How to make a union of polygons without self-touching polygons in the result?

[rburing]

Here's the result of a Union of squares and triangles (all squares have size 50x50, all triangles are half of such a square):

This polygon touches itself at (50,50). I would like to achieve a result without self-touching. How can it be done?

To clarify, I would like a result consisting of (at least, and ideally at most) two polygons, such that neither polygon touches itself (but by necessity one will touch another, which is fine).

Motivation: This is relevant for a downstream Godot issue

• TileMapLayer fails to generate big chunk colliders with some setups godotengine/godot#104452

The C++ code that results in the union with self-touching shown above

#include <clipper2/clipper.h>
#include <iostream>
using namespace Clipper2Lib;

int main(int argc, char *argv[]) {
  Paths64 polygons = {
    MakePath({ 0,0, 50,50, 0,50 }),
    MakePath({ 50,0, 100,0, 100,50, 50,50 }),
    MakePath({ 100,0, 150,0, 150,50, 100,50 }),
    MakePath({ 0,50, 50,50, 50,100, 0,100 }),
    MakePath({ 50,50, 100,100, 50,100 }),
    MakePath({ 100,50, 150,50, 150,100, 100,100 }),
    MakePath({ 0,100, 50,100, 50,150 }),
    MakePath({ 50,100, 100,100, 100,150, 50,150 }),
    MakePath({ 100,100, 150,100, 150,150, 100,150 })
  };

  Paths64 merged_polygons = Union(polygons, FillRule::NonZero);

  for (int i = 0; i < merged_polygons.size(); i++) {
    std::cout << "Polygon:" << std::endl;
    Path64 polygon = merged_polygons[i];
    for (int j = 0; j < polygon.size(); j++) {
      std::cout << "(" << polygon[j].x << ", " << polygon[j].y << ")";
      if (j != polygon.size() - 1) {
        std::cout << ", ";
      }
    }
    std::cout << std::endl;
  }

  std::cout << "Number of polygons in merge result: " << merged_polygons.size() << std::endl;
}

[AngusJohnson]

There is no self-intersection here. While the vertex at (50,50) touches the edge ((0,0),(100,100)), it does not intersect it.

[rburing]

Alright, let's call it touching. My question (with "intersection" replaced by "touching") remains. I updated the phrasing.

[rburing]

Can this be reopened? It's a reasonable question with no answer (so far). I updated it to use your preferred terminology.

[philstopford]

I wonder if you can get what you want by a pair of offset operations. One to size up, then one to size down (opposite sign) that result (possibly piecewise). This should give you the overlap necessary to capture the internal triangle as a distinct entity.