pymath.rotation_matrix

Builds a rotation matrix, either 3×3 (rotation about an axis in space) or 2×2 (rotation in the plane).

The form is selected by the arguments: pass an axis and an angle for the 3×3 matrix, or a single angle for the 2×2 matrix.

This function is located in the pymath module.

mat = pymath.rotation_matrix(axis, angle)   -- 3×3 rotation about axis
mat = pymath.rotation_matrix(angle)         -- 2×2 planar rotation

Parameter	Type	Description
axis	{x,y,z} or string	(3×3 form only) Rotation axis, given as a 3-vector or as an axis keyword string ("x", "y", "z", "-x", "-y", "-z"), as for local coordinate systems. Normalized internally.
angle	number	Rotation angle in degrees.

Return value

Type	Description
mat	A new rotation matrix, represented as an array of row-vectors. 3×3 when an axis is given, 2×2 when only an angle is given.

Notes:

• With two arguments you get the 3×3 axis rotation; with a single (numeric) argument the 2×2 planar rotation.
• All angles are in degrees.
• The 2×2 matrix is {{cos θ, -sin θ}, {sin θ, cos θ}}.
• The 3×3 form is equivalent to pymath.matrix_from_quat(pymath.quat_from_rotation(axis, angle)).

Example:

-- 3×3: 90° about the z-axis
local R3 = pymath.rotation_matrix("z", 90)
-- R3 == {{0, -1, 0},
--        {1,  0, 0},
--        {0,  0, 1}}

-- 2×2: 90° in the plane
local R2 = pymath.rotation_matrix(90)
-- R2 == {{0, -1},
--        {1,  0}}

Version Support:

Minimum PYTHA Version: V27

See also:

pymath, pymath.matrix_from_quat, pymath.matrix_from_euler_angles, pymath.quat_from_rotation, Axes and Directions