On the Design and Invariants of a Ruled Surface
نویسنده
چکیده
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical Bézierlike curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical Bézier-like curve corresponds to a ruled surface. Furthermore, closed ruled surfaces are determined via control points and integral invariants of these surfaces are investigated. The results are illustrated by examples.
منابع مشابه
Characterizations 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 کاملNew Improvement in Interpretation of Gravity Gradient Tensor Data Using Eigenvalues and Invariants: An Application to Blatchford Lake, Northern Canada
Recently, interpretation of causative sources using components of the gravity gradient tensor (GGT) has had a rapid progress. Assuming N as the structural index, components of the gravity vector and gravity gradient tensor have a homogeneity degree of -N and - (N+1), respectively. In this paper, it is shown that the eigenvalues, the first and the second rotational invariants of the GGT (I1 and ...
متن کاملGauge Theoretical Equivariant Gromov-witten Invariants and the Full Seiberg-witten Invariants of Ruled Surfaces
Let F be a differentiable manifold endowed with an almost Kähler structure (J, ω), α a J-holomorphic action of a compact Lie groupˆK on F , and K a closed normal subgroup ofˆK which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F, α, K). The invariants are associated with moduli spaces of solutions of a certain vortex type equatio...
متن کاملfull Seiberg - Witten invariants of ruled surfaces
Let F be a differentiable manifold endowed with an almost Kähler structure (J, ω), α a J-holomorphic action of a compact Lie groupˆK on F , and K a closed normal subgroup ofˆK which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F, α, K). The invariants are associated with moduli spaces of solutions of a certain vortex type equatio...
متن کاملDonaldson invariants of product ruled surfaces and two-dimensional gauge theories
Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of product ruled surfaces Σg × S, where Σg is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabó for g = 1 to any genus g. We give two applications of our results: (1) We derive Thaddeus’ formulae for the intersection pairings on the moduli space of ran...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1706.00267 شماره
صفحات -
تاریخ انتشار 2017