Best-Fit of Implicit Curves and Surfaces

Curve and surface fitting find their applications in various fields of science and engineering, and, are relevant subjects in coordinate metrology. In this paper, we present two new fitting algorithms for implicit surfaces and plane curves, which minimize the square sum of the orthogonal error distances between the model feature and the given data points. By the new algorithms, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The proposed algorithms are applicable to any kind of implicit surface and plane curve. We give fitting examples for cylinder, cone, and torus.