As for machining points data processing, many researches could be applied in our
CAD/CAM model for optimal machining points. Fitting surfaces to 3D cloud points
generated by laser range scanning systems is one of the most important problems in
CAD modelling. The ordinary representation for fitting such data in geometric model-
ling is the tensor product B-spline surfaces. However, it is extremely difficult for
them to handle surfaces with arbitrary topology, and to maintain continuity conditions
near the extraordinary points (Derose T 1998). Then subdivision surfaces become
very popular in movie production and game engines as an alternative to the tensor
product B-spline (Ma W.Y. 2005).
A large number of subdivision theories were widely used in geometric design and
computer graphics for shape design, animation, multi-resolution modelling and many
other engineering applications. With many similar properties to B- spline, it allows
the design with efficient, hierarchical, local, and adaptive algorithms for modelling,
rendering and manipulating free-form objects of arbitrary topology.
By using the Loop subdivision (Loop C 2005), the data points given in triangular
mesh with arbitrary topology, could be approximated with many advantages as sim-
plicity, high speed, high scalability and generality (Yu N. 2008). The algorithm can be
realised with a given triangular/ quadrilateral mesh as a control net of a Loop/
Catmull-Clark subdivision surface.
Applying Loop subdivision into SBG machining model is an original try and some
visual experiment results will be shown in following sections.
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