# math.rs - source
Source of the Rust file `maplibre/src/util/math.rs`.

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    use std::{cmp::Ordering, fmt};

    use cgmath::{
        ulps_eq, BaseFloat, BaseNum, EuclideanSpace, InnerSpace, Point2, Point3, Vector3, Zero,
    };

    /// A 3-dimensional plane formed from the equation: `A*x + B*y + C*z - D = 0`.
    ///
    /// # Fields
    ///
    /// - `n`: a unit vector representing the normal of the plane where:
    ///   - `n.x`: corresponds to `A` in the plane equation
    ///   - `n.y`: corresponds to `B` in the plane equation
    ///   - `n.z`: corresponds to `C` in the plane equation
    /// - `d`: the distance value, corresponding to `D` in the plane equation
    ///
    /// # Notes
    ///
    /// The `A*x + B*y + C*z - D = 0` form is preferred over the other common
    /// alternative, `A*x + B*y + C*z + D = 0`, because it tends to avoid
    /// superfluous negations (see _Real Time Collision Detection_, p. 55).
    ///
    /// Copied from: https://github.com/rustgd/collision-rs
    pub struct Plane<S> {
        /// Plane normal
        pub n: Vector3<S>,
        /// Plane distance value
        pub d: S,
    }

    impl<S: BaseFloat> Plane<S> {
        /// Construct a plane from a normal vector and a scalar distance. The
        /// plane will be perpendicular to `n`, and `d` units offset from the
        /// origin.
        pub fn new(n: Vector3<S>, d: S) -> Plane<S> {
            Plane { n, d }
        }

        /// Constructs a plane that passes through the the three points `a`, `b` and `c`
        pub fn from_points(a: Point3<S>, b: Point3<S>, c: Point3<S>) -> Option<Plane<S>> {
            // create two vectors that run parallel to the plane
            let v0 = b - a;
            let v1 = c - a;

            // find the normal vector that is perpendicular to v1 and v2
            let n = v0.cross(v1);
            if ulps_eq!(n, &Vector3::zero()) {
                None
            } else {
                // compute the normal and the distance to the plane
                let n = n.normalize();
                let d = -a.dot(n);

                Some(Plane::new(n, d))
            }
        }

        /// Construct a plane from a point and a normal vector.
        /// The plane will contain the point `p` and be perpendicular to `n`.
        pub fn from_point_normal(p: Point3<S>, n: Vector3<S>) -> Plane<S> {
            Plane { n, d: p.dot(n) }
        }

        fn intersection_distance_ray(
            &self,
            ray_origin: &Vector3<S>,
            ray_direction: &Vector3<S>,
        ) -> Option<S> {
            let vd: S =
                self.n.x * ray_direction.x + self.n.y * ray_direction.y + self.n.z * ray_direction.z;
            if vd == S::zero() {
                return None;
            }
            let t: S =
                -(self.n.x * ray_origin.x + self.n.y * ray_origin.y + self.n.z * ray_origin.z + self.d)
                    / vd;

            Some(t)
        }

        /// Returns unsorted intersection points with an Aabb3
        /// Adopted from: https://www.asawicki.info/news_1428_finding_polygon_of_plane-aabb_intersection
        /// Inspired by: https://godotengine.org/qa/54688/camera-frustum-intersection-with-plane
        pub fn intersection_points_aabb3(&self, aabb: &Aabb3<S>) -> Vec<Vector3<S>> {
            let mut out_points: Vec<Vector3<S>> = Vec::new();
            let aabb_min: Vector3<S> = aabb.min.to_vec();
            let aabb_max: Vector3<S> = aabb.max.to_vec();

