polygon offset algorithm

What do you mean by an 'offset from a polygon' ?
I also would like to know more about your polygon. Is it in 2d or 3d, can it be concave or is it always convex?
.luc.

I have an array of coordinates x,y (2d) that can be in any direction
and the polygon does not have to be closed

I have the offset in milimiters and can calculate the angle of each vertice

What i need to do is recreate the same ''shape'' but taking into
considaration the offset set by the user. dont worry about conversion of any kind i take care of that already

it is not a copy of the shape, cause if you draw a square, an try
to draw on offset of that square from the inside or outside. the length of each vertices will be shorter or longer tan the original shape. this it what i need to calculate.

So how do you specify an "offset"?  Do you just want to multiply all the coordinates by a constant?

the offset is a double specified by the user

it can be between -1000 and 1000 in mm, but don't worry about
conversion.

How can an offset change the length of the vertices. What do you mean by an 'offset'. It certainly isn't a linear transformation (like a translation (thui's answer), or a rotation) because they don't change the vertices. So what is an 'offset'?
.luc.

I also don't understand what you mean by an offset "from the inside or outside"
Is -10mm inside or outside a square?

Do you mean scaling?

Maybe the idea is to add a border around the polygon?
(in which case, you could just thicken each edge,
but how would you want to handle corner rounding?)

It looks like what you call offset polygone is a new polygone whose lines are at a given distance of the original polygone.
It is not like shrinking or growing the polygone. Except for special shapes like a cube for instance. For a rectangle for instance, after growin, the border distance with the original rectangle will not be constant.

I have heard of a similar application for processing fonts outline. The problem is trivial for convex shapes and complex for concave shapes because in this case the new polygone may have self overlapping parts.

If my understanding is right, you have to find the equation of the prallel line at the given offset(distance) and then compute the instersection of two consecutive segments to compute the new polygone corner points.

For concave polygones, if you want a non overlapping offset polygon, you wil need to clip and this may result in more than one polygone.

Don't you think 200 points is too much for such questions ?

in the case of overlapping i can always find the intersection of the two point, but if you do a mirror of tha line you will find that there is a missing segment this is what i need to resolve my
problem... thank's

maybe 200 hundred is a little too much, but i need a quick answer

So it sounds like you are thickening each edge, and your problem is how to handle the corners?
If so, 4 basic methods are:
1) Extend the lines until they intersect (which can extend long tails at sharp corners)
2) Round the corners with a circular arc.
3) Connect the ends of the "offset" lines with a straight segment
4) Just leave the corner open.