Robust evaluation of differential geometry properties using interval arithmetic techniques
Name
63283290-MIT.pdf
Description
Full printable version
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7.07 MB
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Checksum (MD5)
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Author(s)
Lee, Chih-kuo
Advisor(s)
Nicholas M. Patrikalakis.
Date Issued
2005
Publisher
Massachusetts Institute of Technology
Abstract
This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch. computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the Validated Numerical Ordinary Differential Equations (VNODE) solver which employs rounded interval arithmetic methods. Then. the results generated from the VNODE program are compared with the results from Praxiteles code which uses non-validated ODE solvers operating in double precision floating point arithmetic for the solution of the same problems. From the results of these experiments, we find that the VNODE program performs these computations reliably, but at increased computational cost.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2005.
Includes bibliographical references (p. 79-82).
Subjects
Ocean Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Ocean Engineering
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