Publications related to Plane curve

Distinct Distances on Algebraic Curves in the Plane

Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Cambridge Univ Press2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

Generating Calligraphic Trajectories with Model Predictive Control

Sylvain Calinon

We describe a methodology for the interactive definition of curves and motion paths using a stochastic formulation of optimal control. We demonstrate how the same optimization framework can be used in different ways to generate curves and traces that are g ...

2017

Apparatus for imaging a page of a book or other similar document

Martin Vetterli, Loïc Arnaud Baboulaz

The present invention relates to an apparatus for imaging a page of a book or other similar document comprising: - a table defining a support plane, the book being disposed on the table such that the page to image is substantially parallel to the support p ...

2017

Few distinct distances implies no heavy lines or circles

Frank de Zeeuw

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

Springer Heidelberg2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

2016

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples

Riccardo Grandi

In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve C. There is a family of stability conditions for triples that depends on a positive real parameter Ï. The moduli spaces of Ï-semistable ...

EPFL2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Comb Drive Designs With Minimized Levitation

Matthias Imboden

This paper presents two capacitive comb drive designs for electrostatic actuation of MEMS with the aim to eliminate the levitation effect often observed in such systems. By placing a shield over the comb drive fingers, it is possible to balance the electri ...

Ieee-Inst Electrical Electronics Engineers Inc2016

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Distinct Distances on Algebraic Curves in the Plane

On some algebraic and extremal problems in discrete geometry

Generating Calligraphic Trajectories with Model Predictive Control

Apparatus for imaging a page of a book or other similar document

Few distinct distances implies no heavy lines or circles

An Inner-Product Calculus for Periodic Functions and Curves

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Comb Drive Designs With Minimized Levitation

Apparatus for imaging a page of a book or other similar document

Generating Calligraphic Trajectories with Model Predictive Control

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Distinct Distances on Algebraic Curves in the Plane

On some algebraic and extremal problems in discrete geometry

Few distinct distances implies no heavy lines or circles

An Inner-Product Calculus for Periodic Functions and Curves

Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples

Comb Drive Designs With Minimized Levitation

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients