I have six parametric equations using 18 (not actually 26) different variables, 6 of which are unknown.
I could sit down a couple of packs of paper and find out what the equations are for each of the unknowns, but is there a simple software solution (I think in Matlab) that spits out six equations I'm looking for?
EDIT:
It's a shame that it was closed, but I think I understand why. If anyone is still interested, the equations (I think) are non-linear:
r11^2 = (l_x1*s_x + m_x)^2 + (l_y1*s_y + m_y)^2
r12^2 = (l_x2*s_x + m_x)^2 + (l_y2*s_y + m_y)^2
r13^2 = (l_x3*s_x + m_x)^2 + (l_y3*s_y + m_y)^2
r21^2 = (l_x1*s_x + m_x - t_x)^2 + (l_y1*s_y + m_y - t_y)^2
r22^2 = (l_x2*s_x + m_x - t_x)^2 + (l_y2*s_y + m_y - t_y)^2
r23^2 = (l_x3*s_x + m_x - t_x)^2 + (l_y3*s_y + m_y - t_y)^2
( rS squared , good place @gnovice!)
Where do I need to find t_x t_y m_x m_y s_xands_y
Why am I calculating them? There are two points p1 (AT 0,0) AT and p2 ( t_x,t_y), for each of the three coordinates ( l_x,l_y{1,2,3}) I know the distances ( r1and r2) to the point of p1 and p2, but in a different coordinate system. Variable s_xand s_ydetermine how much I need to scale one set of coordinates to get to the other, and m_x, m_yas I need to be translated (using t_xand t_y- the method of accounting rotation differences between the two systems)
ABOUT! And I forgot to mention, I also know that point ( l_x,l_y) is lower than the highest of p1 and p2, i.e. l_y<max ( 0, t_y), as well as l_y> 0 and l_y< t_y.
It seems concrete enough that I might just have to pull out my pad and do it mathematically!