piecewise-linear surface approximation from noisy scattered samples
We consider the problem of approximating a smooth surface f(x,y), based on n scattered samples {(x i , y i , z i ) n i =1} where the sample values {z i } are contaminated with noise: z i = f(x i , y i ) + ? i . We present an algorithm that generates a PLS (Piecewise Linear Surface) f 1 , defined on a triangulation of the sample locations V = {(x i , y i ) n i =1}, approximating f well. Constructing the PLS involves specifying both the triangulation of V and the values of f 1 at the points of V. We demonstrate that even when the sampling process is not noisy, a better approximation for f is obtained using our algorithm, compared to existing methods. This algorithm is useful for DTM (Digital Terrain Map) manipulation by polygon-based graphics engines for visualization applications.
surface approximation noise sampling smooth values algorithm triangulation locatability point demonstrate process method digitize manipulation graphics visualization applications polygon