This applet handles a problem that occurs if you define a tangential
discrete vector field at the vertices of a triangulation. Tangential means
that every vector lies in one of the planes that are defined by the adjacent
elements. So every vector is in general only tangential to one element. We
want to find the best representative tangential vectors on the other elements
of one vertex star.
This applet compares four different methods that try to solve this problem
(more or less successfully). It creates a (mostly) random vector field on the
model that is imported by the user by the 'Models' panel and then applies one
of the methods to generate integral lines to this vector field.
| projection |
The vector at a vertex is treated to be a 3-dimensial
vector and is then projected onto the plane of the element to get the
representative vector belonging to this element. Creates interesting
artifacts especially at vertices with high curvature. |
| geodesic completion |
Generates the representative vector of an element by
rotating the original vector in the vertex star to the
element and then rotating back the same angle in the elements
plane. |
| geodesic translation (half angle) |
Determines the representative vector of an element by
geodesic translation of the original vector along the bisector of the
element. That is some sort of discrete version of the continuous
geodesic translation method below. |
| geodesic translation (continuous) |
Determines the representative vector of an element by
geodesic translation of the original vector along the connection between
the vertex and the point on the element in which the vector field shall
be evaluated. So each element has not only one representative vector but
a continuous representative vector field. |
You can look at an integral line of the current vector field by pressing
'i' and picking an initial point on the surface the same time. Parameters
'Length' and 'Discr' control this integral line.
Create a LIC texture image of the vector field by pressing the button
'calculate LIC texture'.
