2026-09-19T14:02:07Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/335652022-01-13T07:54:39Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Nicholas M. Patrikalakis.
Lee, Chih-kuo
Massachusetts Institute of Technology. Dept. of Ocean Engineering.
Massachusetts Institute of Technology. Department of Ocean Engineering
2006-07-31T15:13:08Z
2006-07-31T15:13:08Z
2005
2005
http://hdl.handle.net/1721.1/33565
63283290
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2005.
Includes bibliographical references (p. 79-82).
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.
by Chih-kuo Lee.
S.M.
82 p.
2725656 bytes
2729017 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Ocean Engineering.
Robust evaluation of differential geometry properties using interval arithmetic techniques
Thesis
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