Expose 2D polygon boolean operations in Geometry singleton

Clipper 6.4.2 is used internally to perform polypaths clipping, as well
as inflating/deflating polypaths. The following methods were added:

```
Geometry.merge_polygons_2d(poly_a, poly_b) # union
Geometry.clip_polygons_2d(poly_a, poly_b) # difference
Geometry.intersect_polygons_2d(poly_a, poly_b) # intersection
Geometry.exclude_polygons_2d(poly_a, poly_b) # xor

Geometry.clip_polyline_with_polygon_2d(poly_a, poly_b)
Geometry.intersect_polyline_with_polygon_2d(poly_a, poly_b)

Geometry.offset_polygon_2d(polygon, delta) # inflate/deflate
Geometry.offset_polyline_2d(polyline, delta) # returns polygons

// This one helps to implement CSG-like behaviour:
Geometry.transform_points_2d(points, transform)
```

All the methods return an array of polygons/polylines. The resulting
polygons could possibly be holes which could be checked with
`Geometry.is_polygon_clockwise()` which was exposed to scripting as well.

1 files changed, 76 insertions, 1 deletions

diff --git a/core/math/geometry.h b/core/math/geometry.h
index 0b2adf9513..c62573dd13 100644
--- a/core/math/geometry.h
+++ b/core/math/geometry.h
@@ -785,6 +785,78 @@ public:
 		return clipped;
 	}
 
+	enum PolyBooleanOperation {
+		OPERATION_UNION,
+		OPERATION_DIFFERENCE,
+		OPERATION_INTERSECTION,
+		OPERATION_XOR
+	};
+	enum PolyJoinType {
+		JOIN_SQUARE,
+		JOIN_ROUND,
+		JOIN_MITER
+	};
+	enum PolyEndType {
+		END_POLYGON,
+		END_JOINED,
+		END_BUTT,
+		END_SQUARE,
+		END_ROUND
+	};
+
+	static Vector<Vector<Point2> > merge_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
+
+		return _polypaths_do_operation(OPERATION_UNION, p_polygon_a, p_polygon_b);
+	}
+
+	static Vector<Vector<Point2> > clip_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
+
+		return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polygon_a, p_polygon_b);
+	}
+
+	static Vector<Vector<Point2> > intersect_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
+
+		return _polypaths_do_operation(OPERATION_INTERSECTION, p_polygon_a, p_polygon_b);
+	}
+
+	static Vector<Vector<Point2> > exclude_polygons_2d(const Vector<Point2> &p_polygon_a, const Vector<Point2> &p_polygon_b) {
+
+		return _polypaths_do_operation(OPERATION_XOR, p_polygon_a, p_polygon_b);
+	}
+
+	static Vector<Vector<Point2> > clip_polyline_with_polygon_2d(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
+
+		return _polypaths_do_operation(OPERATION_DIFFERENCE, p_polyline, p_polygon, true);
+	}
+
+	static Vector<Vector<Point2> > intersect_polyline_with_polygon_2d(const Vector<Vector2> &p_polyline, const Vector<Vector2> &p_polygon) {
+
+		return _polypaths_do_operation(OPERATION_INTERSECTION, p_polyline, p_polygon, true);
+	}
+
+	static Vector<Vector<Point2> > offset_polygon_2d(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type) {
+
+		return _polypath_offset(p_polygon, p_delta, p_join_type, END_POLYGON);
+	}
+
+	static Vector<Vector<Point2> > offset_polyline_2d(const Vector<Vector2> &p_polygon, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
+
+		ERR_EXPLAIN("Attempt to offset a polyline like a polygon (use offset_polygon_2d instead).");
+		ERR_FAIL_COND_V(p_end_type == END_POLYGON, Vector<Vector<Point2> >());
+
+		return _polypath_offset(p_polygon, p_delta, p_join_type, p_end_type);
+	}
+
+	static Vector<Point2> transform_points_2d(const Vector<Point2> &p_points, const Transform2D &p_mat) {
+
+		Vector<Point2> points;
+
+		for (int i = 0; i < p_points.size(); ++i) {
+			points.push_back(p_mat.xform(p_points[i]));
+		}
+		return points;
+	}
+
 	static Vector<int> triangulate_polygon(const Vector<Vector2> &p_polygon) {
 
 		Vector<int> triangles;
@@ -951,7 +1023,6 @@ public:
 		H.resize(k);
 		return H;
 	}
-
 	static Vector<Vector<Vector2> > decompose_polygon_in_convex(Vector<Point2> polygon);
 
 	static MeshData build_convex_mesh(const PoolVector<Plane> &p_planes);
@@ -961,6 +1032,10 @@ public:
 	static PoolVector<Plane> build_capsule_planes(real_t p_radius, real_t p_height, int p_sides, int p_lats, Vector3::Axis p_axis = Vector3::AXIS_Z);
 
 	static void make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size);
+
+private:
+	static Vector<Vector<Point2> > _polypaths_do_operation(PolyBooleanOperation p_op, const Vector<Point2> &p_polypath_a, const Vector<Point2> &p_polypath_b, bool is_a_open = false);
+	static Vector<Vector<Point2> > _polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type);
 };
 
 #endif