I have six parametric equations using 18 (not actually 26) different variables, 6 of which are unknown.
I could sit down with a couple of pads of paper and work out what the equations for each of the unknowns are, but is there a simple programatic solution (I'm thinking in Matlab) that will spit out the six equations I'm looking for?
EDIT: Shame this has been closed, but I guess I can see why. In case anyone is still interested, the equations are (I believe) 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
(Squared the r
s, good spot @gnovice!)
Where I need to find t_x
t_y
m_x
m_y
s_x
and s_y
Why am I calculating these? There are two points p1 (at 0,0
) and p2 at(t_x,t_y
), for each of three coordinates (l_x,l_y
{1,2,3}) I know the distances (r1
& r2
) to that point from p1 and p2, but in a different coordinate system. The variables s_x
and s_y
define how much I'd need to scale the one set of coordinates to get to the other, and m_x
, m_y
how much I'd need to translate (with t_x
and t_y
being a way to account for rotation differences in the two systems)
Oh! And I forgot to mention, I also know that the point (l_x,l_y
) is below the highest of p1 and p2, ie l_y
< max(0
,t_y
) as well as l_y
> 0 and l_y
< t_y
.
It does seem specific enough that I might have to just get my pad out and work it through mathematically!