A revisit to fitting parametric surfaces to point clouds

We study the performance of algorithms for freeform surface fitting when different error terms are used as quadratic approximations to the squared orthogonal distances from data points to the fitting surface. We review the TD error term and the SD error term in surface fitting to point clouds, present robust surface fitting algorithms using the TD error term and a new variant of the SD error term. We report experimental results on comparing them with the prevailing PD error term in the setting of fitting B-spline surfaces to point cloud data. We conclude that using the TD error term and the SD error term leads to surface fitting algorithms that converge much faster than using the PD error term.

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► We revisit some error terms in freeform surface fitting to point clouds.
► We present robust implementations of the SD and TD error terms.
► We report fast convergence rates of using the TD and SD error terms.