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I need to calculate the intersection of two 3D parametric curves $\vec{C_1}$ and $\vec{C_2}$.

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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:

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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?

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    In general they won't intersect. Do you have any concrete examples that you are working with?2015-01-24

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