Difference between revisions of "Slerp"
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Frionil Fang (talk | contribs) (should maaaybe check for division by zero though, for slightly less speed advantage) |
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'''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. | '''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. | ||
The following slerp algorithm uses '''a''' and '''b''' for ends and '''t''' for the interpolation parameter.<br> | More detail: {{Wikipedia|Slerp}}. | ||
The following slerp algorithm uses '''a''' and '''b''' for ends and '''t''' for the interpolation parameter.<br/> | |||
To continue the rotation past the ends use a value for '''t''' outside the range '''{{interval|gte=0|lte=1|center=t}}'''. | To continue the rotation past the ends use a value for '''t''' outside the range '''{{interval|gte=0|lte=1|center=t}}'''. | ||
< | <syntaxhighlight lang="lsl2"> | ||
rotation slerp( rotation a, rotation b, float t ) { | |||
return llAxisAngle2Rot( llRot2Axis(b /= a), t * llRot2Angle(b)) * a; | return llAxisAngle2Rot( llRot2Axis(b /= a), t * llRot2Angle(b)) * a; | ||
}//Written collectively, Taken from http://forums-archive.secondlife.com/54/3b/50692/1.html</ | }//Written collectively, Taken from http://forums-archive.secondlife.com/54/3b/50692/1.html | ||
</syntaxhighlight> | |||
Source: 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: | |||
<syntaxhighlight lang="lsl2"> | |||
// 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; | |||
} | |||
</syntaxhighlight> | |||
See also: [[Nlerp]] | |||
Latest revision as of 05:58, 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: 
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