Add a way to merge an iterator of transformation matrices

@@ -29,7 +29,7 @@ use fractional::continuous::Continuous;
 use fractional::fractional::{Fractional, from_vector};
 use fractional::trigonometry::Trig;
 use fractional::vector::{Vector};
-use fractional::transform::{translate, rotate_x, rotate_y, rotate_z, rotate_v};
+use fractional::transform::{TMatrix, 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)>{
@@ -228,47 +228,42 @@ fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :Vector<T>)
     where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
            + Mul<Output = T> + Div<Output = T> + Trig
            + From<i32> + Copy + Display {
-    let mt = translate(v);
 
     println!("{:>14} : {}", "Vector v1", v1);
-    println!("{:>14} : {}", "translate v1", mt.apply(&v1));
+    println!("{:>14} : {}", "translate v1", translate(v).apply(&v1));
     println!();
 
-    println!("{:>14} : {}", "Vector v2", v2);
-    for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-             , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        let m = rotate_x(*d as i32);
-        println!("{:>14} : {}", format!("rot_x {} v2", d), m.apply(&v2));
+    fn _rot<T>( o :&str , n :&str , v :&Vector<T>
+              , fs :&[&dyn Fn(i32) -> TMatrix<T>] )
+        where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+               + Mul<Output = T> + Div<Output = T> + Trig
+               + From<i32> + Copy + Display {
+
+        for d in [ 30, 45, 60, 90, 120, 135, 150, 180
+                 , 210, 225, 240, 270, 300, 315, 330 ].iter() {
+            let mi = fs.iter().map(|f| f(*d as i32));
+            println!( "{:>14} : {}"
+                    , format!("{} {} {}", o, d, n)
+                    , TMatrix::combine(mi).apply(v) );
+        }
     }
-    println!();
 
     println!("{:>14} : {}", "Vector v2", v2);
-    for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-             , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        let m = rotate_y(*d as i32);
-        println!("{:>14} : {}", format!("rot_y {} v2", d), m.apply(&v2));
-    }
+    _rot("rot_x", "v2", &v2, &[&rotate_x]);
     println!();
-
-    for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-             , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        let m = rotate_x(*d as i32) * rotate_y(*d as i32);
-        println!("{:>14} : {}", format!("rot_xy {} v2", d), m.apply(&v2));
-    }
+    _rot("rot_y", "v2", &v2, &[&rotate_y]);
+    println!();
+    _rot("rot_xy", "v2", &v2, &[&rotate_x, &rotate_y]);
     println!();
-
     println!("{:>14} : {}", "Vector v3", v3);
-    for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-             , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        let m = rotate_z(*d as i32);
-        println!("{:>14} : {}", format!("rot_z {} v3", d), m.apply(&v3));
-    }
+    _rot("rot_z", "v3", &v3, &[&rotate_z]);
     println!();
 
     for d in [ 30, 45, 60, 90, 120, 135, 150, 180
              , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        let m = rotate_v(&v, *d as i32);
-        println!("{:>14} : {}", format!("rot_v {} v2", d), m.apply(&v2));
+        println!( "{:>14} : {}"
+                , format!("rot_v {} v2", d)
+                , rotate_v(&v, *d as i32).apply(&v2));
     }
 }
 

@@ -19,15 +19,25 @@
 // along with this program.  If not, see <http://www.gnu.org/licenses/>.
 //
 use std::ops::{Add, Sub, Neg, Mul, Div};
+
 use crate::Vector;
 use crate::trigonometry::Trig;
 
+#[derive(Debug, Clone, Copy)]
 pub struct TMatrix<T>( (T, T, T, T)
                      , (T, T, T, T)
                      , (T, T, T, T)
                      , (T, T, T, T) )
     where T: Add + Sub + Neg + Mul + Div + Trig + From<i32> + Copy;
 
+pub fn unit<T>() -> TMatrix<T>
+where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+    TMatrix( (1.into(), 0.into(), 0.into(), 0.into())
+           , (0.into(), 1.into(), 0.into(), 0.into())
+           , (0.into(), 0.into(), 1.into(), 0.into())
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
 pub fn translate<T>(v :Vector<T>) -> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
        + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
@@ -115,6 +125,12 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 impl<T> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
        + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+    pub fn combine<I>(mi :I) -> TMatrix<T>
+        where I: IntoIterator<Item = TMatrix<T>> {
+
+        mi.into_iter().fold(unit(), |acc, x| acc * x)
+    }
+
     pub fn apply(&self, v :&Vector<T>) -> Vector<T> {
         let TMatrix( (a11, a12, a13, a14)
                    , (a21, a22, a23, a24)