Difference between revisions of "Slerp"

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(a faster implementation, though not by much (about 10% by my testing, one extra function call but less demanding functions))
(should maaaybe check for division by zero though, for slightly less speed advantage)
 
Line 19: Line 19:
rotation slerp(rotation a, rotation b, float t) {
rotation slerp(rotation a, rotation b, float t) {
     float theta = llAngleBetween(a, b)*0.5;
     float theta = llAngleBetween(a, b)*0.5;
     float is = 1/llSin(theta);
     if(theta) {
    float st = llSin(t*theta)*is;
        float is = 1/llSin(theta);
    float sti = llSin((1-t)*theta)*is;
        float st = llSin(t*theta)*is;
    return <a.x*sti, a.y*sti, a.z*sti, a.s*sti>+<b.x*st, b.y*st, b.z*st, b.s*st>;
        float sti = llSin((1-t)*theta)*is;
        return <a.x*sti, a.y*sti, a.z*sti, a.s*sti>+<b.x*st, b.y*st, b.z*st, b.s*st>;
    } else return a;
}
}
</syntaxhighlight>
</syntaxhighlight>


See also: [[Nlerp]]
See also: [[Nlerp]]

Latest revision as of 06:58, 28 March 2024

Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant speed motion along a unit radius great circle arc, given the ends and an interpolation parameter between 0 and 1.

More detail: "Wikipedia logo"Slerp.

The following slerp algorithm uses a and b for ends and t for the interpolation parameter.
To continue the rotation past the ends use a value for t outside the range [0, 1].

rotation slerp( rotation a, rotation b, float t ) {
   return llAxisAngle2Rot( llRot2Axis(b /= a), t * llRot2Angle(b)) * a;
}//Written collectively, Taken from http://forums-archive.secondlife.com/54/3b/50692/1.html

Source: http://forums-archive.secondlife.com/54/3b/50692/1.html

A slightly faster, but less concise implementation:

// formula: slerp = (qa*sin((1-t)*theta)+qb*sin(t*theta))/sin(theta)
// where qa, qb are the rotations and theta is half the angle between them
rotation slerp(rotation a, rotation b, float t) {
    float theta = llAngleBetween(a, b)*0.5;
    if(theta) {
        float is = 1/llSin(theta);
        float st = llSin(t*theta)*is;
        float sti = llSin((1-t)*theta)*is;
        return <a.x*sti, a.y*sti, a.z*sti, a.s*sti>+<b.x*st, b.y*st, b.z*st, b.s*st>;
    } else return a;
}

See also: Nlerp