MATLAB Set up: Finding closest point on a surface 1 of 2

This video sets up the plan for how to find the closest point on a surface to a given point. This is a numerical approximation that avoids the inevitable complexities of solving the problem exactly with computational geometry techniques.

[monstercolorfunco]

i was thinking of somehting similar to find normals of vertices of a curved surface... except that i need the closest point on the theoretical surface that generated the geometry, i.e. the formula, rather than the mesh. to find the normals i am going to try to make a slightly larger/smaller version of the surface, and then seek the points close to the vertex and take the closest one. but i donno much about maths its a challenge!