refactor engine and layout into input and output

output/src/coordinate.rs

@@ -0,0 +1,28 @@
+use std::fmt::{Debug, Display};
+use std::ops::{Add, Sub, Mul, Div};
+
+impl Coordinate for u16 {}
+
+/// A linear coordinate.
+pub trait Coordinate: Send + Sync + Copy
+    + Add<Self, Output=Self>
+    + Sub<Self, Output=Self>
+    + Mul<Self, Output=Self>
+    + Div<Self, Output=Self>
+    + Ord + PartialEq + Eq
+    + Debug + Display + Default
+    + From<u16> + Into<u16>
+    + Into<usize>
+    + Into<f64>
+{
+    #[inline] fn minus (self, other: Self) -> Self {
+        if self >= other {
+            self - other
+        } else {
+            0.into()
+        }
+    }
+    #[inline] fn zero () -> Self {
+        0.into()
+    }
+}