# HalfPlane

HalfPlane[{p1,p2},w]

represents the half-plane bounded by the line through p1 and p2 and extended in the direction w.

HalfPlane[p,v,w]

represents the half-plane bounded by the line through p along v and extended in the direction w.

# Details

• HalfPlane is also known as half-space in 2D.
• HalfPlane can be used as a geometric region and graphics primitive.
• HalfPlane represents a planar region , , or .
• HalfPlane can be used in Graphics and Graphics3D.
• HalfPlane will be clipped by PlotRange when rendering.
• In graphics, the points p, pi and vector v can be Scaled and Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.
• FaceForm[front,back] can be used to specify different styles for the front and back in 3D. The front is defined by the right-hand rule and the direction from {p1,w,p2} or {p,v,w}.

# Examples

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## Basic Examples(4)

A HalfPlane in 2D:

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And in 3D:

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Different styles applied to a half-plane:

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The Area of a half-plane is infinite:

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Determine if points belong to a given half-plane:

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