There are numerous mathematical equations used by animators and modelers to describe the curves of the human face and, specifically, the human lip. Physically-based polynomial models, b-splines, and other arbitrarily parameterized equations are used to describe facial and lip contours, though with varied degrees of complexity and resolution. This study examined the constraints and conditions necessary to utilize a standard Euler-Bernoulli beam as an effective model for the human lip. Through this analysis it was determined that general beam theories are flexible enough to create models that can generate curves comparable to actual lip shapes, though no single model studied was appreciably better suited for aU possible Up shapes. Such models could still, however, be utilized in the development of computer-based animation as well as motion tracking systems, computer user interfaces, and teleoperational devices. Beam characteristics such as cross sectional shape, length, and elasticity were investigated in order to define deflection models for four different beam configurations: a clamped prismatic beam, a simply supported prismatic beam, a clamped tapered beam, and a simply supported tapered beam. Multiple beam loading scenarios were simulated to determine the optimal number and arrangement of loads to reproduce the desired deflection curves. Deflection curves defined by each of the four beam models were compared to actual deflection curves digitized from photographs of the human lip and have been presented here.
Library of Congress Subject Headings
Computer animation; Lips
Department, Program, or Center
Mechanical Engineering (KGCOE)
Dufort, Ron, "Paramaterized beams as effective human lip models" (1999). Thesis. Rochester Institute of Technology. Accessed from
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