make_euler_xyz_quaternion

Specification

Location	Author	Maintained by
isl/math/euler.py	Kenny Erleben	DIKU

Find the angle from a euler

This function assumes that the order of the rotation is R(x)R(y)R(z).

Definition

Given a unit quaternion $q = [s, (x,y,z)]$ , the corresponding rotation matrix is

$M= \begin{pmatrix} 1-2(y^2+z^2) & 2xy-2sz & 2sy+2xz \\ 2xy+sy & 1-2(x^2+z^2) & -2sx + syz \\ 2sy+2xz & 2sx+2yz & 1-2(x^2+y^2) \end{pmatrix}$

More information can be found in page 602 in physics-based animation by Erleben, Sporring, Heniksen and Dohlmann. The angles can be found from the above rotation matrix

Example

    radians_x =  0.4 
    radians_y =  1.1
    radians_z = -1.3
    matrix         = np.dot(mat3.Rz(radians_z), np.dot(mat3.Ry(radians_y), mat3.Rx(radians_x)))
    q              = quat.from_matrix(matrix)
    Euler          = eu.make_euler_xyz_from_quaternion(q)
    Euler.alpha, Euler.beta, Euler.gamma

Output

    (0.4000000000000001, 1.1, -1.3)