# Blending Shapes

Combining shapes using `min()` was a good start, but there's nicer approaches available to us as well.

## Smooth Minimum

Distance Functions have a lot of mathematical theory behind them: they're a type of Implicit Function. The maths go deep, but we can cherrypick useful tricks here and there from the theory. One such example is the smooth minimum.

A smooth minimum function takes two values as input, and returns a smoothed out value between the two. There's different types of smooth minimum with different tradeoffs, but here's a few taken from the ever-useful iquilezles.org:

### Exponential

``````float smin( float a, float b, float k )
{
float res = exp( -k*a ) + exp( -k*b );
return -log( res )/k;
}
``````

### Polynomial

``````float smin( float a, float b, float k )
{
float h = clamp( 0.5+0.5*(b-a)/k, 0.0, 1.0 );
return mix( b, a, h ) - k*h*(1.0-h);
}
``````

### Power

``````float smin( float a, float b, float k )
{
a = pow( a, k ); b = pow( b, k );
return pow( (a*b)/(a+b), 1.0/k );
}
``````