In geometry, an anthropomorphic polygon is a
simple polygon
In geometry, a simple polygon is a polygon that does not Intersection (Euclidean geometry), intersect itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pairwise ...
with precisely two
ear
An ear is the organ that enables hearing and, in mammals, body balance using the vestibular system. In mammals, the ear is usually described as having three parts—the outer ear, the middle ear and the inner ear. The outer ear consists of ...
s and one
mouth
In animal anatomy, the mouth, also known as the oral cavity, or in Latin cavum oris, is the opening through which many animals take in food and issue vocal sounds. It is also the cavity lying at the upper end of the alimentary canal, bounded on ...
. That is, for exactly three polygon vertices, the line segment connecting the two neighbors of the vertex does not cross the polygon. For two of these vertices (the ears) the line segment connecting the neighbors forms a
diagonal
In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ ...
of the polygon, contained within the polygon. For the third vertex (the mouth) the line segment connecting the neighbors lies outside the polygon, forming the entrance to a concavity of the polygon.
[.]
Every simple polygon has at least two ears (this is the
two ears theorem
In geometry, the two ears theorem 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 any crossings. The two ears theorem is equivalent to the exis ...
) and every non-convex simple polygon has at least one mouth, so in some sense the anthropomorphic polygons are the simplest possible non-convex simple polygons.
It is possible to recognize anthropomorphic polygons in
linear time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
.
[.]
References
External links
*
Euclidean geometry
Types of polygons
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