Supporting line

Supporting line

In geometry, a supporting line L of a curve C in the plane is a line that contains a point of C, but does not separate any two points of C.[1] In other words, C lies completely in one of the two closed half-planes defined by L and has at least one point on L.

There can be many supporting lines for a curve at a given point. When a tangent exists at a given point, then it is the unique supporting line at this point, if it does not separate the curve.

The notion of supporting line is also discussed for planar shapes. In this case a supporting line may be defined as a line which has common points with the boundary of the shape, but not with its interior.[2]

Two disjoint bounded planar shapes have four common lines of support. Two of them which separate the polygons are called critical support lines.[2]

References

  1. ^ "The geometry of geodesics", Herbert Busemann, p. 158
  2. ^ a b "Encyclopedia of Distances", by Michel M. Deza, Elena Deza, p. 179

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