Results 1  10
of
2,752,684
ON THE UNFOLDING OF SIMPLE CLOSED CURVES
, 809
"... Abstract. I show that every rectifiable simple closed curve in the plane can be continuously deformed into a convex curve in a motion which preserves arc length and does not decrease the Euclidean distance between any pair of points on the curve. This result is obtained by approximating the curve wi ..."
Abstract
 Add to MetaCart
Abstract. I show that every rectifiable simple closed curve in the plane can be continuously deformed into a convex curve in a motion which preserves arc length and does not decrease the Euclidean distance between any pair of points on the curve. This result is obtained by approximating the curve
THE SPANS OF FIVE STARLIKE SIMPLE CLOSED CURVES
"... Abstract. Let X be a continuum, that is a compact, connected, nonempty metric space. The span of X is the least upper bound of the set of real numbers r which satisfy the following conditions: there exists a continuum, C, contained in X × X such that d(x, y) is larger than or equal to r for all (x, ..."
Abstract
 Add to MetaCart
, y) in C and p1(C) = p2(C), where p1, p2 are the usual projection maps. The following question has been asked. If X and Y are two simple closed curves in the plane and Y is contained in the bounded component of the plane minus X, then is the span of X larger than the span of Y? We define a set
Sextactic points on a simple closed curve
, 2000
"... We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method is axiomatic and can be applied in other situations. ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method is axiomatic and can be applied in other situations.
A decomposition of simple closed curves and the order . . .
"... The goal of the article is to introduce an order on a simple closed curve. To do this, we fix two points on the curve and devide it into two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above. ..."
Abstract
 Add to MetaCart
The goal of the article is to introduce an order on a simple closed curve. To do this, we fix two points on the curve and devide it into two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above.
COLLECTIONS OF SIMPLE CLOSED CURVES INTERSECTING AT MOST ONCE
"... Abstract. Given a closed genus g surface in two dimensions, how many simple closed curves can be placed on it so that no two intersect more than once? This question was posed by Farb in 2006 and the precise answer is not known for genus greater than 2. This paper presents a quadratic lower bound and ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. Given a closed genus g surface in two dimensions, how many simple closed curves can be placed on it so that no two intersect more than once? This question was posed by Farb in 2006 and the precise answer is not known for genus greater than 2. This paper presents a quadratic lower bound
Convex Drawings of Intersecting Families of Simple Closed Curves
 IN 11TH CANADIAN CONFERENCE ON COMPUTATIONAL GEOMETRY
, 1998
"... A FISC or family of intersecting simple closed curves is a collection of simple closed curves in the plane with the properties that there is some open region common to the interiors of all the curves, and that every two curves intersect in finitely many points. Let F be a FISC. Intersections of ..."
Abstract

Cited by 17 (8 self)
 Add to MetaCart
A FISC or family of intersecting simple closed curves is a collection of simple closed curves in the plane with the properties that there is some open region common to the interiors of all the curves, and that every two curves intersect in finitely many points. Let F be a FISC. Intersections
SIMPLE CLOSED CURVES AND UNCOUNTABLE COLLECTIONS OF SIMPLE TRIODS
"... In [2], R. L. Moore showed that if, in a space satisfying his Axioms 0 and 1 5, M is a compactum and G is an uncountable collection of compact triodic continua such that the union of all the continua of G is a subset of M, then there is an uncountable subcollection H of G such that every two elemen ..."
Abstract
 Add to MetaCart
elements of H have a point in common. This paper is concerned with uncountable collections H of simple triods in a space satisfying Moore's Axioms 0 and 1 5, and the existence of simple closed curves lying in the union of the elements of H, which will be denoted by H*. For a brief discussion
Topologically Faithful Fitting of Simple Closed Curves
 IEEE PAMI
, 2004
"... Implicit representations of curves have certain advantages over explicit representation, one of them being the ability to determine with ease whether a point is inside or outside the curve (insideoutside functions). However, save for some special cases, it is not known how to construct implicit r ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
representations which are guaranteed to preserve the curve's topology. As a result, points may be erroneously classified with respect to the curve. The paper offers to overcome this problem by using a representation which is guaranteed to yield the correct topology of a simple closed curve by using
PseudoAnosov maps and simple closed curves on surfaces
, 2000
"... Abstract. Suppose C and C ′ are two sets of simple closed curves on a hyperbolic surface F. We will give necessary and sufficient conditions for the existence of a pseudoAnosov map g such that g(C) ∼ = C ′. PseudoAnosov maps are the most important class among surface homeomorphisms [Th3], and th ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. Suppose C and C ′ are two sets of simple closed curves on a hyperbolic surface F. We will give necessary and sufficient conditions for the existence of a pseudoAnosov map g such that g(C) ∼ = C ′. PseudoAnosov maps are the most important class among surface homeomorphisms [Th3
Results 1  10
of
2,752,684