Integer Points on Cubic Curves

1992 ◽  
pp. 145-179
Author(s):  
Joseph H. Silverman ◽  
John Tate
Keyword(s):  
Cubic Curves ◽  
Integer Points

Integer Points on Cubic Curves

2015 ◽  
pp. 167-205
Author(s):  
Joseph H. Silverman ◽  
John T. Tate
Keyword(s):  
Cubic Curves ◽  
Integer Points

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

scholarly journals Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

4OR ◽  
2020 ◽  
Author(s):  
Michele Conforti ◽  
Marianna De Santis ◽  
Marco Di Summa ◽  
Francesco Rinaldi
Keyword(s):  
Integer Point ◽  
Cutting Plane ◽  
Integer Program ◽  
Compact Set ◽  
Cutting Plane Method ◽  
Integer Points ◽  
Gomory Cuts ◽  
The Family ◽  
Split Cuts ◽  
Number Of Iterations

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x ∈ S ∩ Z n } , where $$S\subset \mathbb {R}^n$$ S ⊂ R n is a compact set and $$c\in \mathbb {Z}^n$$ c ∈ Z n . We analyze the number of iterations of our algorithm.

On an algorithm for finding integer points on perfect ellipsoids

2021 ◽  
Author(s):  
Otabek Gulomov ◽  
Sadulla Shodiev
Keyword(s):  
Integer Points

scholarly journals Cubic Curves Over the Finite Field of Order Twenty-Five

2021 ◽  
Vol 1818 (1) ◽  
pp. 012079
Author(s):  
S. H. Naji ◽  
E. B. Al-Zangana
Keyword(s):  
Finite Field ◽  
Cubic Curves

scholarly journals Euler equations on the general linear group, cubic curves, and inscribed hexagons

2016 ◽  
Vol 62 (1) ◽  
pp. 143-170
Author(s):  
Konstantin Aleshkin ◽  
Anton Izosimov
Keyword(s):  
Euler Equations ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Cubic Curves

scholarly journals The proportion of plane cubic curves over ℚ that everywhere locally have a point

2016 ◽  
Vol 12 (04) ◽  
pp. 1077-1092 ◽  
Author(s):  
Manjul Bhargava ◽  
John Cremona ◽  
Tom Fisher
Keyword(s):  
Rational Function ◽  
Rational Point ◽  
Cubic Curves

We show that the proportion of plane cubic curves over [Formula: see text] that have a [Formula: see text]-rational point is a rational function in [Formula: see text], where the rational function is independent of [Formula: see text], and we determine this rational function explicitly. As a consequence, we obtain the density of plane cubic curves over [Formula: see text] that have points everywhere locally; numerically, this density is shown to be [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document