Add tail recursice bresenham line

@@ -18,10 +18,11 @@
 // You should have received a copy of the GNU General Public License
 // along with this program.  If not, see <http://www.gnu.org/licenses/>.
 //
+use std::cmp;
 use std::convert::{TryFrom, TryInto, Into};
-use std::num::TryFromIntError;
 use std::f64::consts::PI as FPI;
 use std::fmt::Display;
+use std::num::TryFromIntError;
 use std::ops::{Add,Sub,Neg,Mul,Div};
 
 use fractional::continuous::Continuous;
@@ -30,6 +31,42 @@ use fractional::trigonometry::Trig;
 use fractional::vector::{Vector};
 use fractional::transform::{translate, rotate_x, rotate_y, rotate_z, rotate_v};
 
+// Tail recursive Bresenham line with integer incremental error.
+fn line(a :(u32, u32), b :(u32, u32)) -> Vec<(u32, u32)>{
+    fn inner( v :&mut [(u32, u32)]
+            , bx :u32, by :u32
+            , dx :i32, dy :i32
+            , sx :i32, sy :i32
+            , err :i32) {
+        let (x, y) = v[0];
+
+        if x != bx || y != by {
+            let (x, y, err) = match (2*err as i32 >= dy, 2*err as i32 <= dx) {
+                (true, false) => ((x as i32 + sx) as u32, y, err + dy),
+                (false, true) => (x, (y as i32 + sy) as u32, err + dx),
+                _             => ( (x as i32 + sx) as u32
+                                 , (y as i32 + sy) as u32
+                                 , err + dx + dy ),
+            };
+            v[1] = (x, y);
+            inner(&mut v[1..], bx, by, dx, dy, sx, sy, err);
+        }
+    }
+
+    let (ax, ay) = a;
+    let (bx, by) = b;
+
+    let dx      = (bx as i32 - ax as i32).abs();
+    let sx :i32 = if ax < bx { 1 } else { -1 };
+    let dy      = -(by as i32 - ay as i32).abs();
+    let sy :i32 = if ay < by { 1 } else { -1 };
+
+    let mut v :Vec<(u32, u32)> = vec!((0, 0); cmp::max(dx, -dy) as usize + 1);
+    v[0] = (ax, ay);
+    inner(&mut v, bx, by, dx, dy, sx, sy, dx + dy);
+    v
+}
+
 fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> {
     let r = v.iter().fold(0, |acc, x| acc + x);
     let l = i64::try_from(v.len())?;
@@ -235,6 +272,17 @@ fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :Vector<T>)
     }
 }
 
+fn _line() {
+    println!("{:>14} : {:?}", "Line", line((0,1), (6,4)));
+    println!("{:>14} : {:?}", "Line", line((0,4), (6,1)));
+    println!("{:>14} : {:?}", "Line", line((6,1), (0,4)));
+    println!("{:>14} : {:?}", "Line", line((6,4), (0,1)));
+    println!("{:>14} : {:?}", "Line", line((0,1), (6,8)));
+    println!("{:>14} : {:?}", "Line", line((0,8), (6,1)));
+    println!("{:>14} : {:?}", "Line", line((6,1), (0,8)));
+    println!("{:>14} : {:?}", "Line", line((6,8), (0,1)));
+}
+
 fn main() {
     common_fractional();
     println!();
@@ -257,4 +305,6 @@ fn main() {
     _transform1();
     println!();
     _transform2();
+    println!();
+    _line();
 }