﻿ plane – Algosim documentation
Algosim documentation: plane

# 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()`