glsl-rotation-2d

vec2 rotate(vec2 v, float a) {
	float s = sin(a);
	float c = cos(a);
	mat2 m = mat2(c, -s, s, c);
	return m * v;
}

glsl-rotation-3d

mat4 rotationMatrix(vec3 axis, float angle) {
    axis = normalize(axis);
    float s = sin(angle);
    float c = cos(angle);
    float oc = 1.0 - c;
    
    return mat4(oc * axis.x * axis.x + c,           oc * axis.x * axis.y - axis.z * s,  oc * axis.z * axis.x + axis.y * s,  0.0,
                oc * axis.x * axis.y + axis.z * s,  oc * axis.y * axis.y + c,           oc * axis.y * axis.z - axis.x * s,  0.0,
                oc * axis.z * axis.x - axis.y * s,  oc * axis.y * axis.z + axis.x * s,  oc * axis.z * axis.z + c,           0.0,
                0.0,                                0.0,                                0.0,                                1.0);
}

vec3 rotate(vec3 v, vec3 axis, float angle) {
	mat4 m = rotationMatrix(axis, angle);
	return (m * vec4(v, 1.0)).xyz;
}

glsl-twist-axis

float theta = 0.;
float s = 0.;
float c = 0.;


// Twist X
theta = position.x;
c = cos( theta );
s = sin( theta );
mat3 twistX = mat3(
  1, 0, 0,
  0, c, -s,
  0, s, c
);

// Twist Y
theta = position.y;
c = cos( theta);
s = sin( theta);
mat3 twistY = mat3(
  c, 0, s,
  0, 1, 0,
  -s, 0, c
);

// Twist Z
theta = position.z;
c = cos( theta );
s = sin( theta );
mat3 twistZ = mat3(
  c, -s, 0,
  s, c, 0,
   0, 0, 1
);