Occlusal contact between upper and lower virtual three-dimensional teeth of a patient when the upper and lower arches are in an occlused condition are determined and displayed to the user on a user interface of a general purpose computing device. Various techniques for determining occlusal contacts are described. The areas where occlusal contact occurs is displayed on the user interface in a readily perceptible manner, such as by showing the occlusal contacts in green. If the proposed set-up would result in a interpenetration of teeth in opposing arches, such locations of interpenetration are illustrated in a contrasting color or shading (e.g., red). The ability to calculate distances and display occlusal contacts in a proposed set-up assists the user in planning treatment for the patient. The process can be extended to interproximal contact detection as well. The concepts also apply to dental prosthetics, such as crowns, fillings and dentures.