Hyperplane

Hyperplane[n,p]

represents the hyperplane with normal n passing through the point p.

Hyperplane[n,c]

represents the hyperplane with normal n given by the points that satisfy .

Details • Hyperplane can be used as a geometric region and a graphics primitive.
• Hyperplane[n] is equivalent to Hyperplane[n,0], a hyperplane through the origin.
• Hyperplane corresponds to an infinite line in and an infinite plane in .
• • Hyperplane represents the set or .
• Hyperplane is defined for nd, pd, and c.
• Hyperplane can be used in Graphics and Graphics3D.
• Hyperplane will be clipped by PlotRange when rendering.
• Graphics rendering is affected by directives such as Thickness, Dashing, Opacity, and color.
• Graphics3D rendering is affected by directives such as Opacity and color. FaceForm[front,back] can be used to specify different styles for the front and back, where front is defined to be in the direction of the normal n.

Examples

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Basic Examples(3)

A Hyperplane in 2D:

 In:= Out= And in 3D:

 In:= Out= Different styles applied to a hyperplane region:

 In:= In:= Out= Determine if points belong to a given hyperplane region:

 In:= In:= Out= Neat Examples(4)

Introduced in 2015
(10.2)