Related papers: Paths of rectangles inscribed in lines over fields
Let S be a set of distinct points in general position in the Euclidean plane. A plane Hamiltonian path on S is a crossing-free geometric path such that every point of S is a vertex of the path. It is known that, if S is sufficiently large,…
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
An efficient way to get implicit equations of conics on five points and quadrics on nine, using pencils of conics and quadrics, is revealed. Parallel axis right cones intersect on a conic. An example, to show how to place five coplanar…
We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
Inscribed angles are investigated in taxicab geometry with application to the existence and uniqueness of inscribed and circumscribed taxicab circles of triangles.
This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt…
The author has been interested in regions surrounded by real algebraic curves of degree $1$ or $2$ in the plane. The author is mainly interested in their shapes and combinatorics. This is a fundamental and natural problem in mathematics…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…
We develop two methods to reconstruct a path of bounded variation from its signature. The first method gives a simple and explicit expression of any axis path in terms of its signature, but it does not apply directlty to more general ones.…
The aim of this note is to give a formula expressing the trace form associated with the 27 lines of a cubic surface.
We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes…
We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area ; they are leaves of a foliation F on the space of star-shaped n-polygons. By the way, we study some geometric properties of convex…
Three methods of least squares are examined for fitting a line to points in the plane. Two well known methods are to minimize sums of squares of vertical or horizontal distances to the line. Less known is to minimize sums of squares of…
We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical…
We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…