positioning maths

Nov 11, 2003 2 Replies

I have 3 light sources on the ceiling that form an equilateral triangle. I'm on the floor looking at them with some kind of high res device so I have rather accurate x-y (angles) coordinates for these 3 points (0.01° rms). From this, I want to precisely compute my position and my orientation.



Does anybody knows where I can find some usable formula or a way to solve this. Before I spend the night doing the math's ;-)



Thanks



Marc



BTW I'm still looking for people to contribute to: cl-typesetting

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and cl-pdf
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Marc Battyani wrote: Hmm,

Sounds similar to the math used to calculate specular reflections from a flat surface in 3D. Check an advanced graphics text, that should get you close. It's fairly complex matrix math though.

DLC

: I have 3 light sources on the ceiling that form an equilateral triangle. : I'm on the floor looking at them with some kind of high res device so I have : rather accurate x-y (angles) coordinates for these 3 points (0.01? rms). From : this, I want to precisely compute my position and my orientation.

: Does anybody knows where I can find some usable formula or a way to solve : this. Before I spend the night doing the math's ;-)

: Thanks

: Marc

: BTW I'm still looking for people to contribute to: : cl-typesetting

formatting link
: and cl-pdf
formatting link

formatting link
See Law of Sines, particularly relating to h (which is height to ceiling in your example, and your only known distance)

See also Law of Cosines.

Given these, you can solve all triangulation problems.

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