What is half planes?

Half planes are geometric shapes that are defined as a portion of a plane that is bounded by a straight line and extends infinitely in one direction. Half planes are also sometimes referred to as half-spaces.

In geometry, a half plane is defined by a boundary line called the hinge line. The border of the half plane existing on one side of the hinge line is said to be 'closed', while the border on the other side is said to be 'open'. A point is said to belong to a half plane if and only if it is located on the closed side of the hinge line.

Half planes are frequently used in mathematics and physics, particularly in fields such as topology, vector analysis, and calculus. They have a variety of applications, including in computer graphics, robotics, and optimization. In addition, half planes have important properties such as symmetry, convexity, and stability, which make them useful in many areas of research.