things often done in geometrical applications

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
already in SVG 1.2?):

                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