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SURFACE MODIFICATION BASED ON THE LOCALLY MEASURED DATA
Iain Ainsworth, Djordje Brujic, Mihailo RisticImperial College of Science, Technology & Medicine
Dept. of Mechanical Engineering
London SW7 2BX, United Kingdom
i.ainsworth@ic.ac.uk
d.brujic@ic.ac.uk
m.ristic@ic.ac.uk
A frequent requirement in computer aided design and manufacture is to update an existing CAD model using measured data. Two fundamental problems must be addressed to accomplish this task: parameterisation of measured data and ill-conditioning of the least squares surface fitting. We propose to solve the parameterisation problem by employing a suitable base surface, automatically generated from the data points, or provided as a CAD model if available. The problem of singular or ill-conditioned matrices results from incomplete data sets and it is particularly evident in situations involving local surface updating and when knot insertion is applied for local surface refinement. The proposed method overcomes ill-conditioning by introducing additional fitting criteria in the minimisation functional, which constrain the fitted surface in the regions with insufficient number of data points.
Two main benefits were realised by this approach. First, local surface updating can be performed by treating the surface as a whole, without the need to specially identify the regions with insufficient data, nor to re-measure those regions. Second, the quality of the unmeasured regions may be controlled to suit specific needs. The realised computational speed and the quality of the results were found to be highly encouraging and the method was found to be especially useful in situations involving knot insertion and large surface deformations.