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BlaschkeProduct.osl
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BlaschkeProduct.osl
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// GLSL version mahalis
// OSL port + modifications by Mads Drøschler
// 5.6.2018
// License CC3.0
vector cM(vector a, vector b) {
return vector(a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0],0);
}
vector cD(vector a, vector b) {
return vector((a[0] * b[0] + a[1] * b[1]), (a[1] * b[0] - a[0] * b[1]),0) / dot(b, b);
}
vector conj(vector a) {
return vector(a[0], -a[1],0);
}
vector blaschkeB(vector a, vector z) {
return cD(a - z, vector(1.,0.,0) - cM(conj(a), z));
}
vector palette(float v) {
return vector(0.5) + 0.5 * cos(M_PI*2 * (v + vector(0.0,0.333,0.667)));
}
vector Position(float t) {
return vector(sin(2.2 * t) - cos(1.4 * t), cos(1.3 * t) + sin(-1.9 * t),0) * 0.2;
}
shader BlaschkeProduct(
point Po = P,
float Time = 0,
output vector Out = 0,
)
{
point pos = Po;
point uv = pos - 0.5;
uv *= 1.;
vector prod = vector(1.,0.,0);
for(int i = 0; i < 43; i++) {
vector a = Position(float(i) * 37. + Time * 0.3);
prod = cM(prod, blaschkeB(a, uv));
}
float angle = atan2(prod[1], prod[0]) * 1.;
Out = vector(palette(angle / M_PI*2 - Time * 1.9));
}