Surface Reconstruction
Poisson's equation is also used to reconstruct a smooth 2D surface (in the sense of curve fitting) based on a large number of points pi (a point cloud) where each point also carries an estimate of the local surface normal ni.
This technique reconstructs the implicit function f whose value is zero at the points pi and whose gradient at the points pi equals the normal vectors ni. The set of (pi, ni) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero. In case this condition is difficult to impose, it is still possible to perform a least-squares fit to minimize the difference between V and the gradient of f.
Read more about this topic: Poisson's Equation
Famous quotes containing the word surface:
“And yet we constantly reclaim some part of that primal spontaneity through the youngest among us, not only through their sorrow and anger but simply through everyday discoveries, life unwrapped. To see a child touch the piano keys for the first time, to watch a small body slice through the surface of the water in a clean dive, is to experience the shock, not of the new, but of the familiar revisited as though it were strange and wonderful.”
—Anna Quindlen (b. 1952)