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.