Cubic curves: a short survey
نویسنده
چکیده
This article discusses cubic curves, some of the ways they arise, and some of their applications in diverse fields such as cryptography and string theory. Key-Words: cubic curve, elliptic curve, Weierstrass equation
منابع مشابه
An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves
In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...
متن کامل3D Reconstruction Using Cubic Bezier Spline Curves and Active Contours (Case Study)
Introduction 3D reconstruction of an object from its 2D cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. In order to perform 3D reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. Mate...
متن کاملRemarks on Iterated Cubic Maps
1. The Parameter Space for Cubic Maps 2. Real Cubic Maps as Real Dynamical Systems 3. Complex Cubics: The Connectedness Locus 4. Hyperbolic Components Appendix A. Normal Forms and Curves in Parameter Space Appendix B. Centers of Some Hyperbolic Components Appendix C. Comments on the Figures References This article discusses the dynamics of iterated cubic maps from the real or complex line to it...
متن کاملQuasiclassical Deformations of Cubic Curves . ∗
A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize these deformations.
متن کاملCertified approximation of parametric space curves with cubic B-spline curves
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...
متن کامل