In this paper we seek to answer the following questions: where do contour lines and visible contour lines (silhouette) tend to occur
in a 3D surface. Our study leads to two novel shape descriptors, the horizon measure and the visible horizon measure, which
we apply to the visualization of 3D shapes including archeological artifacts. In addition to introducing the shape descriptors,
we also provide a closed-form formula for the horizon measure based on classical spherical geometry. To compute the visible
horizon measure, which depends on the exact computation of the surface visibility function, we instead of provide an image-based
approach which can process a model with high complexity within a few minutes.