3. DESCRIPTION OF PROGRAM OR FUNCTION
3DGEOELE is a collection of six programs - LINE, PLANE, CYL, CONE, RING, and TOROID - for nonlinear least squares fitting to a line, plane, circular cylinder, circular cone, ring, and toroid, respectively, in three-dimensional space of a set of measured x, y, z coordinates. The measurements are made by multi-axis coordinate measuring machines. The analysis is based on the residuals being calculated in a direction perpendicular to the surface or line. All six types involve nonlinear relationships, but in the case of the straight line or plane, nonlinear equations are avoided by using linear equations iteratively in repeated two- dimensional fits. In the case of the cylinder, cone, ring, and toroid, the equation of the geometrical shape (element) in the general position is found by taking the standard equation of the element relative to a coordinate system where the principal axis of the element is the z axis of that coordinate system and then by means of transformation equations, converting the equation to be relative to the original coordinate system. These transformation equations are based on three shift constants (in the x, y, z direction) and on two angles of rotation (first counter-clockwise about x, and then counter-clockwise about y). There are two modes of execution: experimental and production. The experimental mode is for checking each program to ensure proper operation and sufficient accuracy in the final results. The production mode is used with measured data where the answers are unknown in advance.