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

Abstract

Large point clouds and surface meshes generated by 3D scanning of existing objects can be converted into parametric models and used as initial solutions for shape optimization based on given excellence criteria and constraints. In many applications, multi-patch NURBS (Non-uniform rational B-splines) parameterizations of 3D shape models are constrained to a small number of shape partitions which do not contain the dominant geometric features. In many cases, the geometry of an object does not include clearly defined natural borders to be used towards subdividing the model into such partitions.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.