Rotation

code:rotation_2D.glsl

mat2 rotation2D(flaot angle){

float c= cos(angle);

float s = sin(angle);

return mat2(c,s,-s,c);

}

mat2 rot2( float th ){ vec2 a = sin(vec2(1.5707963, 0) + th); return mat2(a, -a.y, a.x); }

// Usage

vec2 uv;

uv*=rotation2D(.785);

Shear Rotation

code:shear_rotation.glsl

float angle = iTime;

uv.x +=uv.y*-tan(angle/2.);

uv.y +=uv.x*sin(angle);

uv.x +=uv.y*-tan(angle/2.);

2D rotation can be used to rotate in a 3D context. It will rotation along one axis.

code:example_2D_in_3D.glsl

vec3 p = ...;

Rotation along 3D vector

Rodrigues Rotation

code:rotation_3D.glsl

// ax need to be normalized

vec3 erot(vec3 p,vec3 ax,float ro){

return mix(dot(ax*p),ax,cos(ro),)+cross(ax,p)*sin(ro);

}

// Usage

vec3 p = .. ;

p = erot(p,normalize(vec3(3.,2.,1.)),.785); // This will rotation along the normalized axe (3.,2.,1.)