Identify outer border of bordering polygons C++ - c++

Question

I'm looking for advice on an algorithm I've been struggling with. I have something represented in code (shown later) that looks like the following diagram (initial state on left, desired output on right):
I have this represented in C++ as the following:
#include <vector>
using namespace std;
class Shape {
public:
Shape(vector<vector<float> > c) {
coordinates = c;
}
vector<vector<float> > coordinates; // in format {{x1,y1},{x2,y2}}
};
class Shape_Group {
public:
Shape_Group(vector<Shape> s) {
shapes = s;
}
vector<Shape> shapes;
Shape generate_border();
};
Shape Shape_Group::generate_border() {
/*
define algorithm here
*/
}
int main() {
// define rectangle shapes
Shape s1({{0,0}, {0,1}, {1,1}, {1,0}});
Shape s2({{0,0}, {0,1}, {1,-1}, {-1,0}});
Shape_Group group({s1, s2});
Shape border = group.generate_border(); // should return a shape with the exterior border
// border should be filed with {{1,0}, {1,1}, {1,-1}, {-1,0}};
}
My initial idea for generating this exterior shape was to do something like the following:
loop through each line segment for each shape in the Shape_Group object
loop through every other segment in the Shape_Group object
if both line segments are colinear and overlap, remove them
whatever's left over should be the exterior border
However, with large inputs this is a very slow algorithm. What else can I do?

Answer 1

Geometry O(n^2) approach:
make list of all edges
remove all interrior edges
use hit test to detect interior/exterior edges.
reconnect all remaining edges into new polygon
simply connect edges sharing the same end point.
If you want something simpler then O(n) graphics approach:
render your shape
fill background with specific color
remove all edges not neighboring background color
this is somewhat related:
Render filled complex polygons with large number of vertices with OpenGL
it also combines vector graphics and pixel access ...
There are also different approaches to this problem for example like this one:
Finding holes in 2d point sets?