SpecialOrthogonalGroup-class: The special orthogonal group SO(n), i.e. the Lie group of...

In geomstats/rgeomstats: Geomstats for R

Description

The special orthogonal group SO(n), i.e. the Lie group of rotations in n dimensions.

Methods

Belongs(point)

Evaluate if a point belongs to SO(n).

Compose(point.1, point.2)

Compose two elements of SO(n).

GroupExpFromIdentity(tangent.vec)

Compute the group exponential of the tangent vector at the identity.

GroupLogFromIdentity(point)

Compute the group logarithm of the point at the identity.

Inverse(point)

Compute the group inverse in SO(n).

JacobianTranslation(point, left.or.right = "left")

Compute the jacobian matrix of the differential of the left/right translations from the identity to point in SO(n).

MatrixFromRotationVector(rot.vec)

Convert rotation vector to rotation matrix.

RandomUniform(n.samples = 1)

Sample in SO(n) with the uniform distribution.

Regularize(point)

In 3D, regularize the norm of the rotation vector, to be between 0 and pi, following the axis-angle representation's convention. If the angle angle is between pi and 2pi, the function computes its complementary in 2pi and inverts the direction of the rotation axis.

RotationVectorFromMatrix(rot.mat)

In 3D, convert rotation matrix to rotation vector (axis-angle representation).

Get the angle through the trace of the rotation matrix: The eigenvalues are: 1, cos(angle) + i sin(angle), cos(angle) - i sin(angle) so that: trace = 1 + 2 cos(angle), -1 <= trace <= 3

Get the rotation vector through the formula: S_r = angle / ( 2 * sin(angle) ) (R - R^T)

For the edge case where the angle is close to pi, the formulation is derived by going from rotation matrix to unit quaternion to axis-angle: r = angle * v / |v|, where (w, v) is a unit quaternion.

In nD, the rotation vector stores the n(n-1)/2 values of the skew-symmetric matrix representing the rotation.

SkewMatrixFromVector(vec)

In 3D, compute the skew-symmetric matrix, known as the cross-product of a vector, associated to the vector vec.

VectorFromSkewMatrix(skew.mat)

In 3D, compute the vector defining the cross product associated to the skew-symmetric matrix skew mat.

In nD, fill a vector by reading the values of the upper triangle of skew_mat.

geomstats/rgeomstats documentation built on Aug. 9, 2019, 9:24 a.m.