implement a Spiral region

this isn't 100% what i need for my buffer, but i should be able to
create some morph that wraps this cylinder-like spiral into a torus
spiral.

src/geom/region/primitives.rs

@@ -157,6 +157,36 @@ impl Region for Cube {
     }
 }
 
+/// a Spiral traces out a circle on the xy plane as z increases.
+#[derive(Copy, Clone, Serialize, Deserialize)]
+pub struct Spiral {
+    /// radius of the spiral
+    major: f32,
+    /// effective "width" of the spiral.
+    /// any point within this distance from the 1-dimensional spiral is considered to be in the
+    /// region.
+    minor: f32,
+    /// determines how stretched the spiral is in z-space.
+    /// the xy plane at z=0 looks identical again at t=period.
+    period: f32,
+}
+
+impl Spiral {
+    pub fn new(major: f32, minor: f32, period: f32) -> Self {
+        Self { major, minor, period }
+    }
+}
+
+#[typetag::serde]
+impl Region for Spiral {
+    fn contains(&self, p: Meters) -> bool {
+        let revs = p.z() / self.period;
+        let expected_angle = (revs % 1.0) * std::f32::consts::PI * 2.0;
+        let expected = Meters::new(self.major * expected_angle.cos(), self.major * expected_angle.sin(), p.z());
+        p.distance_sq(*expected) < self.minor * self.minor
+    }
+}
+
 #[cfg(test)]
 mod test {
     use super::*;
@@ -286,6 +316,62 @@ mod test {
         assert!(tor.contains(Meters::new(1.0, 2.0, 12.0)));
         assert!(!tor.contains(Meters::new(1.0, 2.0, 13.0)));
     }
+
+    #[test]
+    fn test_spiral_doesnt_contain_zero() {
+        let spiral = Spiral::new(10.0, 1.0, 4.0);
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 0.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 1.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 2.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 3.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 4.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 5.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 6.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 7.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 8.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 9.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 10.0)));
+        assert!(!spiral.contains(Meters::new(0.0, 0.0, 11.0)));
+    }
+
+    #[test]
+    fn test_spiral_exactly_on_course() {
+        let spiral = Spiral::new(10.0, 1.0, 4.0);
+        assert!(spiral.contains(Meters::new(10.0, 0.0, 0.0)));
+        assert!(spiral.contains(Meters::new(0.0, 10.0, 1.0)));
+        assert!(spiral.contains(Meters::new(-10.0, 0.0, 2.0)));
+        assert!(spiral.contains(Meters::new(0.0, -10.0, 3.0)));
+        assert!(spiral.contains(Meters::new(10.0, 0.0, 4.0)));
+        assert!(spiral.contains(Meters::new(0.0, 10.0, 5.0)));
+    }
+
+    #[test]
+    fn test_spiral_exactly_on_course_negative() {
+        let spiral = Spiral::new(10.0, 1.0, 4.0);
+        assert!(spiral.contains(Meters::new(0.0, -10.0, -1.0)));
+        assert!(spiral.contains(Meters::new(-10.0, 0.0, -2.0)));
+        assert!(spiral.contains(Meters::new(0.0, 10.0, -3.0)));
+        assert!(spiral.contains(Meters::new(10.0, 0.0, -4.0)));
+        assert!(spiral.contains(Meters::new(0.0, -10.0, -5.0)));
+    }
+
+    #[test]
+    fn test_spiral_within_minor_radius() {
+        let spiral = Spiral::new(10.0, 1.0, 4.0);
+        assert!(spiral.contains(Meters::new(10.5, 0.0, 0.0)));
+        assert!(spiral.contains(Meters::new(10.5, -0.5, 0.0)));
+        assert!(spiral.contains(Meters::new(9.1, 0.0, 0.0)));
+        assert!(!spiral.contains(Meters::new(8.9, 0.0, 0.0)));
+        assert!(!spiral.contains(Meters::new(9.1, 0.9, 0.0)));
+
+        assert!(spiral.contains(Meters::new(0.5, 10.5, 1.0)));
+        assert!(spiral.contains(Meters::new(-0.9, 10.0, 1.0)));
+        assert!(!spiral.contains(Meters::new(-0.9, 10.9, 1.0)));
+
+        assert!(spiral.contains(Meters::new(-10.9, 0.0, 2.0)));
+        assert!(spiral.contains(Meters::new(-10.0, 0.6, 2.0)));
+        assert!(!spiral.contains(Meters::new(-10.8, 0.8, 2.0)));
+    }
 }