A physical interface can often be modeled as a surface that moves
with a velocity determined by the local geometry. Accordingly,
there is great interest in algorithms that generate such geometric
interface motions. In this talk, we present an introduction to
convolution-based algorithms for approximating interface motions.
These methods are easy to visualize and analyze because they may
be viewed geometrically as a type of Huygens' principle. They also
have the advantage of a simple analytic formulation which is
well-suited for numerical approximation. Applications to models
arising in excitable media, developmental biology and material
science are also discussed.