Simple polygon information

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...

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"...

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...

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...

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

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...

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...

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

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...

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...

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...

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...

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 (non-self-intersecting) polygon, regardless of whether it is convex or...

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...

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...

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...

In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings...

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...

the origin for any simple polygon on the XY-plane can be computed in general by summing contributions from each segment of the polygon after dividing the...

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...

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...

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...

In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only the topology of the...