Search Results for ""

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

A polygon whose interior consists of all points in the plane which are closer to a particular lattice point than to any other. The generalization to n dimensions is called a ...

Let P be a point with trilinear coordinates alpha:beta:gamma=f(a,b,c):f(b,c,a):f(c,ab) and P^' be a point with trilinear coordinates ...

The problem of polygon intersection seeks to determine if two polygons intersect and, if so, possibly determine their intersection. For example, the intersection of the two ...

Bicentric perspective is the study of the projection of 3D space from a pair of fiducial points instead of a single one, the latter of which may be called "centric" or ...

As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

The (signed) area of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) is A=1/2(|x_1 x_2; y_1 y_2|+|x_2 x_3; y_2 y_3|+...+|x_n x_1; y_n y_1|), ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...