How to determine equation of curves through points in a script?

Hi everyone,

I have a lot of arrays of x-y coordinates of points which curves pass through. I want to determine the point of tangency between a line and a curve. So I need to specify the equation of curves. The number of the curves is not specified, so I can't use Curve Fitting Tool box.

To smooth the curve I also use interp1('pchip') to make interpolated points. In another way, could I save the interpolated results by interp1 as an equation?

Could someone tell me how to do it in a script?

X-Y Coordinates: (1st row is Y coordinate, 2nd is X coordinates)

curve1=[515 525 561 600 632 700 761 800 900 1000 1014 1750;
0 150 300 394 450 540 600 631 696 745 750 865];

curve 2=[442 452 484 500 547 600 658 700 800 856 900 1000 1337 1750;
0 150  300 347  450 532  600 640  716 750  773 816  900 928];

Thanks.