• Polygon Offset

From BTIS Jeff@21:1/5 to All on Sun Sep 4 14:50:07 2016
I'm looking for a way to get the coordinates of vertices of a polygon offset x pixels within a known polygon. This seems to be a non-trivial problem, but I thought of a trick - What if I have the original polygon drawn by Windows with a thick line,
the inside edges of that thick line will then describe a new polygon. Does anyone know a way to get the coordinates of the inside edges of this thickly drawn polygon. I usually work in VB, VB.NET, or C#, but solution in any language would be welcome.

- Jeff

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• From Noskosteve@21:1/5 to All on Mon Sep 5 14:44:55 2016
You say offset, but from your proposal appear to mean scaled smaller.
Depending on the type of polygon, can you define a center of 'mass' from the verticies,then simply scale it to a smaller size?
--
Cheers, Steve

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• From Dr J R Stockton@21:1/5 to All on Mon Sep 5 20:02:59 2016
In comp.graphics.algorithms message <f5d7ded9-97d6-449c-8dc2-d52cf54722f b@googlegroups.com>, Sun, 4 Sep 2016 14:50:07, BTIS Jeff
<btisjb@gmail.com> posted:

I'm looking for a way to get the coordinates of vertices of a polygon
offset x pixels within a known polygon. This seems to be a non-
trivial problem, but I thought of a trick - What if I have the original >polygon drawn by Windows with a thick line, the inside edges of that
thick line will then describe a new polygon. Does anyone know a way
to get the coordinates of the inside edges of this thickly drawn
polygon. I usually work in VB, VB.NET, or C#, but solution in any
language would be welcome.

Firstly, you need to think what "x pixels from a line" means if the line
is not parallel to an axis.

Secondly, there are at least four types of polygon :
self-crossing,
concave in places,
ordinary,
nearly round.

I guess that yours will not be the first case, probably not the second,
and that the third and fourth are not significantly different.

I assume, them, that you have an ordered set of coordinates for the
original vertices, and an offset in the same units.

I would, for each original side, find its middle, find a parallel line
at distance x inside, and calculate the intersections of each adjacent
pair of inner lines. QED.

If any corner has an internal angle very near 180 degrees, the solution
will be ill-conditioned.

For a sanity check, verify that the distances between each pair of inner
and outer vertices are near enough as expected.

--
(c) John Stockton, Surrey, UK. ¬@merlyn.demon.co.uk Turnpike v6.05 MIME.
Merlyn Web Site < > - FAQish topics, acronyms, & links.

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• From BTIS Jeff@21:1/5 to Noskosteve on Tue Sep 6 13:33:06 2016
On Monday, September 5, 2016 at 5:44:58 PM UTC-4, Noskosteve wrote:
You say offset, but from your proposal appear to mean scaled smaller. Depending on the type of polygon, can you define a center of 'mass' from the verticies,then simply scale it to a smaller size?
--
Cheers, Steve

Not really scaled smaller - if there are concave sections of the polygon, then some of the lines of the internally offset polygon will in fact be longer than the original polygon.

Here is a sample drawing showing inner and outer polygons

+---------------+
| |
| +--------+ |
| | | |
| | | |
| | | |
| +----+ | |
| | | |
+---+ | | |
| | | |
| | | |
+---+ | | |
| | | |
| +----+ | |
| | | |
| | | |
| +--------+ |
| |
+---------------+

You can see the desired inner polygon is not just a reduced scale of the outer original polygon.

- Jeff

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• From Nobody@21:1/5 to BTIS Jeff on Tue Sep 6 23:17:01 2016
On Sun, 04 Sep 2016 14:50:07 -0700, BTIS Jeff wrote:

I'm looking for a way to get the coordinates of vertices of a polygon
offset x pixels within a known polygon. This seems to be a non-trivial problem,

It's not that hard, provided that the insetting doesn't cause self-intersection.

For each vertex, offset the lines corresponding to the adjacent edges by
the desired amount then find their intersection.

but I thought of a trick - What if I have the original polygon
drawn by Windows with a thick line, the inside edges of that thick line
will then describe a new polygon. Does anyone know a way to get the coordinates of the inside edges of this thickly drawn polygon. I usually work in VB, VB.NET, or C#, but solution in any language would be welcome.

Rasterising the polygon and then tracing it? This isn't what I'd consider
a credible solution, given how much more inefficient and error-prone it is
than the geometry approach.

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