Re: Polygon coordinates transformation
Tommy wrote:
> Juergen wrote:
>> I don't think that this is the case. I think in your equations:
>> x1 * a + y1 * b + c = u1
>> x2 * a + y2 * b + c = u2
>> x3 * a + y3 * b + c = u3
>> x4 * a + y4 * b + c = u4
>>
>> the variables u? (belonging to the source polygon) are known, but the
>> variables x? and y? (belonging to the destination polygon) are *not*
>> known. If you knew the values of the variables x? and y?, you were
>> already done, and it wouldn't be necessary to do any calculation ... 
>> And what about the variables a, b, and c? I'm not sure whether or not
>> you know them, because I don't know their meaning.
>
> (x?, y?) are the 4 coordinates of the corners of the polygon, so those are
> known. I'm trying to find a, b and c.
>
>> Assumption:
>> You want to be able to change the *size* of any polygon with 4 corners,
>> without changing its shape, i.e. without altering any of its *angles*.
>> Is this true?
>
> No, it's not.
Oops. Then I misunderstood your original post, sorry.
> I have 2 polygons that don't need to be of the same shape.
> Polygon 1 has coordinates {{x1, y1}, {x2, y2}, {x3, y3}, {x4, y4}} and
> polygon 2 has coordinates {{u1, v1}, {u2, v2}, {u3, v3}, {u3, v3}}. If I
> take a random point that is part of polygon 1, I need to find the
> corresponding point in polygon 2.
It sounds to me, as if this problem can't be solved, because it's not
defined exactly. In your original post, you wrote:
| I need to find a formula that transforms a coordinate {x, y} inside
| polygon_destination to a coordinate {u, v} inside polygon_source.
But you didn't specify, what kind of transformation you want to do.
Also, if you have two quadrilaterals with different shapes,
say a trapezoid ( http://mathworld.wolfram.com/Trapezoid.html )
and a kite ( http://mathworld.wolfram.com/Kite.html ),
and then you take a random point of the trapezoid, what do you mean
by "corresponding point" in the kite?
Regards,
Juergen
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