It is possible to split a bezier surface into two pieces. It helps us to slice a surface into several pieces without losing the original shape. In that way we are able to delete one piece of several slices of a whole surface.

function splitBezier(t, p0, p1, p2, p3) {
  const p4 = lerp(t, p0, p1);
  const p5 = lerp(t, p1, p2);
  const p6 = lerp(t, p2, p3);
  const p7 = lerp(t, p4, p5);
  const p8 = lerp(t, p5, p6);
  const p9 = lerp(t, p7, p8);
  return [
    [{...p0}, p4, p7, p9],
    [{...p9}, p8, p6, {...p3}]
  ];
}

This is a javascript code. I create the surface editing software in javascript. The function lerp is identical to Python one that I mentioned my blog post before. It takes the t value between 0 and 1, and returns two bezier curves, one is the half that splitted at t, the other one is other half. Two of them shapes the given bezier curve.

This slices a curve into two pieces. So I slice the main piece until it is one piece of slices I want while I create another surface with the each other half.

let sliceCurrent = 4;
const obj = {
  "wide": 10,
  "fall": 4,
  "points": [] 
}
while (sliceCurrent > 1) {
  const t = (obj["wide"] / sliceCurrent) * (sliceCurrent - 1) / obj["wide"];
  const [halfa, enda] = splitBezier(t, obj.points[0], obj.points[1], obj.points[2], obj.points[3]);
  const [halfb, endb] = splitBezier(t, obj.points[4], obj.points[5], obj.points[6], obj.points[7]);
  const [halfc, endc] = splitBezier(t, obj.points[8], obj.points[9], obj.points[10], obj.points[11]);
  const [halfd, endd] = splitBezier(t, obj.points[12], obj.points[13], obj.points[14], obj.points[15]);
  obj.points[0] = halfa[0];
  obj.points[1] = halfa[1];
  obj.points[2] = halfa[2];
  obj.points[3] = halfa[3];
  obj.points[4] = halfb[0];
  obj.points[5] = halfb[1];
  obj.points[6] = halfb[2];
  obj.points[7] = halfb[3];
  obj.points[8] = halfc[0];
  obj.points[9] = halfc[1];
  obj.points[10] = halfc[2];
  obj.points[11] = halfc[3];
  obj.points[12] = halfd[0];
  obj.points[13] = halfd[1];
  obj.points[14] = halfd[2];
  obj.points[15] = halfd[3];
  const objNew = {
    "id": getNewId(),
    "wide": parseInt((1 - t) * obj["wide"]),
    "fall": obj["fall"],
    "type": "plane",
    "points": [
      enda[0], enda[1], enda[2], enda[3],
      endb[0], endb[1], endb[2], endb[3],
      endc[0], endc[1], endc[2], endc[3],
      endd[0], endd[1], endd[2], endd[3]
    ],
  };
  draft.push(objNew);
  obj["wide"] *= t;
  sliceCurrentWide -= 1;
}
obj["wide"] = int(obj["wide"])

This slices the surface horizontally that it's segments set by "wide" parameter. The "fall" is for the vertical. Same method must be applied the surface if it needs to be sliced horizontally.

Good luck playing with that.