plane

Creates a new rectangular subset of a plane in ℝ³.

Syntax

• plane([a[, f[, d[, α]]]])

  • a is a three-dimensional real vector

  • f is a three-dimensional real vector

  • d is a three-dimensional real vector

  • α is a real number

Description

plane() creates the square [−1, 1]² × { 0 } ⊂ ℝ³.

plane(a, f, d, α) translates the square by a, scales it by diag(f), aligns its normal with d, and rotates it an amount α about its (normal) axis.

Since a plane is flat, the third component of f should be unity. Unless the two first components of f coincide, the resulting object will be a non-square rectangle.

Hence,

• a specifies the position of square’s centre of mass.

• f = (s, t, 1) specifies the half side lengths s and t of the rectangle.

• d specifies the normal direction of the rectangle.

• α specifies the rotation of the rectangle about its (normal) axis.

If omitted, a defaults to ❨0, 0, 0❩, f to ❨1, 1, 1❩, d to ❨0, 0, 1❩, and α to 0.

The object is shown in the current scene and a reference to the object is returned.

The AdjustVisual function can be used to adjust the appearance of the rectangle. See Visual settings for a list of applicable settings.

Examples

plane()

See also

• disk3D

• InfinitePlane