I need to calculate the intersection of two 3D parametric curves $\vec{C_1}$ and $\vec{C_2}$.
Those curves are parameterised by piecewise functions.
$\vec{C_1}= \begin{pmatrix}x_1(t)\\y_1(t)\\z_1(t)\end{pmatrix}\\ \vec{C_2}= \begin{pmatrix}x_2(t)\\y_2(t)\\z_2(t)\end{pmatrix}$
For example, $x_1(t)$ could look like this:
Ultimately, I need to calculate the intersection in C++ where I could use an arbitrary solver library, but first I need to get the math straight.
How can I transform this problem to a computer solvable formulation?
