  Scientific visualization tools tend to be flexible in some ways (e.g., for
exploring isovalues) while restricted in other ways, such as working only on
regular grids, or only on unstructured meshes (as used in the finite element
method, FEM). Our work seeks to expose the common structure of visualization
methods, apart from the specifics of how the fields being visualized are
formed. Recognizing that previous approaches to FEM visualization depend on
efficiently updating computed positions within a mesh, we took an existing
visualization domain-specific language, and added a mesh position type and
associated arithmetic operators. These are orthogonal to the visualization
method itself, so existing programs for visualizing regular grid data work,
with minimal changes, on higher-order FEM data. We reproduce the efficiency
gains of an earlier guided search method of mesh position update for computing
streamlines, and we demonstrate a novel ability to uniformly sample ridge
surfaces of higher-order FEM solutions defined on curved meshes.
