Re: Geometry problem (slightly OT)
Re: Geometry problem (slightly OT)
- Subject: Re: Geometry problem (slightly OT)
- From: Graham Cox <email@hidden>
- Date: Wed, 22 Sep 2004 00:59:07 +1000
On 22 Sep 2004, at 12:26 am, Nicko van Someren wrote:
The knowns are:
* A single point representing the centre of the intersection - both
rects are centred widthwise at this point.
* The angle between the rects and their angles on the plane
* The widths of both rects, which can differ
This is easy. Given the way you have described the rectangles they
can each be considered to consist of two parallel sides which are
important and two ends which are unimportant. If the first rectangle
has important sides A and B and the second has important sides C and D
then the vertices of your rhomboid are the intersection point AC, AD,
BC and BD.
Yes, this is easy ;) However, they aren't really rectangles, they're
lines that go off for a long way and in fact are part of a curve, but
in the local intersection area they can be considered to be rectangles.
Given this, I don't have the points A B C and D, I only have the
specific information listed above. Generating the points A B C D from
this information is as difficult as the solution I'm looking for it
seems. Normally trigonometry is not something I have a problem with,
but in this case I haven't been able to come up with a geometric
construction that yields readily to being worked on with trig
functions. Intuitively I can see that I have all the info I need to
solve the problem, but deriving the solution with only that info is
proving a bit tough. Maybe I'm just too tired...
I'll sleep on it.
Graham
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