Jun 2013 16:06:28 -0400

Message-ID: <003301ce743a\$f9f1c660\$edd55320\$@net>
Hi Doug, all,

Thanks for getting this going. Coincidentally, as it's creation was being
discussed, I in the midst of a project that could have used the fruits of
this labor (assuming they might exist in a couple of years).

Here's just a quick list of things that come to mind that one might often
wish to do

Intersecting things, as per Kevin Lindsay's work (wasn't some of this

Lines, circles, ellipses, bezier (c and q) all with one
another

Points closest to one another  on various pairs of curves (simplest being
two non parallel lines or a line and circle)

Lines tangent to a given curve

Closest to a point

At a point

Passing through a poin

Lines tangent to each of two

Circles (see
http://jwilson.coe.uga.edu/emt669/Student.Folders/Kertscher.Jeff/Essay.3/Tan
gents.html )

Ellipses

Tweening - interpolating curves that are intermediate in shape between two
given curves (see the code that comes with <replicate>

Extrapolation - given curves A and B produce C so that B is 1/nth of the way
from A to C.

Given a set of n lines that divide the plane into (n^2 + n +2)/2 regions -
convert those regions to convex polygons returning a collection of polygons

Given a smooth path, convert it to a polygon having n edges for given n>2
most closely resembling the path.

Given a polygon (convex or concave) or more generally,

Form a triangulation of its interior

Form a slight deformation of it (for glyphs we might
consider arbitrary  svg <path>s rather than just polygons

Produce a smoothed version (see
http://srufaculty.sru.edu/david.dailey/svg/Draw018.html -- draw a rectangle,
select it (by clicking on it) and then choose Smooth from the menu that
appears)

Given n points

Find a polygon passing through them

Produce a Voronoi diagram

Produce random

N-gon

Smooth Bezier curves that pass through N control points and
preserve continuous first derivatives

Tessellations (polygonal, or rectangular - think HTML tables
with colspan and rowspan)

That such things are useful (hence implying the existence of use cases)
seems obvious through a simple glance at the last 2500 years of progress in
algebra, mensuration and geometry.

BTW, Inkscape has some of this stuff already, as does <replicate>, neither
of which I saw in the script library listed in the wiki.

Cheers

David

Received on Friday, 28 June 2013 20:07:04 UTC

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