quaternion::slerp

[JVr]

This method is actually bugged coz it may product quaternion that are not normalized.

Original code (current trunk) - it's much worse code bugged same way in stable branch 1.7.2

Code: Select all

 
inline quaternion& quaternion::slerp(quaternion q1, quaternion q2, f32 time)
{
        f32 angle = q1.dotProduct(q2);
 
        // make sure we use the short rotation
        if (angle < 0.0f)
        {
                q1 *= -1.0f;
                angle *= -1.0f;
        }
 
        if (angle <= 0.95f) // spherical interpolation
        {
                const f32 theta = acosf(angle);
                const f32 invsintheta = reciprocal(sinf(theta));
                const f32 scale = sinf(theta * (1.0f-time)) * invsintheta;
                const f32 invscale = sinf(theta * time) * invsintheta;
                return (*this = (q1*scale) + (q2*invscale));
        }
        else // linear interploation
                return lerp(q1,q2,time);
}
 

modified code

Code: Select all

 
inline quaternion& quaternion::slerp(quaternion q1, quaternion q2, f32 time)
{
        f32 angle = q1.dotProduct(q2);
 
        // make sure we use the short rotation
        if (angle < 0.0f)
        {
                q1 *= -1.0f;
                angle *= -1.0f;
        }
 
        if (angle <= 1.0 - core::ROUNDING_ERROR_f32) // spherical interpolation
        {
                const f32 theta = acosf(angle);
                const f32 invsintheta = reciprocal(sinf(theta));
                const f32 scale = sinf(theta * (1.0f-time)) * invsintheta;
                const f32 invscale = sinf(theta * time) * invsintheta;
                return (*this = (q1*scale) + (q2*invscale));
        }
        else // linear interploation
                return lerp(q1,q2,time);
}
 

So the change is in constant that it's not 0.95 but 0.999999

This way it does not product quaternions with size > 1.

[hybrid]

Do you have quaternions which will return wrong results for the current method?

[JVr]

OK I found that:

Source (-0.803446 0.012917 0.135859 0.579525) and (-0.587987 0.085837 0.129373 0.793830) blend 0.372368 result length 0.977165
Source (result) (-0.723216 0.040070 0.133444 0.659326)
Result scale 0.999113 0.974986 0.975745

Source (-0.687014 -0.001438 -0.097833 0.720027) and (0.870995 0.025545 0.099108 -0.480512) bland 0.589717 result length 0.977789
Source (result) (0.795511 0.015654 0.098585 -0.578781)
Result scale 0.999557 0.971037 0.971470

Source (-0.497304 -0.511197 -0.486029 0.505116) and (-0.280449 -0.571046 -0.669434 0.383554) bland 0.386144 result length 0.976528
Source (result) (-0.413567 -0.534307 -0.556850 0.458175)
Result scale 0.971640 0.977153 0.978334

As you see resultng scales may lead up to 3% deformation in any axis so on higher scale the resulting part may look to be deformed. Especially if it's multipied by some higher scale for example scale 10 would lead to 30% deformation etc..

Its true that using more "spherical interpolation" means a bit more floating point computation however it's not much more and resulting quaterion after linear interpolation of quaternions without same angle may lead to this kind of deformation.