## superShapeSDF (`lygia`/`sdf`/`superShapeSDF`)

It returns a supershape, which is a mathematical function for modelling natural forms develop by Paul Bourke and Johan Gielis. Some notes about the parameters:

``````* `m` determines number of sides/branches
* `m = 0` yields a circle
* `a!=b` results in an assymetrical shape
* `n1=n2=n3<1` the shape is "pinched"
* `n1>n2,n3` the shape is "bloated"
* `n1!=n2!=n3` the shape is assymetrical
* `n1=n2=n3=1` the shape is a square
* `n1=n2=n3=2` the shape is a star
``````

Dependencies:

Use:

``````<float> supershapeSDF(<vec2> st, <vec2> center, <float> size s, <float> a, <float> b, <float> n1, <float> n2, <float> n3, <float> m)
``````
``````<float> supershapeSDF(<vec2> st, <float> size s, <float> a, <float> b, <float> n1, <float> n2, <float> n3, <float> m)
``````

Check it on Github

``````

#ifndef FNC_SUPERSHAPESDF
#define FNC_SUPERSHAPESDF
float superShapeSDF( in vec2 st, in vec2 center, in float s, in float a, in float b, in float n1, in float n2, in float n3, in float m ) {
st -= center;
vec2 polar = cart2polar( st );
float d = polar.y * 5.0;
float theta = polar.x;
float t1 = abs((1.0/a) * cos(m * theta * 0.25));
t1 = pow(t1, n2);
float t2 = abs((1.0/b) * sin(m * theta * 0.25));
t2 = pow(t2, n3);
float t3 = t1 + t2;
float r = pow(t3, -1.0 / n1);
vec2 q = s * r * vec2(cos(theta), sin(theta));
return d - length(q);
}

float superShapeSDF( in vec2 st, in float s, in float a, in float b, in float n1, in float n2, in float n3, in float m ) {
#ifdef CENTER_2D
return superShapeSDF( st, CENTER_2D, s, a, b, n1, n2, n3, m );
#else
return superShapeSDF( st, vec2(0.5), s, a, b, n1, n2, n3, m );
#endif
}
#endif

``````

Dependencies:

Use:

``````<float> supershapeSDF(<float2> st, <float> size s, <float> a, <float> b, <float> n1, <float> n2, <float> n3, <float> m)
``````

Check it on Github

``````

#ifndef FNC_SUPERSHAPESDF
#define FNC_SUPERSHAPESDF
float superShapeSDF( in float2 st, in float2 center, in float s, in float a, in float b, in float n1, in float n2, in float n3, in float m ) {
st -= center;
float2 polar = cart2polar( st );
float d = polar.y * 5.0;
float theta = polar.x;
float t1 = abs((1.0/a) * cos(m * theta * 0.25));
t1 = pow(t1, n2);
float t2 = abs((1.0/b) * sin(m * theta * 0.25));
t2 = pow(t2, n3);
float t3 = t1 + t2;
float r = pow(t3, -1.0 / n1);
float2 q = s * r * float2(cos(theta), sin(theta));
return d - length(q);
}

float superShapeSDF( in float2 st, in float s, in float a, in float b, in float n1, in float n2, in float n3, in float m ) {
#ifdef CENTER_2D
return superShapeSDF( st, CENTER_2D, s, a, b, n1, n2, n3, m );
#else
return superShapeSDF( st, float2(0.5, 0.5), s, a, b, n1, n2, n3, m );
#endif
}
#endif

``````