I need to sample data in space on the faces of a 3D cube.
Is there a parametric equation that approximates the square (in 2D) or the cube (3D) ?
Thanks a lot!
A parametric equation that describes a surface must have two parameters, call them and . Suppose you want a plane that runs through a point which contains two nonparallel lines and . (In the case of a square in the first quadrant of a Cartesian plane with a corner at the origin, your point will be anywhere in the square and the lines can be and .) Suppose the equations of the lines are given as and for constants and suppose the point's coordinates are . Then the parametric equations of the plane will be .
Probably the lesson here is that, whatever you're doing, you don't want to be doing it with parametric equations. I could be wrong.
Thank you very much for your answer! In fact i do need to sample data on the surface of the cube (or more precisely on a surface very close to the cube).
That's to find an optimal configuration of points on the cube for a given energy ( minimization with least square criteria).
The best would be maybe to look at spherical coordinates, it might be more easy...