rotating a quaternion on 1 axis?

Question

I have a model rotated by a quaternion. I can only set the rotation, I can't add or subtract from anything. I need to get the value of an axis, and than add an angle to it (maybe a degree or radian?) and than re-add the modified quaternion.

How can I do this? (answer on each axis).

Solution 1

You can multiply two quaternions together to produce a third quaternion that is the result of the two rotations. Note that quaternion multiplication is not commutative, meaning order matters (if you do this in your head a few times, you can see why).

You can produce a quaternion that represents a rotation by a given angle around a particular axis with something like this (excuse the fact that it is c++, not java):

Quaternion Quaternion::create_from_axis_angle(const double &xx, const double &yy, const double &zz, const double &a)
{
    // Here we calculate the sin( theta / 2) once for optimization
    double factor = sin( a / 2.0 );

    // Calculate the x, y and z of the quaternion
    double x = xx * factor;
    double y = yy * factor;
    double z = zz * factor;

    // Calcualte the w value by cos( theta / 2 )
    double w = cos( a / 2.0 );

    return Quaternion(x, y, z, w).normalize();
}

So to rotate around the x axis for example, you could create a quaternion with createFromAxisAngle(1, 0, 0, M_PI/2) and multiply it by the current rotation quaternion of your model.

Solution 2

Made a runable code from sje397's post for testing other details later, thought I would share. Eventually using C the reason for no Quaternion class.

#include <iostream>
#include <math.h>
using namespace std;

struct float4{
   float x;
   float y;
   float z;
   float w;  
};
float4 make_float4(float x, float y, float z, float w){
   float4 quat = {x,y,z,w};
   return quat;
}
float dot(float4 a)
{
   return (((a.x * a.x) + (a.y * a.y)) + (a.z * a.z)) + (a.w * a.w);
}
float4 normalize(float4 q)
{
   float num = dot(q);
   float inv = 1.0f / (sqrtf(num));
   return make_float4(q.x * inv, q.y * inv, q.z * inv, q.w * inv);
}
float4 create_from_axis_angle(const float &xx, const float &yy, const float &zz, const float &a)
{
   // Here we calculate the sin( theta / 2) once for optimization
   float factor = sinf( a / 2.0f );

   float4 quat;
   // Calculate the x, y and z of the quaternion
   quat.x = xx * factor;
   quat.y = yy * factor;
   quat.z = zz * factor;

   // Calcualte the w value by cos( theta / 2 )
   quat.w = cosf( a / 2.0f );
   return normalize(quat);
}
int main()
{
   float degrees = 10.0f;
   float4 quat = create_from_axis_angle(1, 0, 0, degrees*(3.14159f/180.0f));
   cout << "> (" << quat.x << ", " <<quat.y << ", " <<quat.z << ", " <<quat.w << ")" << endl; 
   return 0;
}

Output

(0.0871557, 0, 0, 0.996195)

Comments

[VladN]

So if I want to create a quaternion with a -15 degrees rotation on the X axis, I should call createFromAxisAngle(1, 0, 0, -15*PI/180)? Thanks!

[sje397]

@Hubrus: Yep, that'd be correct. Then, if you call that quaternion x and your model quaternion y, you would normally set the total rotation using x * y (depending on how you implement multiplication of course).

[lahjaton_j]

Naming a variable "result" is not a good convention, it gives the impression it would be the return value. How about "factor"?

[sje397]

@lahjaton_j Agreed. Fixed.