منابع مشابه
Approximation by ruled surfaces
Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in archite...
متن کاملCharacterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
متن کاملConchoid surfaces of rational ruled surfaces
The conchoid surface G of a given surface F with respect to a point O is roughly speaking the surface obtained by increasing the radius function of F with respect to O by a constant d. This paper studies real rational ruled surfaces in this context and proves that their conchoid surfaces possess real rational parameterizations, independently on the position of O. Thus any rational ruled surface...
متن کاملRuled Laguerre minimal surfaces
A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...
متن کاملCovering Rational Ruled Surfaces
We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization without affine base points and such that the degree of the corresponding maps is preserved.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1929
ISSN: 0002-9947
DOI: 10.2307/1989531