The inspection of free-form surfaces is an important task in manufacturing process control. This task motivated researchers to develop methodologies and technologies for fixtureless inspection. The motivation for performing fixtureless inspection rises from the fact that a datum or an exact fixture is not always available for free-form objects. When datum and fixtures are not present, the location and rotation of the object in space relative to the sensor coordinate system are unknown. Thus, scanning along a proper trajectory is not trivial especially when dealing with high precision sensors with small depth of field (DOF). In this paper we introduce a theoretical scheme for real time curve extrapolation. This scheme performs real time automatic adjustment to the sensor depth of field by smoothly changing the position of the sensor. The proposed scheme can handle local C1 discontinuity (C0 continuity). In the proposed scheme, the velocity of the motion stages can be controlled by the curvature of the extrapolated curve, thus controlling the density of the sampled data. Also, no knowledge of the surface orientation and location is needed nor any reference plane or other datum. The scheme was tested using computer simulation that was developed for this purpose. The robustness of the scheme is shown at the end of this paper through simulation results using high order polynomial surfaces as test cases.

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