Study Hodge splitting of discrete vector fields. A vector field is split
in a rotation free part (gradU) that has divergence, a divergence free part
(CoGradW) that has rotation and a remaining harmonic component. A potential
is calculated for each of the rotation free (u) and divergence free (w)
parts. The rotation free vector field is the gradient of it's potential u
and the divergence free vector field is the 90 degree rotated gradient of
the potential w.
In this example a potential creates the original vector field that is
then decomposed. The centers of the potential are the vertices of a point
set. Keep pressing key 'a' while clicking the left mouse button to add a
vertex of type as specified at 'Vertex Type'. Click and drag single vertices
to move them around and see the decomposition follow your changes.
You may also invoke a LIC image generator that computes Line Integral
Convolution images for the original and all decomposed vector fields. Press
the button 'Compute LIC Image' to do that.
Description of the other panels:
| Domain |
Change dimensions and discretization of the
triangulation. |
| Min U |
Panel that controls the minimization process
that is used to generate the potential of the rotation free
component. |
| Min W |
Panel that controls the minimization process
that is used to generate the potential of the divergence
free component. |
