It is necessary to smooth the point cloud data in reverse engineering or freeform surface inspection. The smoothing
method based on the heat diffusion has a good effect to the point cloud with noise points, but how to choose a proper
penalty function to smooth the point cloud is no answer. The paper proposes a method to decide the penalty function
based on the fuzzy mathematics' relevant function concept. The four special functions, such as rectangular distribution,
drop hemi- distribution, drop hemi-normal distribution and drop hemi-Cauchy distribution, have been analyzed. Each
penalty function has been used to smooth the point cloud by experiment, the result show that drop hemi-Cauchy function
and drop hemi-normal function are fit to be the penalty function. The conclusion is gotten that the variant has a no-linear
relationship with the result of penalty function. Some cases are used to validate the characteristics of penalty function.
There is a new way to handle the point cloud during the preprocessing of reverse engineering or complex surface
inspection.
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