| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 84 === The paper presents new numerical techniques to blend 3-D curves
satisfying some containment and tangent requirements. Their
parametric functions x(s),y(s) and z(s) are governed by the
fourth order ordinary differential equations (ODEs). New
techniques are proposed to deal with arbitrariness arising from
the tangent requirements in the parametric functions. The
Hermite finite element methods are adopted to solve a system of
boundary value problems of the fourth order ODEs, accompanied
with a brief error analysis. The important results in this
thesis lie in exploration on the conditions of unique solutions
and the consistent conditions of infinite solutions to both ODE
and FEM. Numerical experiments have been carried out to confirm
the error analysis made, and constructed some good blending
curves. The results have applied directly to the airplane
landing where the landing point is arbitrary along the
airstrip, and other kinds of trajectory problems. The study of
this paper can also be applied to blending curves and surfaces
of airlpane, ships, grand building and astronautic shuttle-
station.
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