Title: Structured Grid Generation over Biparametric Surfaces

Abstract

Structured grid generation over biparametric polynomial surfaces
is a difficult problem, given that the grid must satisfy constraints
such as smoothness, control over clustering of points and
orthogonality at the intersections of grid lines. In this work
we have studied the established methods for grid generation and
defined some new methods for tackling the problem. 

The first method views the problem of structured grid generation
as an energy minimization problem. An energy value can be
associated with the given state of a system by formulating an
appropriate function over the system variables. The function should
be formulated such that it has the minimum value
for the desired state. We formulate energy functions such that
the desired configuration of grid points (system variables)
minimizes these functions.
 
The second method recognizes the non-linearity of the functions
defining the parametric surfaces as one of the major problems in
achieving an intuitive control over the distribution grid points.
Here, we reparameterize the surface patch of interest to determine
a mapping that is as length-preserving as possible.
This new parameterization is then used to generate structured
grid on the surface. Further, a method for generating grids over
arbitrary four-sided trimmed surface patches using reparameterization
scheme has been proposed.

Keywords: structured grid generation, energy minimization, 
	mesh relaxation, reparameterization, trimmed surface patches