I have a 3D triangular mesh representing cortical surface of a brain. I also have one vertex of interest. I would like to unfold a neighborhood of this vertex in such a way that both the angles (their ratios) and distances of paths from this vertex are preserved as much as possible.I read some reviews on mesh parameterization techniques (eg. this one by Scheffer et al.). My understanding is that all the algorithms try to preserve a certain property (angle, distance, area) or a combination of those properties for all of the vertices or faces. In my case I need to preserve angles and distance of paths going from only one point. My intuition tells me that what I need should be quite simple because I demand much less from the output than all those parameterization algorithms. Yet I cannot come up with the solution. Any help is greatly appreciated.
Algorithm to map a triangular mesh onto plane preserving angles and distances from one vertex
mesh;uv mapping