[Numpy-discussion] Creating parallel curves

Jonathan Hilmer jkhilmer@gmail....
Sun Feb 12 14:59:12 CST 2012


Andrea,

I realized that my answer wouldn't be complete, but as people have
pointed out that's a substantially more difficult question, so I
wanted to give you a complete answer to just a subset of your problem.

I'm currently writing a variant that avoids the overlapping normal
vectors by interatively 1.) expanding along normals then 2.)
condensing points, for every iteration.  However, I'm doing it mostly
for my own interest since I'm pretty sure it will not be functional
when complete: your problem is that calculation of derivatives/normals
is going to become unstable in acute convex regions, and the overlap
issue there will become more severe.  I would strongly recommend
adapting some existing library for this problem.


Jonathan


On Sun, Feb 12, 2012 at 1:37 PM, Charles R Harris
<charlesr.harris@gmail.com> wrote:
>
>
> On Sun, Feb 12, 2012 at 1:26 PM, Andrea Gavana <andrea.gavana@gmail.com>
> wrote:
>>
>> Charles,
>>
>> On 12 February 2012 21:00, Charles R Harris wrote:
>> >
>> >
>> > On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana <andrea.gavana@gmail.com>
>> > wrote:
>> >>
>> >> Hi All,
>> >>
>> >>    my apologies for my deep ignorance about math stuff; I guess I
>> >> should be able to find this out but I keep getting impossible results.
>> >>
>> >> Basically I have a set of x, y data (around 1,000 elements each) and I
>> >> want to create 2 parallel "curves" (offset curves) to the original
>> >> one; "parallel" means curves which are displaced from the base curve
>> >> by a constant offset, either positive or negative, in the direction of
>> >> the curve's normal. Something like this:
>> >>
>> >
>> > Note that curves produced in this way aren't actually 'parallel' and can
>> > even cross themselves.
>>
>> I know, my definition of "parallel" was probably not orthodox enough.
>> What I am looking for is to generate 2 curves that look "graphically
>> parallel enough" to the original one, and not "parallel" in the true
>> mathematical sense.
>>
>
> You could try setting a point and 'contracting' the curve towards the point.
> A point a infinity would give the usual parallel curves. There are probably
> a lot of perspective like transformations that would do something similar.
>
> Chuck
>
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