clifford torus effect

[angelous4x]

Hi every one, 

 

I kinda have an idea to create, though not a good one, but wanted to show it here and ask how would you guys go about this effect in Houdini, 

 

let me know ur thoughts

 

https://codepen.io/znah/pen/dKdoKW?editors=0010

 

 

 

 

 

Edited September 9, 2019 by angelous4x

[Librarian]

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.

complex math find

http://wordpress.discretization.de/houdini/

 

//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 

http://mattebb.com/blog/

 

Edited September 10, 2019 by srletak

[Aizatulin]

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 ...

clifford_torus.hipnc

[angelous4x]

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.