In differential geometry, surfaces of revolution form a large class of illuminating examples. These surfaces are also useful in applications, where the assumption of rotational symmetry can simplify a modeling problem substantially. Particularly for some problems in biology, one might want to simulate the deformation of such surfaces. One discretized model based on interpolation by linear segments has been presented previously in the literature. We present a new model based on interpolation by arcs of parabolas in a way that properly generalizes the previous approach; a third model which is useful as a benchmark is obtained as a special case. We present the results of the simulation and discuss the models' performance and error properties.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Spinelli, Kamryn P.

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-121120-095858
• 4931

Keyword

• numerical analysis
• mathematical modeling
• vertex model
• elastic surfaces
• differential geometry

Advisor

• Wu, Min

Year

• 2020

Date created

• 2020-12-11

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright