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
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