Algorithms for blending surface generation.

262 Pages·2.5 MB·en_US

by  Filkins, Peter Charles.

3002

Algorithms
for Blending Surface Generation
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by P4^&
Peter Charles Filkins
Submitted to the Department of Ocean Engineering
on May
10, 1991, in partial fulfillment of the
requirements for the degrees of
Naval Engineer
and
Master of Science in Mechanical Engineering

Algorithms for Blending Surface Generation
by
Peter Charles Filkins
B.S. in Ocean Engineering (June 1977)
United States Naval Academy
Submitted to the Department of Ocean Engineering
in partial fulfillment of the requirements for the degrees of
Naval Engineer
and
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1991
©
MCMXCI.
Peter Charles Filkins, All rights reserved.
The author hereby grants to MIT and the U.S. Government
permission to reproduce and to distribute copies of this
thesis document in whole or in part.
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Algorithms for Blending Surface Generation
by
Peter Charles Filkins
Submitted to the Department of Ocean Engineering
on May 10. 1991. in partial fulfillment of the
requirements for the degrees of
Naval Engineer
and
Master of Science in Mechanical Engineering
Abstract
This thesis presents a general algorithm for the representation and approximation of
blending surfaces between two non-uniform rational B-spline (NURBS) surfaces using
surfaces of the same class. The algorithm permits the approximation of blending
surfaces with up to curvature continuous boundary conditions along the intersection
of the blending surface with the primary surfaces to be joined. These intersections
are called the linkage curves.
The blending surfaces are approximated by low degree B-spline surfaces, created
using a lofting method. Isoparameter curves of the approximating blending surface
are constructed based on differential geometry properties of the underlying surfaces.
First derivative properties are required to satisfy tangent plane continuity bound-
ary conditions. To satisfy curvature continuity conditions, the cross-link curves are
constructed to match the curvature of a normal section of the underlying surface at
the end point of the cross-link curves on the linkage curves. An adaptive sampling
procedure is used to improve the approximation.
Finally, the algorithm is applied to the practical problem of designing a fillet for
the intersection of a marine propeller blade with a hub. An adaptation of the method
which creates a standard marine propeller fillet automatically is also presented.
Thesis Supervisor: Nicholas M. Patrikalakis
Title: Associate Professor of Ocean Engineering