Determine tangent lines on contour

Hi,

I have the following plot (a surf plot with a contour3 plot): http://postimg.org/image/snb7nqilj/

Basically I need to determine the tangent lines at black. First I think to detect the lower and higher value of X to determine the above points of the image. However if the image is more rotated to the right the higher value of X could be in the toe region (this cant be seen in this image but is possible to occur). There is any function that could help me determine this points to draw these tangent lines?

[Armindo]

Any help would be apreciated. As You can see in the image bellow I can get the tangent lines at red by determine the most right and left X positions for the lower and higher regions of the image. In this processed I used the contourc to retrieve the contour line. The problem is that due the rotation of the image sometimes the tangent pass inside the image. The red line at right should be like the yellow tangent. Any details and help about how to acomplish this would be apreciated.

http://postimg.org/image/tsmd6l7qt/ee125063/

[Armindo]

solved through the use of convhull()