codenano 0.5.1

A library for editing DNA molecular designs
Documentation 
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extern crate num_traits;
extern crate serde;
use num_traits::Float;

/// Represents 3D coordinates of the point of a finite element system
#[derive(Debug, Clone, Copy, Serialize, Deserialize)]
#[repr(C)]
pub struct Point<F: Float> {
    /// x coordinate
    pub x: F,
    /// y coordinate
    pub y: F,
    /// z coordinate
    pub z: F,
}

impl<F: Float> Point<F> {
    /// Convert an array of 3 floats into a Point
    pub fn from_coord(coord: [F; 3]) -> Self {
        Point {
            x: coord[0],
            y: coord[1],
            z: coord[2],
        }
    }
}

/// Represents the difference between two `Point`s
#[derive(Debug, Clone, Copy, Serialize, Deserialize)]
#[repr(C)]
pub struct Vector<F: Float> {
    /// x coordinate
    pub x: F,
    /// y coordinate
    pub y: F,
    /// z coordinate
    pub z: F,
}

impl<F: Float> std::ops::Index<usize> for Vector<F> {
    type Output = F;
    fn index(&self, i: usize) -> &F {
        unsafe { &*(self as *const Vector<F> as *const [F; 3]) }.index(i)
    }
}

impl<F: Float> std::ops::IndexMut<usize> for Vector<F> {
    fn index_mut(&mut self, i: usize) -> &mut F {
        unsafe { &mut *(self as *mut Vector<F> as *mut [F; 3]) }.index_mut(i)
    }
}

impl<F: Float> Vector<F> {
    /// Return a Vector with null coordinates
    pub fn zero() -> Self {
        Vector {
            x: F::zero(),
            y: F::zero(),
            z: F::zero(),
        }
    }
    /// Convert an array of 3 floats into a Vector
    pub fn from_coord(coord: [F; 3]) -> Self {
        Vector {
            x: coord[0],
            y: coord[1],
            z: coord[2],
        }
    }
    /// Returns the Euclidian norm of `self`.
    pub fn norm(&self) -> F {
        self.norm2().sqrt()
    }

    /// Returns the square of the Euclidian norm of `self`.
    pub fn norm2(&self) -> F {
        self.x * self.x + self.y * self.y + self.z * self.z
    }

    /// Return the cross product of `self` and `other`
    pub fn cross_product(&self, other: &Vector<F>) -> Self {
        Vector {
            x: self.y * other.z - self.z * other.y,
            y: self.z * other.x - self.x * other.z,
            z: self.x * other.y - self.y * other.x,
        }
    }

    /// Return the dot product of `self` and `other`
    pub fn dot(&self, other: &Vector<F>) -> F {
        self.x * other.x + self.y * other.y + self.z * other.z
    }
}

impl<F: Float> std::ops::Sub<Point<F>> for Point<F> {
    type Output = Vector<F>;
    fn sub(self, b: Point<F>) -> Self::Output {
        Vector {
            x: self.x - b.x,
            y: self.y - b.y,
            z: self.z - b.z,
        }
    }
}

impl<F: Float> std::ops::Add<Vector<F>> for Point<F> {
    type Output = Point<F>;
    fn add(self, b: Vector<F>) -> Self::Output {
        Point {
            x: self.x + b.x,
            y: self.y + b.y,
            z: self.z + b.z,
        }
    }
}
impl<F: Float> std::ops::AddAssign<Vector<F>> for Point<F> {
    fn add_assign(&mut self, b: Vector<F>) {
        self.x = b.x + self.x;
        self.y = b.y + self.y;
        self.z = b.z + self.z;
    }
}

impl<F: Float> std::ops::Sub<Vector<F>> for Vector<F> {
    type Output = Vector<F>;
    fn sub(self, b: Vector<F>) -> Self::Output {
        Vector {
            x: self.x - b.x,
            y: self.y - b.y,
            z: self.z - b.z,
        }
    }
}

impl<F: Float> std::ops::Neg for Vector<F> {
    type Output = Vector<F>;
    fn neg(self) -> Self::Output {
        Vector {
            x: -self.x,
            y: -self.y,
            z: -self.z,
        }
    }
}

impl<F: Float> std::ops::Add<Vector<F>> for Vector<F> {
    type Output = Vector<F>;
    fn add(self, b: Vector<F>) -> Self::Output {
        Vector {
            x: self.x + b.x,
            y: self.y + b.y,
            z: self.z + b.z,
        }
    }
}

