Struct Vector3D

#[repr(C)]
pub struct Vector3D<T, U> {
    pub x: T,
    pub y: T,
    pub z: T,
    /* private fields */
}

A 3d Vector tagged with a unit.

Fields

x: T

The x (traditionally, horizontal) coordinate.

y: T

The y (traditionally, vertical) coordinate.

z: T

The z (traditionally, depth) coordinate.

Implementations

impl<T, U> Vector3D<T, U>

pub fn zero() -> Vector3D<T, U>

where T: Zero,

Constructor, setting all components to zero.

pub fn one() -> Vector3D<T, U>

where T: One,

Constructor, setting all components to one.

pub const fn new(x: T, y: T, z: T) -> Vector3D<T, U>

Constructor taking scalar values directly.

pub fn splat(v: T) -> Vector3D<T, U>

where T: Clone,

Constructor setting all components to the same value.

pub fn from_lengths( x: Length<T, U>, y: Length<T, U>, z: Length<T, U>, ) -> Vector3D<T, U>

Constructor taking properly Lengths instead of scalar values.

pub fn from_untyped(p: Vector3D<T, UnknownUnit>) -> Vector3D<T, U>

Tag a unitless value with units.

pub fn map<V, F>(self, f: F) -> Vector3D<V, U>

where F: FnMut(T) -> V,

Apply the function f to each component of this vector.

Example

This may be used to perform unusual arithmetic which is not already offered as methods.

use euclid::default::Vector3D;

let p = Vector3D::<u32>::new(5, 11, 15);
assert_eq!(p.map(|coord| coord.saturating_sub(10)), Vector3D::new(0, 1, 5));

pub fn zip<V, F>(self, rhs: Vector3D<T, U>, f: F) -> Vector3D<V, U>

where F: FnMut(T, T) -> V,

Apply the function f to each pair of components of this point and rhs.

Example

This may be used to perform unusual arithmetic which is not already offered as methods.

use euclid::default::Vector3D;

let a: Vector3D<u8> = Vector3D::new(50, 200, 10);
let b: Vector3D<u8> = Vector3D::new(100, 100, 0);
assert_eq!(a.zip(b, u8::saturating_add), Vector3D::new(150, 255, 10));

pub fn abs(self) -> Vector3D<T, U>

where T: Signed,

Computes the vector with absolute values of each component.

Example

enum U {}

assert_eq!(vec3::<_, U>(-1, 0, 2).abs(), vec3(1, 0, 2));

let vec = vec3::<_, U>(f32::NAN, 0.0, -f32::MAX).abs();
assert!(vec.x.is_nan());
assert_eq!(vec.y, 0.0);
assert_eq!(vec.z, f32::MAX);

Panics

The behavior for each component follows the scalar type’s implementation of num_traits::Signed::abs.

pub fn dot(self, other: Vector3D<T, U>) -> T

where T: Add<Output = T> + Mul<Output = T>,

Dot product.

impl<T, U> Vector3D<T, U>

where T: Copy,

pub fn cross(self, other: Vector3D<T, U>) -> Vector3D<T, U>

where T: Sub<Output = T> + Mul<Output = T>,

Cross product.

pub fn component_mul(self, other: Vector3D<T, U>) -> Vector3D<T, U>

where T: Mul<Output = T>,

Returns the component-wise multiplication of the two vectors.

pub fn component_div(self, other: Vector3D<T, U>) -> Vector3D<T, U>

where T: Div<Output = T>,

Returns the component-wise division of the two vectors.

pub fn to_point(self) -> Point3D<T, U>

Cast this vector into a point.

Equivalent to adding this vector to the origin.

pub fn xy(self) -> Vector2D<T, U>

Returns a 2d vector using this vector’s x and y coordinates

pub fn xz(self) -> Vector2D<T, U>

Returns a 2d vector using this vector’s x and z coordinates

pub fn yz(self) -> Vector2D<T, U>

Returns a 2d vector using this vector’s x and z coordinates

pub fn to_array(self) -> [T; 3]

Cast into an array with x, y and z.

pub fn to_array_4d(self) -> [T; 4]

where T: Zero,

Cast into an array with x, y, z and 0.

pub fn to_tuple(self) -> (T, T, T)

Cast into a tuple with x, y and z.

pub fn to_tuple_4d(self) -> (T, T, T, T)

where T: Zero,

Cast into a tuple with x, y, z and 0.

pub fn to_untyped(self) -> Vector3D<T, UnknownUnit>

Drop the units, preserving only the numeric value.

pub fn cast_unit<V>(self) -> Vector3D<T, V>

Cast the unit.

pub fn to_2d(self) -> Vector2D<T, U>

Convert into a 2d vector.

pub fn round(self) -> Vector3D<T, U>

where T: Round,

Rounds each component to the nearest integer value.

This behavior is preserved for negative values (unlike the basic cast).

enum Mm {}

assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).round(), vec3::<_, Mm>(0.0, -1.0, 0.0))

pub fn ceil(self) -> Vector3D<T, U>

where T: Ceil,

Rounds each component to the smallest integer equal or greater than the original value.

This behavior is preserved for negative values (unlike the basic cast).

enum Mm {}

assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).ceil(), vec3::<_, Mm>(0.0, 0.0, 1.0))

pub fn floor(self) -> Vector3D<T, U>

where T: Floor,

Rounds each component to the biggest integer equal or lower than the original value.

