In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting...

is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself...

In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of...

notable ones can arise through truncation operations on regular simple or star polygons. Branko Grünbaum identified two primary usages of this terminology...

simple closed polygonal chain in the plane is the boundary of a simple polygon. Often the term "polygon" is used in the meaning of "closed polygonal chain"...

issue of the Ray Tracing News. One simple way of finding whether the point is inside or outside a simple polygon is to test how many times a ray, starting...

geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon. It is a special case of the more...

A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that...

In geometry, a weakly simple polygon is a generalization of a simple polygon, allowing the polygon sides to touch each other in limited ways. Different...

surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane...

In geometry, an angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or...

as for finite point sets, convex hulls have also been studied for simple polygons, Brownian motion, space curves, and epigraphs of functions. Convex...

interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that...

polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may...

simple polygon, the orientation of the resulting polygon is directly related to the sign of the angle at any vertex of the convex hull of the polygon...

case, in which the points are given in the order of traversal of a simple polygon's boundary, is described later in a separate subsection. If not all points...

rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are...

complexes are its zero-dimensional faces. A polygon vertex xi of a simple polygon P is a principal polygon vertex if the diagonal [x(i − 1), x(i + 1)]...

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional...

states that every simple polygon with more than three vertices has at least two ears, vertices that can be removed from the polygon without introducing...

extended to allow cases when some edges of P are orthogonal to L, and a simple polygon may be called monotone if a line segment that connects two points in...

Look up polygon in Wiktionary, the free dictionary. A polygon is a geometric figure. Polygon may also refer to: Simple polygon, a single contiguous closed...

lies inside or outside a simple polygon. From a given point, trace a ray that does not pass through any vertex of the polygon (all rays but a finite number...

points inside a simple polygon or a rectifiable simple closed curve. Let P {\displaystyle P} be a simple polygon or a rectifiable simple closed curve, and...

the obstacles are the edges of a simple polygon and p is inside the polygon. In the latter case the visibility polygon may be found in linear time. Formally...

An established strategy for recognising a general polygonal object is to decompose it into simpler components, then identify the components and their...

In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points...

represented by a simple polygon and each guard is represented by a point in the polygon. A set S {\displaystyle S} of points is said to guard a polygon if, for...

Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other. They contrast with simple polygons, whose...

that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one...