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 )_i=1ⁿ} where the sample values {z_i} are contaminated with noise: z_i=f(x_i , y_i)=ε_i. We present an algorithm that generates a PLS (piecewise linear surface) f´, defined on a triangulation of the sample locations V={(x_i, y_i) _i=1ⁿ}, approximating f well. Constructing the PLS involves specifying both the triangulation of V and the values of f´ 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