Add basic geometric transformations

@@ -23,5 +23,8 @@ extern crate lazy_static;
 pub mod fractional;
 pub mod trigonometry;
 pub mod vector;
+pub mod transform;
 
 use fractional::{Fractional};
+use trigonometry::{sin, cos};
+use vector::{Vector};

@@ -25,6 +25,7 @@ use std::f64::consts::PI as FPI;
 use fractional::fractional::{Fractional, from_vector, Continuous};
 use fractional::trigonometry::{sin, cos, tan, PI};
 use fractional::vector::{Vector};
+use fractional::transform::{translate, rotate_x, rotate_y, rotate_z, rotate_v};
 
 fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> {
     let r = v.iter().fold(0, |acc, x| acc + x);
@@ -148,6 +149,55 @@ fn _vector() {
     println!("{:>14} : {}", "v2 * v1", v2 * v1);
 }
 
+fn _transform() {
+    let v   = Vector(1.into(), 1.into(), 1.into());
+    let v1  = Vector(1.into(), 2.into(), 3.into());
+    let mt  = translate(v);
+
+    println!("{:>14} : {}", "Vector v1", v1);
+    println!("{:>14} : {}", "translate v1", mt.apply(&v1));
+    println!();
+
+    let v2  = Vector(1.into(), 1.into(), 0.into());
+    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));
+    }
+    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));
+    }
+    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));
+    }
+    println!();
+
+    let v3  = Vector(1.into(), 0.into(), 1.into());
+    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));
+    }
+    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));
+    }
+}
+
 fn main() {
     common_fractional();
     println!();
@@ -164,4 +214,6 @@ fn main() {
     _tan();
     println!();
     _vector();
+    println!();
+    _transform();
 }

+//
+// Transformation of vectors in a given coordinate system...
+//
+// Georg Hopp <georg@steffers.org>
+//
+// Copyright © 2019 Georg Hopp
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// 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::ops::{Mul};
+use crate::{Fractional, cos, sin, Vector};
+
+pub struct TMatrix( (Fractional, Fractional, Fractional, Fractional)
+                  , (Fractional, Fractional, Fractional, Fractional)
+                  , (Fractional, Fractional, Fractional, Fractional)
+                  , (Fractional, Fractional, Fractional, Fractional) );
+
+pub fn translate(v :Vector) -> TMatrix {
+    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()) )
+}
+
+pub fn rotate_x(a :i32) -> TMatrix {
+    TMatrix( (1.into(), 0.into(), 0.into(), 0.into())
+           , (0.into(),   cos(a),  -sin(a), 0.into())
+           , (0.into(),   sin(a),   cos(a), 0.into())
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
+
+pub fn rotate_y(a :i32) -> TMatrix {
+    TMatrix( (  cos(a), 0.into(),   sin(a), 0.into())
+           , (0.into(), 1.into(), 0.into(), 0.into())
+           , ( -sin(a), 0.into(),   cos(a), 0.into())
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
+
+pub fn rotate_z(a :i32) -> TMatrix {
+    TMatrix( (  cos(a),  -sin(a), 0.into(), 0.into())
+           , (  sin(a),   cos(a), 0.into(), 0.into())
+           , (0.into(), 0.into(), 1.into(), 0.into())
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
+
+pub fn rotate_v(v :&Vector, a :i32) -> TMatrix {
+    let Vector(x, y, z) = *v;
+
+    let zero :Fractional = 0.into();
+    let one  :Fractional = 1.into();
+
+    TMatrix( ( (one - cos(a)) * x * x + cos(a)
+             , (one - cos(a)) * x * y - sin(a) * z
+             , (one - cos(a)) * x * z + sin(a) * y
+             , zero )
+           , ( (one - cos(a)) * x * y + sin(a) * z
+             , (one - cos(a)) * y * y + cos(a)
+             , (one - cos(a)) * y * z - sin(a) * x
+             , zero )
+           , ( (one - cos(a)) * x * z - sin(a) * y
+             , (one - cos(a)) * y * z + sin(a) * x
+             , (one - cos(a)) * z * z + cos(a)
+             , zero )
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
+
+pub fn scale(v :Vector) -> TMatrix {
+    let Vector(x, y, z) = v;
+
+    TMatrix( (       x, 0.into(), 0.into(), 0.into())
+           , (0.into(),        y, 0.into(), 0.into())
+           , (0.into(), 0.into(),        z, 0.into())
+           , (0.into(), 0.into(), 0.into(), 1.into()) )
+}
+
+impl TMatrix {
+    pub fn apply(&self, v :&Vector) -> Vector {
+        let TMatrix( (a11, a12, a13, a14)
+                   , (a21, a22, a23, a24)
+                   , (a31, a32, a33, a34)
+                   , (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 Fractional(wn, wd) = a14 * x + a24 * y + a34 * z + a44;
+
+        v.mul(&Fractional(wd, wn))
+    }
+}
+
+impl Mul for TMatrix {
+    type Output = Self;
+
+    // ATTENTION: This is not commutative, nor assoziative.
+    fn mul(self, other :Self) -> Self {
+        let TMatrix( (a11, a12, a13, a14)
+                   , (a21, a22, a23, a24)
+                   , (a31, a32, a33, a34)
+                   , (a41, a42, a43, a44) ) = self;
+        let TMatrix( (b11, b12, b13, b14)
+                   , (b21, b22, b23, b24)
+                   , (b31, b32, b33, b34)
+                   , (b41, b42, b43, b44) ) = other;
+
+        TMatrix( ( a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41
+                 , a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42
+                 , a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43
+                 , a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44 )
+               , ( a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41
+                 , a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42
+                 , a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43
+                 , a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44 )
+               , ( a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41
+                 , a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42
+                 , a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43
+                 , a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44 )
+               , ( a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41
+                 , a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42
+                 , a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43
+                 , a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44 ) )
+    }
+}