Determination of angle to tangent surface for 3d data in Matlab

Skills required: Matlab (data import, 3d plotting), linear algebra (tangential planes to surfaces, vector description of planes). The goal of this project is to provide a function which tells the angle at an arbitrary x,y position between the z-axis and the surface normal. For this a function in matlab should be written which returns the normal vector of a tangential plane to a surface described by 3d-data (x coordinate in mm, y coordinate in mm, z coordinate in micro meter). Input parameters for the function are arbitrary x and y positions. The data and an example script for loading the data into matlab will be provided. An additional (preperation) step is a plane correction to account for a tilting of the holder base (see picture). This surface can be assumed to be flat but it is not perfectly aligned parallel to the x,y-plane. Thus the data for the actual sample should be corrected for this imperfection by fitting a plane to the holder base altitude data.