2026-09-19T11:01:13Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/331672022-01-13T07:55:08Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Nicholas M. Patrikalakis.
Mukundan, Harish
Massachusetts Institute of Technology. Dept. of Mechanicla Engineering.
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Ocean Engineering
2006-06-20T12:52:50Z
2006-06-20T12:52:50Z
2005
2005
http://hdl.handle.net/1721.1/33167
63516909
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 97-100).
This thesis presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. Using a validated ordinary differential equation (ODE) system solver based on interval arithmetic, we obtain a continuous, validated upper bound for the intersection curve segment in the parametric space of each surface. Application of the validated ODE solver in the context of eliminating the pathological phenomena of straying and looping is discussed. We develop a method to achieve a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space. This bound in parametric space is further mapped to an upper bound for the intersection curve error in 3D model space, denoted as model space error, which assists in defining robust boundary representation models of complex three-dimensional solids. In addition, we also discuss a method for controlling this model space error so that it takes values below a predefined threshold (tolerance). Application of the above method to various examples is further demonstrated.
by Harish Mukundan.
S.M.
100 p.
7169137 bytes
9081249 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Ocean Engineering.
Mechanicla Engineering.
Surface-surface intersection with validated error bounds
Thesis
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<Abstract>This thesis presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. Using a validated ordinary differential equation (ODE) system solver based on interval arithmetic, we obtain a continuous, validated upper bound for the intersection curve segment in the parametric space of each surface. Application of the validated ODE solver in the context of eliminating the pathological phenomena of straying and looping is discussed. We develop a method to achieve a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space. This bound in parametric space is further mapped to an upper bound for the intersection curve error in 3D model space, denoted as model space error, which assists in defining robust boundary representation models of complex three-dimensional solids. In addition, we also discuss a method for controlling this model space error so that it takes values below a predefined threshold (tolerance). Application of the above method to various examples is further demonstrated.</Abstract>
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