impl<F: Float> std::ops::SubAssign<Vector<F>> for Vector<F> {
    fn sub_assign(&mut self, b: Vector<F>) {
        self.x = b.x - self.x;
        self.y = b.y - self.y;
        self.z = b.z - self.z;
    }
}

impl<F: Float> std::ops::AddAssign<Vector<F>> for Vector<F> {
    fn add_assign(&mut self, b: Vector<F>) {
        self.x = b.x + self.x;
        self.y = b.y + self.y;
        self.z = b.z + self.z;
    }
}

impl<F: Float> std::ops::Mul<Vector<F>> for f32 {
    type Output = Vector<F>;
    fn mul(self, b: Vector<F>) -> Self::Output {
        Vector {
            x: b.x * F::from(self).unwrap(),
            y: b.y * F::from(self).unwrap(),
            z: b.z * F::from(self).unwrap(),
        }
    }
}

impl<F: Float> std::ops::Mul<Vector<F>> for f64 {
    type Output = Vector<F>;
    fn mul(self, b: Vector<F>) -> Self::Output {
        Vector {
            x: b.x * F::from(self).unwrap(),
            y: b.y * F::from(self).unwrap(),
            z: b.z * F::from(self).unwrap(),
        }
    }
}

impl<F: Float> std::ops::Mul<F> for Vector<F> {
    type Output = Vector<F>;
    fn mul(self, b: F) -> Self::Output {
        Vector {
            x: self.x * b,
            y: self.y * b,
            z: self.z * b,
        }
    }
}

impl<F: Float> std::ops::Div<F> for Vector<F> {
    type Output = Vector<F>;
    fn div(self, b: F) -> Self::Output {
        Vector {
            x: self.x / b,
            y: self.y / b,
            z: self.z / b,
        }
    }
}

/// Return the distance between the segmens [a, b] and [c, d]
pub fn distance_segment<F: Float>(
    a: Point<F>,
    b: Point<F>,
    c: Point<F>,
    d: Point<F>,
) -> (F, Vector<F>) {
    let u = b - a;
    let v = d - c;
    let n = u.cross_product(&v);

    if n.norm() < F::from(1e-5).unwrap() {
        // the segment are almost parallel
        return ((a - c).norm(), (a - c));
    }

    // lambda u.norm2() - mu u.dot(v) + ((a - c).dot(u)) = 0
    // mu v.norm2() - lambda u.dot(v) + ((c - a).dot(v)) = 0
    let normalise = u.dot(&v) / u.norm2();

    // mu (v.norm2() - normalise * u.dot(v)) = (-(c - a).dot(v)) - normalise * ((a - c).dot(u))
    let mut mu =
        (-((c - a).dot(&v)) - normalise * ((a - c).dot(&u))) / (v.norm2() - normalise * u.dot(&v));

    let mut lambda = (-((a - c).dot(&u)) + mu * u.dot(&v)) / (u.norm2());

    if F::zero() <= mu && mu <= F::one() && F::zero() <= lambda && lambda <= F::one() {
        let vec = (a + u * lambda) - (c + v * mu);
        (vec.norm(), vec)
    } else {
        let mut min_dist = F::infinity();
        let mut min_vec = Vector::zero();
        lambda = F::zero();
        mu = -((c - a).dot(&v)) / v.norm2();
        if F::zero() <= mu && mu <= F::one() {
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        } else {
            mu = F::zero();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
            mu = F::one();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        }
        lambda = F::one();
        mu = (-(c - a).dot(&v) + u.dot(&v)) / v.norm2();
        if F::zero() <= mu && mu <= F::one() {
            min_dist = min_dist.min(((a + u * lambda) - (c + v * mu)).norm());
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        } else {
            mu = F::zero();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
            mu = F::one();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        }
        mu = F::zero();
        lambda = (-((a - c).dot(&u)) + mu * u.dot(&v)) / (u.norm2());
        if F::zero() <= lambda && F::one() >= lambda {
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        } else {
            lambda = F::zero();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
            lambda = F::one();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        }
        mu = F::one();
        lambda = (-((a - c).dot(&u)) + mu * u.dot(&v)) / (u.norm2());
        if F::zero() <= lambda && F::one() >= lambda {
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        } else {
            lambda = F::zero();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
            lambda = F::one();
            let vec = (a + u * lambda) - (c + v * mu);
            if min_dist > vec.norm() {
                min_dist = vec.norm();
                min_vec = vec.clone();
            }
        }
        (min_dist, min_vec)
    }
}