Bezier-rs: Add function to smoothly join bezier curves (#1037)

* Added bezier join

* Stylistic changes per review

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

@@ -52,15 +52,19 @@ impl Bezier {
 		}
 	}
 
-	/// Returns a normalized unit vector representing the tangent at the point `t` along the curve.
-	/// <iframe frameBorder="0" width="100%" height="400px" src="https://graphite.rs/bezier-rs-demos#bezier/tangent/solo" title="Tangent Demo"></iframe>
-	pub fn tangent(&self, t: TValue) -> DVec2 {
-		let t = self.t_value_to_parametric(t);
+	/// Returns the non-normalized vector representing the tangent at the point `t` along the curve.
+	fn non_normalized_tangent(&self, t: f64) -> DVec2 {
 		match self.handles {
 			BezierHandles::Linear => self.end - self.start,
 			_ => self.derivative().unwrap().evaluate(TValue::Parametric(t)),
 		}
-		.normalize()
+	}
+
+	/// Returns a normalized unit vector representing the tangent at the point `t` along the curve.
+	/// <iframe frameBorder="0" width="100%" height="400px" src="https://graphite.rs/bezier-rs-demos#bezier/tangent/solo" title="Tangent Demo"></iframe>
+	pub fn tangent(&self, t: TValue) -> DVec2 {
+		let t = self.t_value_to_parametric(t);
+		self.non_normalized_tangent(t).normalize()
 	}
 
 	/// Returns a normalized unit vector representing the direction of the normal at the point `t` along the curve.
@@ -390,6 +394,15 @@ impl Bezier {
 		.flat_map(|bezier| self.intersections(bezier, None, None))
 		.collect()
 	}
+
+	/// Returns a cubic bezier which joins this with the provided bezier curve.
+	/// The resulting path formed by the Bezier curves is continuous up to the first derivative.
+	/// <iframe frameBorder="0" width="100%" height="325px" src="https://graphite.rs/bezier-rs-demos#bezier/join/solo" title="Join Demo"></iframe>
+	pub fn join(&self, other: &Bezier) -> Bezier {
+		let handle1 = self.non_normalized_tangent(1.) / 3. + self.end;
+		let handle2 = other.start - other.non_normalized_tangent(0.) / 3.;
+		Bezier::from_cubic_dvec2(self.end, handle1, handle2, other.start)
+	}
 }
 
 #[cfg(test)]

website/other/bezier-rs-demos/src/features/bezier-features.ts

@@ -483,6 +483,56 @@ const bezierFeatures = {
 		},
 		chooseTVariant: true,
 	},
+	join: {
+		name: "Join",
+		callback: (bezier: WasmBezierInstance): string => {
+			const points = JSON.parse(bezier.get_points());
+			let examplePoints = [];
+			if (points.length === 2) {
+				examplePoints = [
+					[120, 155],
+					[40, 155],
+				];
+			} else if (points.length === 3) {
+				examplePoints = [
+					[40, 150],
+					[95, 195],
+					[155, 145],
+				];
+			} else {
+				examplePoints = [
+					[140, 150],
+					[85, 110],
+					[65, 180],
+					[30, 140],
+				];
+			}
+			return bezier.join(examplePoints);
+		},
+		demoOptions: {
+			Linear: {
+				customPoints: [
+					[45, 40],
+					[130, 90],
+				],
+			},
+			Quadratic: {
+				customPoints: [
+					[153, 40],
+					[40, 20],
+					[75, 85],
+				],
+			},
+			Cubic: {
+				customPoints: [
+					[20, 80],
+					[40, 20],
+					[90, 100],
+					[130, 55],
+				],
+			},
+		},
+	},
 };
 
 export type BezierFeatureKey = keyof typeof bezierFeatures;

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

@@ -621,4 +621,44 @@ impl WasmBezier {
 			.fold(original_curve_svg, |acc, item| format!("{acc}{item}"));
 		wrap_svg_tag(arcs_svg)
 	}
+
+	pub fn join(&self, js_points: &JsValue) -> String {
+		let other_bezier: Bezier = match self.0.get_points().count() {
+			2 => {
+				let points: [DVec2; 2] = serde_wasm_bindgen::from_value(js_points.into()).unwrap();
+				Bezier::from_linear_dvec2(points[0], points[1])
+			}
+			3 => {
+				let points: [DVec2; 3] = serde_wasm_bindgen::from_value(js_points.into()).unwrap();
+				Bezier::from_quadratic_dvec2(points[0], points[1], points[2])
+			}
+			4 => {
+				let points: [DVec2; 4] = serde_wasm_bindgen::from_value(js_points.into()).unwrap();
+				Bezier::from_cubic_dvec2(points[0], points[1], points[2], points[3])
+			}
+			_ => unreachable!(),
+		};
+
+		let mut other_bezier_svg = String::new();
+		other_bezier.to_svg(
+			&mut other_bezier_svg,
+			CURVE_ATTRIBUTES.to_string().replace(BLACK, GRAY),
+			ANCHOR_ATTRIBUTES.to_string().replace(BLACK, GRAY),
+			String::new(),
+			String::new(),
+		);
+
+		let joining_bezier: Bezier = self.0.join(&other_bezier);
+		let mut joining_bezier_svg = String::new();
+		joining_bezier.to_svg(
+			&mut joining_bezier_svg,
+			CURVE_ATTRIBUTES.to_string().replace(BLACK, RED),
+			ANCHOR_ATTRIBUTES.to_string().replace(BLACK, RED),
+			String::new(),
+			String::new(),
+		);
+
+		let bezier_svg = self.get_bezier_path();
+		wrap_svg_tag(format!("{bezier_svg}{joining_bezier_svg}{other_bezier_svg}"))
+	}
 }