GLSL rotation about an arbitrary axis

11th of January 2013

A quick trip to the Great Oracle of Geekiness (Google) left me empty-handed so here’s a function that gives you a rotation matrix in GLSL…

Comments (15)

Marc St-Jacques
January 5, 2014 Reply
Very useful function. Thanks.
shrek
August 26, 2014 Reply
A quick trip to the Great Oracle of Geekiness (Google) brought me here. Thanks! Exactly what I needed.
Drew Lustro
September 26, 2014 Reply
Good god, thank you.
mkim1030
February 16, 2015 Reply
you may notice that this function rotates in the clockwise direction as the angle parameter increases. if you’d like it to rotate in the counter-clockwise direction (as in the math world), multiply the variable ‘s’ (float s = sin(angle)) by -1.
Craig Reynolds
June 23, 2015 Reply
Thanks, I found derivations of the matrix on the web (eg Wikipedia) but was pretty sure I would make a typo or two while converting it to GLSL code, then waste time debugging it. Thanks for letting me skip that and concentrate on what I was doing.
david van brink
October 28, 2015 Reply
Just what I needed. Thanks for posting! Saved me a bit of time (and a lot of lines of code compared to what I was planning).
anonymus
April 12, 2016 Reply
Very useful, saved me a lot of time, thanks!
Teshla
September 1, 2016 Reply
Cheers, thx
Matthew Wagerfield
November 21, 2016 Reply
This is awesome, thank you so much! For those who want to optimise further, I refined the above to:
mat4 rotationMatrix(vec3 axis, float angle) {
vec3 a = normalize(axis);
float s = sin(angle);
float c = cos(angle);
float oc = 1.0 – c;
float sx = s * a.x;
float sy = s * a.y;
float sz = s * a.z;
float ocx = oc * a.x;
float ocy = oc * a.y;
float ocz = oc * a.z;
float ocxx = ocx * a.x;
float ocxy = ocx * a.y;
float ocxz = ocx * a.z;
float ocyy = ocy * a.y;
float ocyz = ocy * a.z;
float oczz = ocz * a.z;
return mat4(
vec4(ocxx + c, ocxy – sz, ocxz + sy, 0.0),
vec4(ocxy + sz, ocyy + c, ocyz – sx, 0.0),
vec4(ocxz – sy, ocyz + sx, oczz + c, 0.0),
vec4( 0.0, 0.0, 0.0, 1.0)
);
}
blarg
August 6, 2017 Reply
Simplified it further (I think it’s correct, haven’t used it much):
mat3 rotAxis(vec3 axis, float a) {
float s=sin(a);
float c=cos(a);
float oc=1.0-c;
vec3 as=axis*s;
mat3 p=mat3(axis.x*axis,axis.y*axis,axis.z*axis);
mat3 q=mat3(c,-as.z,as.y,as.z,c,-as.x,-as.y,as.x,c);
return p*oc+q;
}
Case Prince
October 22, 2018 Reply
Yes please and thank you. This rotates my vectors on axes they’ve never been rotated on before, and they love it!
Elie Zananiri
January 17, 2019 Reply
This is still my favorite webpage
lars
November 2, 2019 Reply
same here. I just keep coming back, sometimes when I least expect it here i am.
blackle mori
July 16, 2020 Reply
If you just want to rotate a single vector, you can use this function:
vec3 rotateAxis(vec3 p, vec3 axis, float angle) {
return mix(dot(axis, p)*axis, p, cos(angle)) + cross(axis,p)*sin(angle);
}

szamil
January 22, 2021 Reply
Sweet! Simple, clever and compact. Needed it for CG, so mix->lerp and vec3->float3, but still works as expected.
Do you have source?

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GLSL rotation about an arbitrary axis