add clock and bezier example

turtle-lib/examples/bezier.rs

@@ -0,0 +1,56 @@
+//! Cubic Bézier curve example
+//! <https://en.wikipedia.org/wiki/B%C3%A9zier_curve>
+
+use turtle_lib::{turtle_main, vec2};
+
+struct CubicBezier {
+    point0: (f32, f32),
+    point1: (f32, f32),
+    point2: (f32, f32),
+    point3: (f32, f32),
+}
+
+impl CubicBezier {
+    /// Returns the value of this curve at the given parameter t (0.0 to 1.0)
+    pub fn at(&self, t: f64) -> (f32, f32) {
+        let t = t as f32;
+        let mt = 1.0 - t; // (1 - t)
+
+        // Cubic Bézier formula from Wikipedia
+        let p0_weight = mt.powi(3);
+        let p1_weight = 3.0 * mt.powi(2) * t;
+        let p2_weight = 3.0 * mt * t.powi(2);
+        let p3_weight = t.powi(3);
+
+        (
+            self.point0.0 * p0_weight
+                + self.point1.0 * p1_weight
+                + self.point2.0 * p2_weight
+                + self.point3.0 * p3_weight,
+            self.point0.1 * p0_weight
+                + self.point1.1 * p1_weight
+                + self.point2.1 * p2_weight
+                + self.point3.1 * p3_weight,
+        )
+    }
+}
+
+#[turtle_main("Bézier Curve")]
+fn draw(turtle: &mut TurtlePlan) {
+    let curve = CubicBezier {
+        point0: (-200.0, -100.0),
+        point1: (-100.0, 400.0),
+        point2: (100.0, -500.0),
+        point3: (300.0, 200.0),
+    };
+
+    let start = curve.at(0.0);
+    turtle.pen_up().go_to(vec2(start.0, start.1)).pen_down();
+
+    let samples = 100;
+    for i in 0..samples {
+        let t = f64::from(i) / f64::from(samples);
+        let point = curve.at(t);
+        turtle.go_to(vec2(point.0, point.1));
+    }
+}