sknano.core.math.transformation_matrix¶

sknano.core.math.transformation_matrix(angle=None, axis=None, anchor_point=None, rot_point=None, from_vector=None, to_vector=None, degrees=False, verbose=False, **kwargs)[source][source]¶

Generate an $(n+1)\times(n+1)$ transformation matrix for an affine transformation in $n$ dimensions.

New in version 0.3.0.

Parameters:

Parameters:	angle : float Rotation angle in radians. If degrees is True, `angle` will be converted to radians from degrees. The sense of the rotation is defined by the right hand rule: If your right-hand’s thumb points along the axis, then your fingers wrap around the axis in the positive sense of the rotation angle. axis : {None, array_like, str}, optional An $n$ -element array_like sequence defining the $n$ components of the rotation axis or the string x, y, or z representing the $x, y, z$ axes of a Cartesian coordinate system in 3D with unit vectors $\mathbf{v}_x=\mathbf{\hat{x}}$ , $\mathbf{v}_y=\mathbf{\hat{y}}$ , and $\mathbf{v}_z=\mathbf{\hat{z}}$ , respectively. anchor_point : {None, array_like}, optional An $n$ -element list or ndarray or `Point` defining the origin of the rotation axis. If anchor_point is not None and axis is a `Vector` instance, then the origin of the vector defined by `Vector.p0` will be changed to anchor_point. If anchor_point is None, then it defaults to an $n$ -element array of zeros. degrees : bool, optional If True, convert `angle` from degrees to radians.
Returns:	Tmat : ndarray $n+1\times n+1$ transformation matrix for an affine transform in $n$ dimensions. If axis is None and anchor_point is None, then Tmat will be a $2D$ rotation matrix $R(\theta)$ that rotates $2D$ vectors counterclockwise by `angle` $\theta$ . If axis is None and anchor_point is a 2-element sequence, then Rmat will be a $2D$ rotation matrix $R(\theta)$ about the $2D$ `Point` anchor_point by `angle` $\theta$ . If axis is not None and anchor_point is None, then Rmat will be a rotation matrix that gives a rotation around the direction of the vector axis.

angle : float

Rotation angle in radians. If degrees is True, angle will be converted to radians from degrees. The sense of the rotation is defined by the right hand rule: If your right-hand’s thumb points along the axis, then your fingers wrap around the axis in the positive sense of the rotation angle.

axis : {None, array_like, str}, optional

An $n$ -element array_like sequence defining the $n$ components of the rotation axis or the string x, y, or z representing the $x, y, z$ axes of a Cartesian coordinate system in 3D with unit vectors $\mathbf{v}_x=\mathbf{\hat{x}}$ , $\mathbf{v}_y=\mathbf{\hat{y}}$ , and $\mathbf{v}_z=\mathbf{\hat{z}}$ , respectively.

anchor_point : {None, array_like}, optional

An $n$ -element list or ndarray or Point defining the origin of the rotation axis.

If anchor_point is not None and axis is a Vector instance, then the origin of the vector defined by Vector.p0 will be changed to anchor_point.

If anchor_point is None, then it defaults to an $n$ -element array of zeros.

degrees : bool, optional

If True, convert angle from degrees to radians.

Returns:

Tmat : ndarray

$n+1\times n+1$ transformation matrix for an affine transform in $n$ dimensions.

If axis is None and anchor_point is None, then Tmat will be a $2D$ rotation matrix $R(\theta)$ that rotates $2D$ vectors counterclockwise by angle $\theta$ .

If axis is None and anchor_point is a 2-element sequence, then Rmat will be a $2D$ rotation matrix $R(\theta)$ about the $2D$ Point anchor_point by angle $\theta$ .

If axis is not None and anchor_point is None, then Rmat will be a rotation matrix that gives a rotation around the direction of the vector axis.