Math Help needed: Polevector for Ik System

This might get you started...

4 Coplanar points

| x1  y1  z1  1|
| x2  y2  z2  1|
| x3  y3  z3  1| = 0
| x4  y4  z4  1|

Since you know that the vectors for P1 + Y = P4 and simultaneously P3 + M = P4 you can equate these and (I think) solve for the x,y,z of P4.

Here Y is the vector representing the Yellow line and M is the vector for the Magenta line.

the above matrix becomes

| x1      y1     z1     1|
| x2      y2     z2     1|
| x3      y3     z3     1| = 0
| x1+Yx   y1+Yy  z1+Yz  1|

and

| x1      y1     z1     1|
| x2      y2     z2     1|
| x3      y3     z3     1| = 0
| x3+Mx   y3+My  z3+Mz  1|


so... uh... now you need to do the math for the cross and dot products to calculate the determinant.

... this might help Determinant Expansion by Minors

My head hurts now... and I'm not sure if all that is doable :-)