Compound complex curves: the authentic geometry of esthetic dentistry

Observers are drawn to the intricate and unpredictable way light reflects off the compound complex curved surfaces seen in nature, art, and industry. Teeth are no exception, containing as they do such detail in their gross anatomy, fine anatomic detail, and surface texture. Compound complex curves are particularly important when engineered materials are used to mimic naturally occurring objects, including prosthetic teeth, and they can provide both authenticity and beauty. The purpose of this article was to describe the nature of compound complex curves, their historical context, and their importance in creating natural-looking prostheses. Classically, such curves have been described by using descriptive qualitative methods or quantitative mathematical methods; now these approaches merge. Natural tooth anatomy contains interlinked features at different levels of scale from gross to fine surface texture detail. These curves should be created appropriately for individual restorative treatments.