Bezier-rs: Add method to check subpath insideness (#2183)

* add function to calculate if a subpath is inside polygon

* make is_subpath_inside_polygon() flexible

* obtimize is_subpath_inside_polygon function

* move is_inside_subpath function to Subpath struct method

* add interactive demo for subpath insideness

* Code review

---------

Co-authored-by: Keavon Chambers <keavon@keavon.com>

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

@@ -1,6 +1,6 @@
 use super::*;
 use crate::consts::MAX_ABSOLUTE_DIFFERENCE;
-use crate::utils::{compute_circular_subpath_details, line_intersection, SubpathTValue};
+use crate::utils::{compute_circular_subpath_details, is_rectangle_inside_other, line_intersection, SubpathTValue};
 use crate::TValue;
 
 use glam::{DAffine2, DMat2, DVec2};
@@ -237,6 +237,47 @@ impl<PointId: crate::Identifier> Subpath<PointId> {
 		false
 	}
 
+	/// Returns `true` if this subpath is completely inside the `other` subpath.
+	/// <iframe frameBorder="0" width="100%" height="350px" src="https://graphite.rs/libraries/bezier-rs#subpath/inside-other/solo" title="Inside Other Subpath Demo"></iframe>
+	pub fn is_inside_subpath(&self, other: &Subpath<PointId>, error: Option<f64>, minimum_separation: Option<f64>) -> bool {
+		// Eliminate any possibility of one being inside the other, if either of them is empty
+		if self.is_empty() || other.is_empty() {
+			return false;
+		}
+
+		// Safe to unwrap because the subpath is not empty
+		let inner_bbox = self.bounding_box().unwrap();
+		let outer_bbox = other.bounding_box().unwrap();
+
+		// Eliminate this subpath if its bounding box is not completely inside the other subpath's bounding box.
+		// Reasoning:
+		// If the (min x, min y) of the inner subpath is less than or equal to the (min x, min y) of the outer subpath,
+		// or if the (min x, min y) of the inner subpath is greater than or equal to the (max x, max y) of the outer subpath,
+		// then the inner subpath is intersecting with or outside the outer subpath. The same logic applies for (max x, max y).
+		if !is_rectangle_inside_other(inner_bbox, outer_bbox) {
+			return false;
+		}
+
+		// Eliminate this subpath if any of its anchors are outside the other subpath.
+		for anchors in self.anchors() {
+			if !other.contains_point(anchors) {
+				return false;
+			}
+		}
+
+		// Eliminate this subpath if it intersects with the other subpath.
+		if !self.subpath_intersections(other, error, minimum_separation).is_empty() {
+			return false;
+		}
+
+		// At this point:
+		// (1) This subpath's bounding box is inside the other subpath's bounding box,
+		// (2) Its anchors are inside the other subpath, and
+		// (3) It is not intersecting with the other subpath.
+		// Hence, this subpath is completely inside the given other subpath.
+		true
+	}
+
 	/// Returns a normalized unit vector representing the tangent on the subpath based on the parametric `t`-value provided.
 	/// <iframe frameBorder="0" width="100%" height="350px" src="https://graphite.rs/libraries/bezier-rs#subpath/tangent/solo" title="Tangent Demo"></iframe>
 	pub fn tangent(&self, t: SubpathTValue) -> DVec2 {
@@ -267,7 +308,7 @@ impl<PointId: crate::Identifier> Subpath<PointId> {
 		})
 	}
 
-	/// Return the min and max corners that represent the bounding box of the subpath.
+	/// Return the min and max corners that represent the bounding box of the subpath. Return `None` if the subpath is empty.
 	/// <iframe frameBorder="0" width="100%" height="300px" src="https://graphite.rs/libraries/bezier-rs#subpath/bounding-box/solo" title="Bounding Box Demo"></iframe>
 	pub fn bounding_box(&self) -> Option<[DVec2; 2]> {
 		self.iter().map(|bezier| bezier.bounding_box()).reduce(|bbox1, bbox2| [bbox1[0].min(bbox2[0]), bbox1[1].max(bbox2[1])])
@@ -876,6 +917,28 @@ mod tests {
 
