Add first vector math stuff

@@ -22,5 +22,6 @@ extern crate lazy_static;
 
 pub mod fractional;
 pub mod trigonometry;
+pub mod vector;
 
 use fractional::{Fractional};

@@ -23,13 +23,8 @@ use std::num::TryFromIntError;
 use std::f64::consts::PI as FPI;
 
 use fractional::fractional::{Fractional, from_vector, Continuous};
-use fractional::trigonometry::{sin, cos, PI};
-
-struct Vector {
-    x: Fractional,
-    y: Fractional,
-    z: Fractional,
-}
+use fractional::trigonometry::{sin, cos, tan, PI};
+use fractional::vector::{Vector};
 
 fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> {
     let r = v.iter().fold(0, |acc, x| acc + x);
@@ -98,7 +93,8 @@ fn pi() {
 }
 
 fn _sin() {
-    for d in [9, 17, 31, 45, 73, 123, 213, 312, 876].iter() {
+    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
         let s       = sin(*d as i32);
         let sr :f64 = s.try_into().unwrap();
         let _s      = f64::sin(*d as f64 * FPI / 180.0);
@@ -107,8 +103,20 @@ fn _sin() {
     }
 }
 
+fn _tan() {
+    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
+        let s       = tan(*d as i32);
+        let sr :f64 = s.try_into().unwrap();
+        let _s      = f64::tan(*d as f64 * FPI / 180.0);
+
+        println!("{:>14} : {} {} / {}", format!("tan {}", d), s, sr, _s);
+    }
+}
+
 fn _cos() {
-    for d in [9, 17, 31, 45, 73, 123, 213, 312, 876].iter() {
+    for d in [ 0, 45, 90, 135, 180, 225, 270, 315
+             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
         let s       = cos(*d as i32);
         let sr :f64 = s.try_into().unwrap();
         let _s      = f64::cos(*d as f64 * FPI / 180.0);
@@ -117,6 +125,29 @@ fn _cos() {
     }
 }
 
+fn _vector() {
+    let v1 = Vector(1.into(), 2.into(), 3.into());
+    let v2 = Vector(2.into(), 2.into(), 3.into());
+    let s :Fractional = 3.into();
+
+    println!("{:>14} : {:?}", "Vector v1", v1);
+    println!("{:>14} : {:?}", "Vector v2", v2);
+    println!("{:>14} : {}"  , "abs v1", v1.abs());
+    println!("{:>14} : {:?}", "-v1", -v1);
+    println!("{:>14} : {:?}", "v1 + v1", v1 + v1);
+    println!("{:>14} : {:?}", "v1 - v1", v1 - v1);
+    println!("{:>14} : {:?}", "v2 - v1", v2 - v1);
+    println!("{:>14} : {:?}", format!("v1 * {}", s), v1.mul(&s));
+    println!("{:>14} : {:?}", "norm v1", v1.norm());
+    println!("{:>14} : {}"  , "abs norm v1", v1.norm().abs());
+    println!("{:>14} : {}"  , "distance v1 v2", v1.distance(v2));
+    println!("{:>14} : {}"  , "distance v2 v1", v2.distance(v1));
+    println!("{:>14} : {}"  , "v1 dot v2", v1.dot(v2));
+    println!("{:>14} : {}"  , "v2 dot v1", v2.dot(v1));
+    println!("{:>14} : {:?}", "v1 * v2", v1 * v2);
+    println!("{:>14} : {:?}", "v2 * v1", v2 * v1);
+}
+
 fn main() {
     common_fractional();
     println!();
@@ -129,4 +160,8 @@ fn main() {
     _sin();
     println!();
     _cos();
+    println!();
+    _tan();
+    println!();
+    _vector();
 }

+//
+// Stuff for manipulating 3 dimensional vectors.
+//
+// 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::{Add, Sub, Neg, Mul};
+use crate::{Fractional};
+
+#[derive(Debug, Eq, Clone, Copy)]
+pub struct Vector(pub Fractional, pub Fractional, pub Fractional);
+
+impl Vector {
+    pub fn x(self) -> Fractional { self.0 }
+    pub fn y(self) -> Fractional { self.1 }
+    pub fn z(self) -> Fractional { self.2 }
+
+    pub fn abs(self) -> Fractional {
+        let Vector(x, y, z) = self;
+        (x * x + y * y + z * z).sqrt().unwrap()
+    }
+
+    pub fn mul(self, s :&Fractional) -> Self {
+        let Vector(x, y, z) = self;
+        Vector(x * *s, y * *s, z * *s)
+    }
+
+    pub fn dot(self, other :Self) -> Fractional {
+        let Vector(x1, y1, z1) = self;
+        let Vector(x2, y2, z2) = other;
+
+        x1 * x2 + y1 * y2 + z1 * z2
+    }
+
+    pub fn norm(self) -> Self {
+        let Fractional(n, d) = self.abs();
+        // TODO This can result in 0 or inf Vectors…
+        //      Maybe we need to handle zero and inf abs here…
+        self.mul(&Fractional(d, n))
+    }
+
+    pub fn distance(self, other :Self) -> Fractional {
+        (self - other).abs()
+    }
+}
+
+impl PartialEq for Vector {
+    fn eq(&self, other :&Self) -> bool {
+        let Vector(x1, y1, z1) = self;
+        let Vector(x2, y2, z2) = other;
+        x1 == x2 && y1 == y2 && z1 == z2
+    }
+}
+
+impl Add for Vector {
+    type Output = Self;
+
+    fn add(self, other :Self) -> Self {
+        let Vector(x1, y1, z1) = self;
+        let Vector(x2, y2, z2) = other;
+        Vector(x1 + x2, y1 + y2, z1 + z2)
+    }
+}
+
+impl Sub for Vector {
+    type Output = Self;
+
+    fn sub(self, other :Self) -> Self {
+        self + -other
+    }
+}
+
+impl Neg for Vector {
+    type Output = Self;
+
+    fn neg(self) -> Self {
+        let Vector(x, y, z) = self;
+        Self(-x, -y, -z)
+    }
+}
+
+impl Mul for Vector {
+    type Output = Self;
+
+    fn mul(self, other :Self) -> Self {
+        let Vector(ax, ay, az) = self;
+        let Vector(bx, by, bz) = other;
+
+        Vector( ay * bz - az * by
+              , az * bx - ax * bz
+              , ax * by - ay * bx )
+    }
+}