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clifford torus effect

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Hi @angelous4x  you have an idea I have an idea, + + =  maybe.

transform before /$PI *2 = x and y

Confuse a cat

play with this and your idea.:wub:

complex math find



//q=(1+i+j+k)/2  must be 1 Möbius strip

float cos = v@P.z;
float sin = v@P.x;
float r = v@P.y;

float c_sqr = pow(cos,1) -pow(sin, 1);
float s2 = 1*sin*cos;

vector C = set(c_sqr, 0, s2);
vector B = {0, 1, 0};
vector N = cos * C + sin * B;

v@P = C + r * N;
//Sudanese surface.

vector4 gamma(float t) {
    return set(cos(t), sin(t), 0, 0);

vector4 N(float tau; float t) {
    float tau_t = tau * t;
    return set(0, 0, cos(tau_t), sin(tau_t));

vector4 f_tau(float tau; float x; float y) {
    return cos(y) * gamma(x) + sin(y) * N(tau, x);

vector sigma(vector4 v) {
    return set(v.x / (1 - v.w), v.y / (1 - v.w), v.z / (1 - v.w));

float tau = chf("tau");

vector4 q = {1, 1, 1.5, 1};
q /= length(q);

v@P = sigma(qmultiply(f_tau(tau, v@P.x, v@P.y), q));












or just use file from Matt Ebb a long time ago 



Edited by srletak
  • Like 2

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Here is another approach (definition somewhere from web).

  • Using the clifford torus defintion from wiki.
  • Using a 4d rotation (in my case between the first and the last component)
  • applying a stereographic projection, to map from 4d space back into 3d space

I'm not sure if this is correct, because it looks a bit weird for me ...


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I need to work on my math big time. yeah what i was thinking is all in sop level, getting a circle rotating it and getting the closest part of the curve and giving it a value to use a displace by a normal. 

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