 
Summary: LIC on Surfaces
Detlev Stalling
KonradZuseZentrum f¨ur Informationstechnik Berlin (ZIB)
1 Introduction
In this lecture we will discuss how line integral convolution can be generalized to depict vector fields defined
on surfaces in 3D. The surfaces are assumed to be topologically equivalent to a 2D plane at least in a
local neighbourhood. In principle, any 2D imaging technique can be applied to such a surface as well. In
particular, it is possible to map standard 2D LIC images onto the surface to visualize directional information.
This is very similar to conventional texture mapping in computer graphics. Applying LIC on surfaces
implies a number of interesting questions, e.g. how to compute field lines on a surface, how to define a
suitable input noise, or how to perform the texture mapping in detail. Different methods have been proposed
to solve these problems. Basically, surface LIC algorithms can be divided into two groups depending on
whether they operate in parameter space or in physical space. After introducing tangent curves on surfaces
mathematically, we will discuss and compare both groups of algorithms in detail.
Of course, line integral convolution is not the only method to depict directional information on a surface.
Other methods for 2D vector field visualization can be generalized to surfaces as well, e.g. arrows or contour
lines. Such tools are provided by many visualization systems today. Spot noise methods have also been
applied on surfaces for some time. Van Wijk already described texture mapping on parametric surfaces
in his 1991 spot noise paper [10]. Improvements are described in [2]. In both, spot noise and surface
LIC, a main issue is to ensure that the mapped texture is not distorted and faithfully represents the desired
