GLM: Euler Angles to Quaternion

Question

I hope you know GL Mathematics (GLM) because I've got a problem, I can not break:

I have a set of Euler Angles and I need to perform smooth interpolation between them. The best way is converting them to Quaternions and applying SLERP alrogirthm.

The issue I have is how to initialize glm::quaternion with Euler Angles, please?

I read GLM Documentation over and over, but I can not find appropriate Quaternion constructor signature, that would take three Euler Angles. The closest one I found is angleAxis() function, taking angle value and an axis for that angle. Note, please, what I am looking for si a way, how to parse RotX, RotY, RotZ.

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For your information, this is the above metnioned angleAxis() function signature:

detail::tquat< valType > angleAxis (valType const &angle, valType const &x, valType const &y, valType const &z)

Answer 1

I'm not familiar with GLM, but in the absence of a function to directly convert from Euler angles into quaternions, you can use the "rotation around an axis" functions (such as "angleAxis") to it yourself.

Here's how (pseudocode):

Quaternion QuatAroundX = Quaternion( Vector3(1.0,0.0,0.0), EulerAngle.x );
Quaternion QuatAroundY = Quaternion( Vector3(0.0,1.0,0.0), EulerAngle.y );
Quaternion QuatAroundZ = Quaternion( Vector3(0.0,0.0,1.0), EulerAngle.z );
Quaternion finalOrientation = QuatAroundX * QuatAroundY * QuatAroundZ;

(Or you may need to switch those quaternion multiplies around, depending on the order in which your euler angle rotations are intended to be applied)

Alternately, from looking through GLM's documentation, it appears that you may be able to convert euler angles -> matrix3 -> quaternion like this:

toQuat( orient3( EulerAngles ) )

Answer 2

glm::quat myquaternion = glm::quat(glm::vec3(angle.x, angle.y, angle.z));

Where angle is a glm::vec3 containing pitch, yaw, roll respectively.

PS. If in doubt, just go to the headers and look. The definition can be found in glm/gtc/quaternion.hpp:

explicit tquat(tvec3<T> const & eulerAngles) {
        tvec3<T> c = glm::cos(eulerAngle * value_type(0.5));
    tvec3<T> s = glm::sin(eulerAngle * value_type(0.5));

    this->w = c.x * c.y * c.z + s.x * s.y * s.z;
    this->x = s.x * c.y * c.z - c.x * s.y * s.z;
    this->y = c.x * s.y * c.z + s.x * c.y * s.z;
    this->z = c.x * c.y * s.z - s.x * s.y * c.z;    
}

Where quat is a float typedef for tquat.

Answer 3

Solution is in wikipedia: http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles

using that:

sx = sin(x/2); sy = sin(y/2); sz = sin(z/2);
cx = cos(x/2); cy = cos(y/2); cz = cos(z/2);

q( cx*cy*cz + sx*sy*sz,
   sx*cy*cz - cx*sy*sz,
   cx*sy*cz + sx*cy*sz,
   cx*cy*sz - sx*sy*cz ) // for XYZ application order

q( cx*cy*cz - sx*sy*sz,
   sx*cy*cz + cx*sy*sz,
   cx*sy*cz - sx*cy*sz,
   cx*cy*sz + sx*sy*cz ) // for ZYX application order

Constructors for a quaternion, given an Euler (where application of rotation is XYZ or ZYX). However, it's only two of six possible combinations of Euler angles. You really need to find out what order the Euler angles are constructed when converting to transform matrix. Only then can the solution be defined.

In the old company I worked at, we had Z as forwards (like most graphics cards) so the application order was ZYX, and at my current company the Y axis is forwards and Z is up, so our application order is YZX. This order is the order you multiply your quaternions together in to generate your final transform, and the order matters for rotations are the multiplications are not commutative.

Answer 4

vec3 myEuler (fAngle[0],fAngle[1],fAngle[2]);
glm::quat myQuat (myEuler);

fAngle must be in radians!