A cubic bezier curve linearly interpolates between 4 point positions. The first interpolation between point 0 and 1 and the second between 2 and 3. Then it interpolates between the first and the second interpolation.

Thus resulting in a smooth curve that starts at point 0, ends at point 3 and bends towards point 1 and 2. In this code the linear interpolations are driven by `u`

. A for loop is adding a new point at the calculated positions.

```
int steps = chi('steps');
vector pos_0 = point(1, "P", 0);
vector pos_1 = point(1, "P", 1);
vector pos_2 = point(1, "P", 2);
vector pos_3 = point(1, "P", 3);
int prim = addprim(0, "polyline");
for(int i = 0; i < steps; i++) {
float u = i / float(steps - 1);
vector pos_a = lerp(pos_0, pos_1, u);
vector pos_b = lerp(pos_2, pos_3, u);
vector pos = lerp(pos_a, pos_b, u);
int pt = addpoint(0, pos);
addvertex(0, prim, pt);
}
```

Houdini comes with a built-in spline function which offers various interpolation types, as well:

https://www.sidefx.com/docs/houdini/vex/functions/spline.html