Novel re-parameterization for shape optimization and comparison with knot-based gradient fitting method

In order to avoid a large number of partitions without geometric features, this paper develops a re-distribution method of the matrix representation of the geometry. Along with the outlined single-patch NURBS parameterization approach and projection of geometry into a rectangular domain, the proposed method allows numerically sufficient representations of the geometry of each partition. The procedure develops a redistribution of the matrix representation of the 3D geometry based on shape features, whereby other scalar fields (e.g. loading-related) can also be used. Another original contribution of the paper is the developed analytic expression for gradient-based enhanced fitting with respect to knot values.