Correct transformation matrix handling

@@ -19,6 +19,7 @@
 // along with this program.  If not, see <http://www.gnu.org/licenses/>.
 //
 use std::ops::{Add, Sub, Neg, Mul, Div};
+use std::fmt::Debug;
 
 use crate::Vector;
 use crate::trigonometry::Trig;
@@ -28,30 +29,34 @@ 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;
+    where T: Add + Sub + Neg + Mul + Div + Debug + 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 {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + 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 {
-    let Vector(x, y, z) = v;
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
+    let Vector(x, y, z)    = v;
 
-    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())
-           , (       x,        y,        z, 1.into()) )
+    TMatrix( (1.into(), 0.into(), 0.into(),        x)
+           , (0.into(), 1.into(), 0.into(),        y)
+           , (0.into(), 0.into(), 1.into(),        z)
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
 }
 
 pub fn rotate_x<T>(a :i32) -> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     let sin :T = Trig::sin(a);
     let cos :T = Trig::cos(a);
 
@@ -63,7 +68,8 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 
 pub fn rotate_y<T>(a :i32) -> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     let sin :T = Trig::sin(a);
     let cos :T = Trig::cos(a);
 
@@ -75,7 +81,8 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 
 pub fn rotate_z<T>(a :i32) -> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     let sin :T = Trig::sin(a);
     let cos :T = Trig::cos(a);
 
@@ -87,7 +94,8 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 
 pub fn rotate_v<T>(v :&Vector<T>, a :i32) -> TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     let Vector(x, y, z) = *v;
 
     let sin :T = Trig::sin(a);
@@ -113,7 +121,8 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 
 pub fn scale<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 {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     let Vector(x, y, z) = v;
 
     TMatrix( (       x, 0.into(), 0.into(), 0.into())
@@ -124,11 +133,19 @@ 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 {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
+    pub fn new( r1 :(T, T, T, T)
+              , r2 :(T, T, T, T)
+              , r3 :(T, T, T, T)
+              , r4 :(T, T, T, T) ) -> TMatrix<T> {
+        TMatrix(r1, r2, r3, r4)
+    }
+
     pub fn combine<I>(mi :I) -> TMatrix<T>
         where I: IntoIterator<Item = TMatrix<T>> {
 
-        mi.into_iter().fold(unit(), |acc, x| acc * x)
+        mi.into_iter().fold(unit(), |acc, x| x * acc)
     }
 
     pub fn apply(&self, v :&Vector<T>) -> Vector<T> {
@@ -138,10 +155,10 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
                    , (a41, a42, a43, a44) ) = *self;
         let Vector(x, y, z) = *v;
 
-        let v = Vector( a11 * x + a21 * y + a31 * z + a41
-                      , a12 * x + a22 * y + a32 * z + a42
-                      , a13 * x + a23 * y + a33 * z + a43 );
-        let w = a14 * x + a24 * y + a34 * z + a44;
+        let v = Vector( a11 * x + a12 * y + a13 * z + a14
+                      , a21 * x + a22 * y + a23 * z + a24
+                      , a31 * x + a32 * y + a33 * z + a34 );
+        let w = a41 * x + a42 * y + a43 * z + a44;
 
         v.mul(&w.recip())
     }
@@ -149,7 +166,8 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 
 impl<T> Mul for TMatrix<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + From<i32> + Copy {
+       + Mul<Output = T> + Div<Output = T>
+       + Debug + Trig + From<i32> + Copy {
     type Output = Self;
 
     // ATTENTION: This is not commutative, nor assoziative.