            // Test edges along X axis, pointing right.
            let mut dir: Vector3<S> = Vector3::new(aabb_max.x - aabb_min.x, S::zero(), S::zero());
            let mut orig = aabb_min;
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_min.x, aabb_max.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_min.x, aabb_min.y, aabb_max.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_min.x, aabb_max.y, aabb_max.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            // Test edges along Y axis, pointing up.
            dir = Vector3::new(S::zero(), aabb_max.y - aabb_min.y, S::zero());
            orig = Vector3::new(aabb_min.x, aabb_min.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_max.x, aabb_min.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_min.x, aabb_min.y, aabb_max.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_max.x, aabb_min.y, aabb_max.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            // Test edges along Z axis, pointing forward.
            dir = Vector3::new(S::zero(), S::zero(), aabb_max.z - aabb_min.z);
            orig = Vector3::new(aabb_min.x, aabb_min.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_max.x, aabb_min.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_min.x, aabb_max.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            orig = Vector3::new(aabb_max.x, aabb_max.y, aabb_min.z);
            if let Some(t) = self.intersection_distance_ray(&orig, &dir) {
                if t >= S::zero() && t <= S::one() {
                    out_points.push(orig + dir * t);
                }
            }

            out_points
        }

        pub fn intersection_polygon_aabb3(&self, aabb: &Aabb3<S>) -> Vec<Vector3<S>> {
            let mut points = self.intersection_points_aabb3(aabb);

            if points.is_empty() {
                return points;
            };

            let plane_normal = Vector3::new(self.n.x, self.n.y, self.n.z);
            let origin = points[0];

            points.sort_by(|a, b| {
                let cmp = (a - origin).cross(b - origin).dot(plane_normal);
                if cmp < S::zero() {
                    Ordering::Less
                } else if cmp == S::zero() {
                    Ordering::Equal
                } else {
                    Ordering::Greater
                }
            });

            points
        }
    }

    impl<S: BaseFloat> fmt::Debug for Plane<S> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            write!(
                f,
                "{:?}x + {:?}y + {:?}z - {:?} = 0",
                self.n.x, self.n.y, self.n.z, self.d
            )
        }
    }

    pub(crate) fn min<S: PartialOrd + Copy>(lhs: S, rhs: S) -> S {
        match lhs.partial_cmp(&rhs) {
            Some(Ordering::Less) | Some(Ordering::Equal) | None => lhs,
            _ => rhs,
        }
    }

    pub(crate) fn max<S: PartialOrd + Copy>(lhs: S, rhs: S) -> S {
        match lhs.partial_cmp(&rhs) {
            Some(Ordering::Greater) | Some(Ordering::Equal) | None => lhs,
            _ => rhs,
        }
    }

    /// A two-dimensional AABB, aka a rectangle.
    pub struct Aabb2<S> {
        /// Minimum point of the AABB
        pub min: Point2<S>,
        /// Maximum point of the AABB
        pub max: Point2<S>,
    }

    impl<S: BaseNum> Aabb2<S> {
        /// Construct a new axis-aligned bounding box from two points.
        #[inline]
        pub fn new(p1: Point2<S>, p2: Point2<S>) -> Aabb2<S> {
            Aabb2 {
                min: Point2::new(min(p1.x, p2.x), min(p1.y, p2.y)),
                max: Point2::new(max(p1.x, p2.x), max(p1.y, p2.y)),
            }
        }

        /// Compute corners.
        #[inline]
        pub fn to_corners(&self) -> [Point2<S>; 4] {
            [
                self.min,
                Point2::new(self.max.x, self.min.y),
                Point2::new(self.min.x, self.max.y),
                self.max,
            ]
        }
    }

    impl<S: BaseNum> fmt::Debug for Aabb2<S> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            write!(f, "[{:?} - {:?}]", self.min, self.max)
        }
    }

    /// A three-dimensional AABB, aka a rectangular prism.
    pub struct Aabb3<S> {
        /// Minimum point of the AABB
        pub min: Point3<S>,
        /// Maximum point of the AABB
        pub max: Point3<S>,
    }

    impl<S: BaseNum> Aabb3<S> {
        /// Construct a new axis-aligned bounding box from two points.
        #[inline]
        pub fn new(p1: Point3<S>, p2: Point3<S>) -> Aabb3<S> {
            Aabb3 {
                min: Point3::new(min(p1.x, p2.x), min(p1.y, p2.y), min(p1.z, p2.z)),
                max: Point3::new(max(p1.x, p2.x), max(p1.y, p2.y), max(p1.z, p2.z)),
            }
        }

