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As with any simple polygon, the sum of the internal angles of a concave polygon is π × (n − 2) radians, equivalently 180× (n − 2) degrees (°), where n is the number of sides. It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex ...
In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is in a sense the opposite of the ...
Polygon. Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. In geometry, a polygon (/ ˈpɒlɪɡɒn /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal ...
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1] Equivalently, a polygon is convex if every line that ...
Curve orientation. In mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates, the x -axis is traditionally oriented toward the right, and the y -axis is upward oriented. In the case of a planar simple closed curve (that is, a curve in the ...
Polygon triangulation. In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
Convex curve. A convex curve (black) forms a connected subset of the boundary of a convex set (blue), and has a supporting line (red) through each of its points. A parabola, a convex curve that is the graph of the convex function. In geometry, a convex curve is a plane curve that has a supporting line through each of its points.
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 of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons . The sum of external angles of a simple polygon is .