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Figure 2 Determine unknown object point coordinate (absolute modeling approach).

x 0, y 0, is principal point coordinate.

Figure 4 Determine unknown model point coordinate (relative modeling approach).

Then the geometric error is computed from the set of point coordinates provided by the machine.

A moving coordinate system, with origin, is used for the target point coordinates, where =.

The seed point consists of a point coordinate and its associated normal.

And the track also reserves an entry which stores 3D point coordinate.

The objective and constraints are nonlinear polynomial functions of the point coordinates defining the cross-sectional shape.

The transformation from the absolute coordinates to the contact point coordinates, relative coordinates that have z-axis in the nominal direction of the surface, are described below.

The motion trail is solved according to the feature point coordinates on the reference plane in different frames.

Finally, the effect of uncertainty in the point coordinates is considered by means of a bootstrap analysis.