Quote:
Originally Posted by ris8_allo_zen0  Hi all,
during some hobby research I encountered a geometrical problem I can't solve for my knowledge. I hope you can give me some help:
I have a square which I know the edge length (1); then I have a point, outside of it, and segments that connect it to each square's vertex. I know the angles between each segment and the next.
I need to know the length of at least two segments, and/or the coordinates of the observer if we place all them in a Cartesian plane.
This is needed for me for a sort of "perspective identification": i need to know the observer's orientation (yaw/pitch/roll) and distance w.r.t. to the reference square. Only when the above problem is solved, I think I can easily adapt it into 3D. But if you have good solution for this "bigger" problem too, feel free to inform me 
Many many many thanks!!! and greetings from Italy!
Enrico |
If you don't know the coordinates of the point outside of the square, then one solution is to draw the four different triangles formed by two segments and a side of the square. In each triangle you know the length of a side (edge length of square = 1) and the angle between the two unknown sides (the angle between two segments). You can then use the cosine rule to write down four equations, each equation will have the length of two segments in it.
Four equations (cosine rule applied to each triangle) and four unknowns (four segments). Solve simultaneously.