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.
