Monotone polygon

Lines orthogonal to $L$ :
  1 intersection

  2 intersections

  3+ intersections
The top two polygons are monotone with respect to $L$ while the bottom two are not.

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.

For many practical purposes this definition may be 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 $P$ and is orthogonal to $L$ lies completely in $P$ .

Following the terminology for monotone functions, the former definition describes polygons strictly monotone with respect to $L$ .

^ Preparata, Franco P.; Shamos, Michael Ian (1985), Computational Geometry – An Introduction, Springer-Verlag, ISBN 0-387-96131-3, 1st edition; 2nd printing, corrected and expanded, 1988:; Russian translation, 1989

[PS-1] Preparata, Franco P.; Shamos, Michael Ian (1985), Computational Geometry – An Introduction, Springer-Verlag, ISBN 0-387-96131-3, 1st edition; 2nd printing, corrected and expanded, 1988:; Russian translation, 1989

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