GENERATION OF TOPOLOGICALLY CONTINUOUS,SMOOTH,AND FAIR TRIANGULAR ELEMENTS FOR SHIP SURFACES

Abstract

Surface discretization is an essential part of any analytical tool for effective and accurate geometric representation. Triangular element generation is important because it allows topological simplicity, which enables local mesh adaptivity, and it also provides a unique informative database. Most of the existing techniques deal with generation of flat rectangular or triangular elements, using tessellation over Bspline or NURBS surfaces defined over a rectangular domain, and thus may suffer from geometric and topological inconsistencies in the case of triangular domains. This work explores the possibility of the application of surface discretization that deals with topologically continuous, smooth and fair triangular elements using piecewise polynomial parametric surfaces which interpolate prescribed R ^3 scattered data using spaces of parametric splines defined on R ^2 triangulations in the case of ship surfaces. The method is based upon minimizing a certain physics based natural energy expression (i.e. as a fairness norm) over the parametric surface. As for topological continuities between two triangular patches, C ^0 or C ^1 continuity or both have been imposed as required. Approximate C ^2 continuity can also be achieved with the addition of a penalty term, and this has also been considered as a smoothness norm. The geometry is defined as a set of stitched triangles prior to the triangular element generation, and it's selection is based upon the distribution of aspect ratio of the triangular domain over the complete point set, and also the flatness of the geometry. The surface discretization is analyzed using intersection curves with three-dimensional planes for topological continuity, smoothness and fairness. The problems involving triangular element generation for ship surfaces with single or hybrid continuities have been considered.