Handle intersections between two bezier curves (#735)

* Refactor intersections function

* Implement intersect for quadratic and cubic bezier curves

* Return t value instead of point

* Change project return the t value

* Add error threshold for curve intersection

* Refactor to use if let statements and improve comments

* Refactor intersection helper to return vector, other minor name/text changes

* Rename function

* Minor change

* Minor fixes

* Add missing test tag

* Address comments

* Adjust comment

* Change function call

* Edit comments

bezier-rs/lib/src/utils.rs

@@ -146,6 +146,14 @@ pub fn solve_cubic(a: f64, b: f64, c: f64, d: f64) -> Vec<f64> {
 	}
 }
 
+/// Determine if two rectangles have any overlap. The rectangles are represented by a pair of coordinates that designate the top left and bottom right corners (in a graphical coordinate system).
+pub fn do_rectangles_overlap(rectangle1: [DVec2; 2], rectangle2: [DVec2; 2]) -> bool {
+	let [bottom_left1, top_right1] = rectangle1;
+	let [bottom_left2, top_right2] = rectangle2;
+
+	top_right1.x >= bottom_left2.x && top_right2.x >= bottom_left1.x && top_right2.y >= bottom_left1.y && top_right1.y >= bottom_left2.y
+}
+
 /// Returns the intersection of two lines. The lines are given by a point on the line and its slope (represented by a vector).
 pub fn line_intersection(point1: DVec2, point1_slope_vector: DVec2, point2: DVec2, point2_slope_vector: DVec2) -> DVec2 {
 	assert!(point1_slope_vector.normalize() != point2_slope_vector.normalize());
@@ -243,6 +251,20 @@ mod tests {
 		assert!(roots7 == vec![1.]);
 	}
 
+	#[test]
+	fn test_do_rectangles_overlap() {
+		// Rectangles overlap
+		assert!(do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(20., 20.)], [DVec2::new(10., 10.), DVec2::new(30., 20.)]));
+		// Rectangles share a side
+		assert!(do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(10., 10.)], [DVec2::new(10., 10.), DVec2::new(30., 30.)]));
+		// Rectangle inside the other
+		assert!(do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(10., 10.)], [DVec2::new(2., 2.), DVec2::new(6., 4.)]));
+		// No overlap, rectangles are beside each other
+		assert!(!do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(10., 10.)], [DVec2::new(20., 0.), DVec2::new(30., 10.)]));
+		// No overlap, rectangles are above and below each other
+		assert!(!do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(10., 10.)], [DVec2::new(0., 20.), DVec2::new(20., 30.)]));
+	}
+
 	#[test]
 	fn test_find_intersection() {
 		// y = 2x + 10