Good continuation is a fundamental principle of perceptual organization that guides the grouping of parts based on how they should succeed one another within coherent wholes. Despite the general language that was used by the Gestalt psychologists in phrasing this principle, computational work has focused almost exclusively on the study of curve-like structures. Here we offer, for the first time, a rigorous generalization of good continuation to arbitrary visual structures that can be abstracted as scalar functions over the image plane. The differential geometry of these structures dictates that their good continuation should be based both on their value and on the geometry of their levelsets, which yield a coupled system of equations solvable for a formal model. We exhibit the resulting computation on shading and intensity functions, demonstrating how it eliminates spurious measurements while preserving both regular structure and singularities. Related implementations could be applied to color channels, motion magnitude, and disparity signals.