ANALYTICAL SOLUTION OF GLOBAL 2D DESCRIPTION OF SHIP GEOMETRY WITH DISCONTINUITIES USING COMPOSITION OF POLYNOMIAL RADIAL BASIS FUNCTIONS

Sa？etak One of the well-known problems in the curves and surfaces reconstruction theory regarding global analytic object description, besides the description of its curvature changes, inflexions and non-bijective parts, is the existence of oscillations near point discontinuities in the middle of the range and at the boundaries of the description. In the ship geometric modelling, ship hull form is usually described globally using parametric methods based on B-spline and NURB-spline, for they have general property of describing discontinuities. Nevertheless, they are not enabling direct, exact calculation of ship's geometric properties, i.e. the calculation of the integrals for determining geometric and other geometry properties or the intersection with water surface. Because of above mentioned, the predominant way of computing geometric properties of the ships is still numerical computation using Simpson integration methods, which also dictates mesh based description of an observed geometry. Analytical solution of global 2D description for ship geometry with discontinuities will be shown in this paper, using the composition of polynomial RBFs, thus solving computational geometry problems, too