I want to solve this two non-linear equations for t1 and t2 and do an implementation in C++ afterwards. (Only with the solution functions for t1,t2 only).
Each of the equations should result in 2 solutions, therefore at all 4 solution.
I: x1*t1^2 + y1*t1 - x3*t2^2 - y3*t2 + z1 == 0
II: x2*t1^2 + y2*t1 - x4*t2^2 - y4*t2 + z2 == 0
x1,x2,x3,x4,y1,y2,y3,y4,z1,z2 are known
t1,t2 are only unknown and should be calculated
In Matlab is is possible to solve it easily with
solve(I,II,[t1 t2])
, but I am not able to to is by hand to get the 4 equations to calculate t1/t2.
How can I do this? Or which kind of topic is this problem?
Update:
My question is based on the following solution for the intersection of two rotated parabola, which results in
0 = xa'(t1) - xb'(t2)
0 = ya'(t1) - yb'(t2)
In this solution he describes:
Each of these equation is just a order 2 polynomial. These are easy to solve.