Three different reformulations of a free surface problem as shape optimization problems are considered. These give rise to three different cost functionals which apparently have not been exploited in literature. The shape derivatives of the cost functionals are explicitly determined. The gradient information is combined with the boundary variation method in a steepest descent algorithm to solve...

This paper deals with the problem of General Shape Analysis. Simple shape measures based on a minimum bounding rectangle are investigated so as to obtain and compare general shape characteristics. The goal of General Shape Analysis is to find for each test object the one or few most similar templates. Thanks to this we can determine general information about a shape, such as how rectangular it ...

The equivalent radius for any solution property is the radius of a spherical particle having the same value of solution property as that of the macromolecule under consideration. Equivalent radii for different properties present a dependence on size and shape that are more similar than the values of the properties themselves. Furthermore, the ratios of equivalent radii of two properties depend ...

The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. However, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameteriza...