transform.rs
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//
// 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::{Add, Sub, Neg, Mul, Div};
use std::fmt::Debug;
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 + Debug + Trig + From<i32> + Copy;
pub trait Transformable<T>
where T: Add + Sub + Neg + Mul + Div + Debug + Trig + From<i32> + Copy {
fn transform(&self, m :&TMatrix<T>) -> Self;
}
impl<T> TMatrix<T>
where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+ 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) ) -> Self {
TMatrix(r1, r2, r3, r4)
}
pub fn unit() -> Self {
Self::new( (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(v :Vector<T>) -> Self {
let Vector(x, y, z) = v;
Self::new( (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(a :i32) -> Self {
let sin :T = Trig::sin(a);
let cos :T = Trig::cos(a);
Self::new( (1.into(), 0.into(), 0.into(), 0.into())
, (0.into(), cos , -sin , 0.into())
, (0.into(), sin , cos , 0.into())
, (0.into(), 0.into(), 0.into(), 1.into()) )
}
pub fn rotate_y(a :i32) -> Self {
let sin :T = Trig::sin(a);
let cos :T = Trig::cos(a);
Self::new( (cos , 0.into(), sin , 0.into())
, (0.into(), 1.into(), 0.into(), 0.into())
, (-sin , 0.into(), cos , 0.into())
, (0.into(), 0.into(), 0.into(), 1.into()) )
}
pub fn rotate_z(a :i32) -> Self {
let sin :T = Trig::sin(a);
let cos :T = Trig::cos(a);
Self::new( (cos , -sin , 0.into(), 0.into())
, (sin , cos , 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<T>, a :i32) -> Self {
let Vector(x, y, z) = *v;
let sin :T = Trig::sin(a);
let cos :T = Trig::cos(a);
let zero :T = 0.into();
let one :T = 1.into();
Self::new( ( (one - cos) * x * x + cos
, (one - cos) * x * y - sin * z
, (one - cos) * x * z + sin * y
, zero )
, ( (one - cos) * x * y + sin * z
, (one - cos) * y * y + cos
, (one - cos) * y * z - sin * x
, zero )
, ( (one - cos) * x * z - sin * y
, (one - cos) * y * z + sin * x
, (one - cos) * z * z + cos
, zero )
, (0.into(), 0.into(), 0.into(), 1.into()) )
}
pub fn scale(v :Vector<T>) -> Self {
let Vector(x, y, z) = v;
Self::new( ( 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()) )
}
pub fn combine<I>(mi :I) -> TMatrix<T>
where I: IntoIterator<Item = TMatrix<T>> {
mi.into_iter().fold(Self::unit(), |acc, x| x * acc)
}
pub fn apply(&self, v :&Vector<T>, w :T) -> (Vector<T>, T) {
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 + a12 * y + a13 * z + a14 * w
, a21 * x + a22 * y + a23 * z + a24 * w
, a31 * x + a32 * y + a33 * z + a34 * w );
let w = a41 * x + a42 * y + a43 * z + a44 * w;
//v.mul(&w.recip())
(v, w)
}
}
impl<T> Mul for TMatrix<T>
where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+ Mul<Output = T> + Div<Output = T>
+ Debug + Trig + From<i32> + Copy {
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 ) )
}
}