Am 16.06.2009 um 18:33 schrieb Marco Certelli:
Just speculation:
I've a and b that defines a line. I look for the distance between a
point p and the line.
Given the triangle p-a-b where p is the vertex and a-b is the
"base", the area of the triangle can be calculated from the lenght
of its 3 sides (pa, pb, ab).
After that, since the area is also base x height / 2 we can
calculate the height = area / base * 2
well, the height is exactly the distance of the point p from the
line a-b
Maybe...
You are right. It is Heron's formula. And from what I see the
implementation is correct. Even the coordinates on the sphere are no
problem, because the formula itself doesn't use lat and lon and we can
assume the triangle to be flat locally. So I think the implementation
is quite clever indeed.
Okay.
But that still doesn't explain why the map looks better if I reduce
the error distance setting for the Douglas-Peucker filter. The error
should be already invisible at the default setting.
Regards
Thilo
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