If you know the values of a function at the three points of a triangle, how can I determine the values at points in the interior? {details}?

If you know the values of a function at the three points of a triangle, how can I determine the values at points in the interior? {details}?
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1 Answer

Answer :

Noticing the fact that on the first two triangles in the image that points of equal values lay on parallel lines, I wonder if this is the case for the larger triangle. If it is, then the parallel lines are not parallel to the sides of the triangle, and I wonder how to find the equations for the lines.
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