1 research outputs found
Smooth Bezier Surfaces over Arbitrary Quadrilateral Meshes
We solve the following problem: given a polynomial of order and the
corresponding tensor product patches over an unstructured regular
quadrilateral mesh of any valence, find a solution to the or
approximation (resp. interpolation) problem ! Constraints defining regularity
conditions across patches have to be satisfied. The resulting number of free
degrees of freedom must be such that for instance the interpolation problem has
a solution. This is similar to studying the minimal determining set (MDS) for a
continuity construction. The givenunstructured quadrilateral mesh can
include a cubic boundary curve. The final surface approximation or PDE solution
is obtained by energy methods. We completely solve the problem and show that
there is always a solution for and under some mesh restrictions for
. From a practical point of view, the present paper provides a way to
build first order smooth interpolation/approximation and solutions to partial
differential equations for arbitrary structures of quadrilateral meshes.Comment: 170 pages, 56 figures Revised version to include a new result by J
Peters on G1/C1 IGA matching of a pair of patches,, and some recent
reference