Abstract:
Designing tensor fields in the plane and on surfaces
is a necessary task in many graphics applications, such as
painterly rendering, pen-and-ink sketch of smooth surfaces, and
anisotropic remeshing. In this paper, we present an interactive
design system that allows a user to create a wide variety of
surface tensor fields with control over the number and location
of degenerate points. Our system combines basis tensor fields
to make an initial tensor field that satisfies a set of user specifications.
However, such a field often contains unwanted
degenerate points that cannot always be eliminated due to
topological constraints of the underlying surface. To reduce the
artifacts caused by these degenerate points, our system allows the
user to move a degenerate point or to cancel a pair of degenerate
points that have opposite tensor indices.
We observe that a tensor field can be locally converted into
a vector field such that there is a one-to-one correspondence
between the set of degenerate points in the tensor field and the
set of singularities in the vector field. This conversion allows
us to effectively perform degenerate point pair cancellation
and movement by using similar operations for vector fields. In
addition, we adapt the image-based flow visualization technique
to tensor fields, therefore allowing interactive display of tensor
fields on surfaces.
We demonstrate the capabilities of our tensor field design
system with painterly rendering, pen-and-ink sketch of surfaces,
and anisotropic remeshing.
