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A simple polygonal chain A self-intersecting polygonal chain A closed polygonal chain. In geometry, a polygonal chain [a] is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (,, …,) called its vertices. The curve itself consists of the line segments connecting the ...
A simple polygon is the boundary of a region of the plane that is called a solid polygon. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. In contexts where one 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 ...
A closed polygonal curve, assuming consistent orientation, has null boundary. The boundary of a chain is the linear combination of boundaries of the simplices in the chain. The boundary of a k-chain is a (k−1)-chain. Note that the boundary of a simplex is not a simplex, but a chain with coefficients 1 or −1 – thus chains are the closure ...
In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
In solid geometry, a prismatic surface is a polyhedral surface generated by all the lines that are parallel to a given line and that intersect a polygonal chain in a plane that is not parallel to the given line. [1] The polygonal chain is the directrix of the surface; the parallel lines are its generators (or elements).
In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects the boundary of P at most twice. [1] Similarly, a polygonal chain C is called monotone with respect to a straight line L, if every line orthogonal to L intersects C at most once.
A Polygonal chain or Polyline is an ordered list of points (termed vertices in this context). The software is expected to interpolate the intervening shape of the line between adjacent points in the list as a parametric curve, most commonly a straight line, but other types of curves are frequently available, including circular arcs , cubic ...