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The main difficulty in combining
free-form shapes and parametric shapes lies in finding a way
to unite these two seemingly different representations into
a single analytical and computational framework which supports
free-form and parametric shape control simultaneously, and
lends itself to rigorous shape sensitivity analysis to
guide the shape optimization procedure. We propose to represent
both free-form shapes and parametric shapes implicitly using
level sets of higher-dimensional functions (hyper-surfaces)
and use the theory of R-functions to represent arbitrary set
combinations of such shapes.
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