Implemented unimplemented things

src/math.rs

@@ -42,8 +42,33 @@ impl Region<Scalar> for Region1 {
         }
     }
 
-    fn nearest(&self, n: &Scalar) -> Option<Scalar> {
-        unimplemented!();
+    fn nearest(&self, s: &Scalar) -> Option<Scalar> {
+        use Region1::*;
+        match self {
+            Empty => None,
+            Full => Some(*s),
+            Singleton(n) => Some(*n),
+            Range(l, u) => match (l < s, s < u) {
+                (true, true) => Some(*s),
+                (true, false) => Some(*u),
+                (false, true) => Some(*l),
+                _ => None,
+            },
+            Union(r1, r2) => {
+                let distance = |a: Scalar, b: Scalar| (a - b).abs();
+                match (r1.nearest(s), r2.nearest(s)) {
+                    (None, None) => None,
+                    (Some(n), None) | (None, Some(n)) => Some(n),
+                    (Some(n1), Some(n2)) => Some({
+                        if distance(*s, n1) <= distance(*s, n2) {
+                            n1
+                        } else {
+                            n2
+                        }
+                    }),
+                }
+            }
+        }
     }
 }
 
@@ -153,6 +178,15 @@ impl Region<Point2> for Region2 {
 }
 
 impl Region2 {
+    pub fn union(r1: Region2, r2: Region2) -> Region2 {
+        use Region2::*;
+        match (r1, r2) {
+            (Empty, r) | (r, Empty) => r,
+            (Full, _) | (_, Full) => Full,
+            (r1, r2) => Union(Box::new(r1), Box::new(r2)),
+        }
+    }
+
     pub fn intersect(&self, other: &Region2) -> Region2 {
         use Region2::*;
         match (self, other) {
@@ -173,7 +207,9 @@ impl Region2 {
                 }
             }
             (Line(l1), Line(l2)) => l1.intersect(l2),
-            _ => unimplemented!(),
+            (Union(un1, un2), o) | (o, Union(un1, un2)) => {
+                Self::union(un1.intersect(o), un2.intersect(o))
+            }
         }
     }
 }