        /// Compute corners.
        #[inline]
        pub fn to_corners(&self) -> [Point3<S>; 8] {
            [
                self.min,
                Point3::new(self.max.x, self.min.y, self.min.z),
                Point3::new(self.min.x, self.max.y, self.min.z),
                Point3::new(self.max.x, self.max.y, self.min.z),
                Point3::new(self.min.x, self.min.y, self.max.z),
                Point3::new(self.max.x, self.min.y, self.max.z),
                Point3::new(self.min.x, self.max.y, self.max.z),
                self.max,
            ]
        }
    }

    impl<S: BaseNum> fmt::Debug for Aabb3<S> {
        fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
            write!(f, "[{:?} - {:?}]", self.min, self.max)
        }
    }

    pub fn bounds_from_points<P, T>(points: impl Iterator<Item = P>) -> Option<([T; 2], [T; 2])>
    where
        P: Into<[T; 2]>,
        T: PartialOrd + Copy,
    {
        let mut min: Option<[T; 2]> = None;
        let mut max: Option<[T; 2]> = None;

        for point in points {
            let [x, y] = point.into();

            if let Some([min_x, min_y]) = &mut min {
                if x < *min_x {
                    *min_x = x;
                }
                if y < *min_y {
                    *min_y = y;
                }
            } else {
                min = Some([x, y])
            }

            if let Some([max_x, max_y]) = &mut max {
                if x > *max_x {
                    *max_x = x;
                }
                if y > *max_y {
                    *max_y = y;
                }
            } else {
                max = Some([x, y])
            }
        }

        if let (Some(min), Some(max)) = (min, max) {
            Some((min, max))
        } else {
            None
        }
    }

    /// A wrapper type that enables ordering floats. This is a work around for the famous "rust float
    /// ordering" problem. By using it, you acknowledge that sorting NaN is undefined according to spec.
    /// This implementation treats NaN as the "smallest" float.
    #[derive(Debug, Copy, Clone, PartialOrd)]
    pub struct FloatOrd(pub f32);

    impl PartialEq for FloatOrd {
        fn eq(&self, other: &Self) -> bool {
            if self.0.is_nan() && other.0.is_nan() {
                true
            } else {
                self.0 == other.0
            }
        }
    }

    impl Eq for FloatOrd {}

    #[allow(clippy::derive_ord_xor_partial_ord)]
    impl Ord for FloatOrd {
        fn cmp(&self, other: &Self) -> Ordering {
            self.0.partial_cmp(&other.0).unwrap_or_else(|| {
                if self.0.is_nan() && !other.0.is_nan() {
                    Ordering::Less
                } else if !self.0.is_nan() && other.0.is_nan() {
                    Ordering::Greater
                } else {
                    Ordering::Equal
                }
            })
        }
    }

    pub const fn div_away(lhs: i32, rhs: i32) -> i32 {
        if rhs < 0 {
            panic!("rhs must be positive")
        }

        if lhs < 0 {
            div_floor(lhs, rhs)
        } else {
            div_ceil(lhs, rhs)
        }
    }

    pub const fn div_ceil(lhs: i32, rhs: i32) -> i32 {
        let d = lhs / rhs;
        let r = lhs % rhs;
        if (r > 0 && rhs > 0) || (r < 0 && rhs < 0) {
            d + 1
        } else {
            d
        }
    }

    pub const fn div_floor(lhs: i32, rhs: i32) -> i32 {
        let d = lhs / rhs;
        let r = lhs % rhs;
        if (r > 0 && rhs < 0) || (r < 0 && rhs > 0) {
            d - 1
        } else {
            d
        }
    }

    #[cfg(test)]
    mod tests {
        use crate::{coords::EXTENT_SINT, util::math::div_ceil};

        #[test]
        pub fn test_div_floor() {
            assert_eq!(div_ceil(7000, EXTENT_SINT), 2);
            assert_eq!(div_ceil(-7000, EXTENT_SINT), -1);
        }
    }