Bezier-rs: Added function to find intersections between a bezier and a rectangle (#897)

* added function to find intersections for a rectangle

* Added is_contained_within function

libraries/bezier-rs/src/bezier/solvers.rs

@@ -139,6 +139,12 @@ impl Bezier {
 		[endpoints_min, endpoints_max]
 	}
 
+	/// Returns `true` if the bounding box of the bezier is contained entirely within a rectangle defined by its minimum and maximum corners.
+	pub fn is_contained_within(&self, min_corner: DVec2, max_corner: DVec2) -> bool {
+		let [bounding_box_min, bounding_box_max] = self.bounding_box();
+		min_corner.x <= bounding_box_min.x && min_corner.y <= bounding_box_min.y && bounding_box_max.x <= max_corner.x && bounding_box_max.y <= max_corner.y
+	}
+
 	// TODO: Use an `impl Iterator` return type instead of a `Vec`
 	/// Returns list of `t`-values representing the inflection points of the curve.
 	/// The inflection points are defined to be points at which the second derivative of the curve is equal to zero.
@@ -355,6 +361,19 @@ impl Bezier {
 			.flat_map(|(index, (subcurve, t_pair))| Bezier::intersections_between_vectors_of_curves(&[(subcurve, t_pair)], &combined_list2[index + 2..], error))
 			.collect()
 	}
+
+	/// Returns a list of `t` values that correspond to the intersection points between the curve and a rectangle defined by opposite corners.
+	pub fn rectangle_intersections(&self, corner1: DVec2, corner2: DVec2) -> Vec<f64> {
+		[
+			Bezier::from_linear_coordinates(corner1.x, corner1.y, corner2.x, corner1.y),
+			Bezier::from_linear_coordinates(corner2.x, corner1.y, corner2.x, corner2.y),
+			Bezier::from_linear_coordinates(corner2.x, corner2.y, corner1.x, corner2.y),
+			Bezier::from_linear_coordinates(corner1.x, corner2.y, corner1.x, corner1.y),
+		]
+		.iter()
+		.flat_map(|bezier| self.intersections(bezier, None, None))
+		.collect()
+	}
 }
 
 #[cfg(test)]

website/other/bezier-rs-demos/src/App.vue

@@ -554,6 +554,14 @@ export default defineComponent({
 						},
 					},
 				},
+				{
+					name: "Intersect (Rectangle)",
+					callback: (bezier: WasmBezierInstance): string =>
+						bezier.intersect_rectangle([
+							[50, 50],
+							[150, 150],
+						]),
+				},
 				{
 					name: "Rotate",
 					callback: (bezier: WasmBezierInstance, options: Record<string, number>): string => bezier.rotate(options.angle * Math.PI, 100, 100),

website/other/bezier-rs-demos/wasm/src/bezier.rs

@@ -477,6 +477,33 @@ impl WasmBezier {
 		wrap_svg_tag(intersect_self_svg)
 	}
 
+	pub fn intersect_rectangle(&self, js_points: &JsValue) -> String {
+		let points: [DVec2; 2] = js_points.into_serde().unwrap();
+
+		let bezier_curve_svg = self.get_bezier_path();
+
+		let mut rectangle_svg = String::new();
+		[
+			Bezier::from_linear_coordinates(points[0].x, points[0].y, points[1].x, points[0].y),
+			Bezier::from_linear_coordinates(points[1].x, points[0].y, points[1].x, points[1].y),
+			Bezier::from_linear_coordinates(points[1].x, points[1].y, points[0].x, points[1].y),
+			Bezier::from_linear_coordinates(points[0].x, points[1].y, points[0].x, points[0].y),
+		]
+		.iter()
+		.for_each(|line| line.to_svg(&mut rectangle_svg, CURVE_ATTRIBUTES.to_string().replace(BLACK, RED), String::new(), String::new(), String::new()));
+
+		let intersections_svg = self
+			.0
+			.rectangle_intersections(points[0], points[1])
+			.iter()
+			.map(|intersection_t| {
+				let point = &self.0.evaluate(ComputeType::Parametric(*intersection_t));
+				draw_circle(*point, 4., RED, 1.5, WHITE)
+			})
+			.fold(String::new(), |acc, item| format!("{acc}{item}"));
+		wrap_svg_tag(format!("{bezier_curve_svg}{rectangle_svg}{intersections_svg}"))
+	}
+
 	pub fn reduce(&self) -> String {
 		let original_curve_svg = self.get_bezier_path();
 		let bezier_curves_svg: String = self