Intersection of a line with a surface?

I have a 3D array of points generated by repeatedly solving a given system of equations. This array of points (not evenly spaced) is used to generate a surface in Matlab. Independent of this surface, a straight line outside of the surface is generated and placed so that it intersects this surface at a single point only. What I need to know are the coordinates of the point of intersection of the line with the surface. To extract this information, I need to know the equation which describes the surface. Can I extract such an equation for the surface plotted in Matlab and if so how? If not, is there some way in Matlab to determine the coordinates of this point of intersection? Thank you for your help.