 	// TODO: add more intersection tests
 
+	#[test]
+	fn is_inside_subpath() {
+		let boundary_polygon = [DVec2::new(100., 100.), DVec2::new(500., 100.), DVec2::new(500., 500.), DVec2::new(100., 500.)].to_vec();
+		let boundary_polygon = Subpath::from_anchors_linear(boundary_polygon, true);
+
+		let curve = Bezier::from_quadratic_dvec2(DVec2::new(189., 289.), DVec2::new(9., 286.), DVec2::new(45., 410.));
+		let curve_intersecting = Subpath::<EmptyId>::from_bezier(&curve);
+		assert_eq!(curve_intersecting.is_inside_subpath(&boundary_polygon, None, None), false);
+
+		let curve = Bezier::from_quadratic_dvec2(DVec2::new(115., 37.), DVec2::new(51.4, 91.8), DVec2::new(76.5, 242.));
+		let curve_outside = Subpath::<EmptyId>::from_bezier(&curve);
+		assert_eq!(curve_outside.is_inside_subpath(&boundary_polygon, None, None), false);
+
+		let curve = Bezier::from_cubic_dvec2(DVec2::new(210.1, 133.5), DVec2::new(150.2, 436.9), DVec2::new(436., 285.), DVec2::new(247.6, 240.7));
+		let curve_inside = Subpath::<EmptyId>::from_bezier(&curve);
+		assert_eq!(curve_inside.is_inside_subpath(&boundary_polygon, None, None), true);
+
+		let line = Bezier::from_linear_dvec2(DVec2::new(101., 101.5), DVec2::new(150.2, 499.));
+		let line_inside = Subpath::<EmptyId>::from_bezier(&line);
+		assert_eq!(line_inside.is_inside_subpath(&boundary_polygon, None, None), true);
+	}
+
 	#[test]
 	fn round_join_counter_clockwise_rotation() {
 		// Test case where the round join is drawn in the counter clockwise direction between two consecutive offsets

libraries/bezier-rs/src/utils.rs

@@ -1,5 +1,5 @@
 use crate::consts::{MAX_ABSOLUTE_DIFFERENCE, STRICT_MAX_ABSOLUTE_DIFFERENCE};
-use crate::ManipulatorGroup;
+use crate::{ManipulatorGroup, Subpath};
 
 use glam::{BVec2, DMat2, DVec2};
 
@@ -171,7 +171,7 @@ pub fn solve_cubic(a: f64, b: f64, c: f64, d: f64) -> [Option<f64>; 3] {
 	}
 }
 
-/// 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).
+/// Determines 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;
@@ -179,6 +179,17 @@ pub fn do_rectangles_overlap(rectangle1: [DVec2; 2], rectangle2: [DVec2; 2]) ->
 	top_right1.x >= bottom_left2.x && top_right2.x >= bottom_left1.x && top_right2.y >= bottom_left1.y && top_right1.y >= bottom_left2.y
 }
 
+/// Determines if a point is completely inside a rectangle, which is represented as a pair of coordinates [top-left, bottom-right].
+pub fn is_point_inside_rectangle(rect: [DVec2; 2], point: DVec2) -> bool {
+	let [top_left, bottom_right] = rect;
+	point.x > top_left.x && point.x < bottom_right.x && point.y > top_left.y && point.y < bottom_right.y
+}
+
+/// Determines if the inner rectangle is completely inside the outer rectangle. The rectangles are represented as pairs of coordinates [top-left, bottom-right].
+pub fn is_rectangle_inside_other(inner: [DVec2; 2], outer: [DVec2; 2]) -> bool {
+	is_point_inside_rectangle(outer, inner[0]) && is_point_inside_rectangle(outer, inner[1])
+}
+
 /// 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());
@@ -286,7 +297,7 @@ pub fn compute_circular_subpath_details<PointId: crate::Identifier>(left: DVec2,
 #[cfg(test)]
 mod tests {
 	use super::*;
-	use crate::consts::MAX_ABSOLUTE_DIFFERENCE;
+	use crate::{consts::MAX_ABSOLUTE_DIFFERENCE, Bezier, EmptyId};
 
 	/// Compare vectors of `f64`s with a provided max absolute value difference.
 	fn f64_compare_vector(a: Vec<f64>, b: Vec<f64>, max_abs_diff: f64) -> bool {
@@ -352,6 +363,16 @@ mod tests {
 		assert!(!do_rectangles_overlap([DVec2::new(0., 0.), DVec2::new(10., 10.)], [DVec2::new(0., 20.), DVec2::new(20., 30.)]));
 	}
 
+	#[test]
+	fn test_is_rectangle_inside_other() {
+		assert!(!is_rectangle_inside_other([DVec2::new(10., 10.), DVec2::new(50., 50.)], [DVec2::new(10., 10.), DVec2::new(50., 50.)]));
+		assert!(is_rectangle_inside_other(
+			[DVec2::new(10.01, 10.01), DVec2::new(49., 49.)],
+			[DVec2::new(10., 10.), DVec2::new(50., 50.)]
+		));
+		assert!(!is_rectangle_inside_other([DVec2::new(5., 5.), DVec2::new(50., 9.99)], [DVec2::new(10., 10.), DVec2::new(50., 50.)]));
+	}
+
 	#[test]
 	fn test_find_intersection() {
 		// y = 2x + 10