# How to determine surface from given normal vectors and their distance on that surface

Situation:

• We have a bendable, non-stretchable surface, like a piece of cloth, with a regular grid on it.
• Unknown manipulation of the surface is done while preserving it's structure
• We recieve 3 dimensional normal vectors from each of the grid points of the surface (but not their coordinates) (V1,...VN)
• Length of each grid unit on a flat surface is equal (L).

The question: What methods could be used to reproduce the surface from these vectors and L?

Reduced question: If we have two (2-dimensional) vectors (angles) and know the length of the curve connecting them, as well as that one of these vectors start from coordinate (0;0) in 2-dimensional plane. How can we approximate the position of the second vector and preferrably the whole curve (assuming, that the curve is quadratic)?

• If say we have two points $p_1$ and $p_2$, we know the normal vector $n_1$ and $n_2$ associated with them respectively, but we do not know $p_1$ or $p_2$'s coordinate? – Shuhao Cao May 31 '13 at 0:35