This behavior is preserved for negative values (unlike the basic cast).

enum Mm {}

assert_eq!(vec3::<_, Mm>(-0.1, -0.8, 0.4).floor(), vec3::<_, Mm>(-1.0, -1.0, 0.0))

pub fn to_transform(self) -> Transform3D<T, U, U>

where T: Zero + One,

Creates translation by this vector in vector units

impl<T, U> Vector3D<T, U>

where T: Copy + Mul<Output = T> + Add<Output = T>,

pub fn square_length(self) -> T

Returns the vector’s length squared.

pub fn project_onto_vector(self, onto: Vector3D<T, U>) -> Vector3D<T, U>

where T: Sub<Output = T> + Div<Output = T>,

Returns this vector projected onto another one.

Projecting onto a nil vector will cause a division by zero.

impl<T, U> Vector3D<T, U>

where T: Float,

pub fn robust_normalize(self) -> Vector3D<T, U>

Return the normalized vector even if the length is larger than the max value of Float.

pub fn is_finite(self) -> bool

Returns true if all members are finite.

impl<T, U> Vector3D<T, U>

where T: Real,

pub fn angle_to(self, other: Vector3D<T, U>) -> Angle<T>

where T: Trig,

Returns the positive angle between this vector and another vector.

The returned angle is between 0 and PI.

pub fn length(self) -> T

Returns the vector length.

pub fn normalize(self) -> Vector3D<T, U>

Returns the vector with length of one unit

pub fn try_normalize(self) -> Option<Vector3D<T, U>>

Returns the vector with length of one unit.

Unlike Vector2D::normalize, this returns None in the case that the length of the vector is zero.

pub fn with_max_length(self, max_length: T) -> Vector3D<T, U>

Return this vector capped to a maximum length.

pub fn with_min_length(self, min_length: T) -> Vector3D<T, U>

Return this vector with a minimum length applied.

pub fn clamp_length(self, min: T, max: T) -> Vector3D<T, U>

Return this vector with minimum and maximum lengths applied.

impl<T, U> Vector3D<T, U>

where T: One + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy,

pub fn lerp(self, other: Vector3D<T, U>, t: T) -> Vector3D<T, U>

Linearly interpolate each component between this vector and another vector.

Example

use euclid::vec3;
use euclid::default::Vector3D;

let from: Vector3D<_> = vec3(0.0, 10.0, -1.0);
let to:  Vector3D<_> = vec3(8.0, -4.0,  0.0);

assert_eq!(from.lerp(to, -1.0), vec3(-8.0,  24.0, -2.0));
assert_eq!(from.lerp(to,  0.0), vec3( 0.0,  10.0, -1.0));
assert_eq!(from.lerp(to,  0.5), vec3( 4.0,   3.0, -0.5));
assert_eq!(from.lerp(to,  1.0), vec3( 8.0,  -4.0,  0.0));
assert_eq!(from.lerp(to,  2.0), vec3(16.0, -18.0,  1.0));

pub fn reflect(self, normal: Vector3D<T, U>) -> Vector3D<T, U>

Returns a reflection vector using an incident ray and a surface normal.

impl<T, U> Vector3D<T, U>

where T: PartialOrd,

pub fn min(self, other: Vector3D<T, U>) -> Vector3D<T, U>

Returns the vector each component of which are minimum of this vector and another.

pub fn max(self, other: Vector3D<T, U>) -> Vector3D<T, U>

Returns the vector each component of which are maximum of this vector and another.

pub fn clamp(self, start: Vector3D<T, U>, end: Vector3D<T, U>) -> Vector3D<T, U>

where T: Copy,

Returns the vector each component of which is clamped by corresponding components of start and end.

Shortcut for self.max(start).min(end).

pub fn greater_than(self, other: Vector3D<T, U>) -> BoolVector3D

Returns vector with results of “greater than” operation on each component.

pub fn lower_than(self, other: Vector3D<T, U>) -> BoolVector3D

Returns vector with results of “lower than” operation on each component.

impl<T, U> Vector3D<T, U>

where T: PartialEq,

pub fn equal(self, other: Vector3D<T, U>) -> BoolVector3D

Returns vector with results of “equal” operation on each component.

pub fn not_equal(self, other: Vector3D<T, U>) -> BoolVector3D

Returns vector with results of “not equal” operation on each component.

impl<T, U> Vector3D<T, U>

where T: NumCast + Copy,

pub fn cast<NewT>(self) -> Vector3D<NewT, U>

where NewT: NumCast,

Cast from one numeric representation to another, preserving the units.

When casting from floating vector to integer coordinates, the decimals are truncated as one would expect from a simple cast, but this behavior does not always make sense geometrically. Consider using round(), ceil() or floor() before casting.

pub fn try_cast<NewT>(self) -> Option<Vector3D<NewT, U>>

where NewT: NumCast,

Fallible cast from one numeric representation to another, preserving the units.

When casting from floating vector to integer coordinates, the decimals are truncated as one would expect from a simple cast, but this behavior does not always make sense geometrically. Consider using round(), ceil() or floor() before casting.

pub fn to_f32(self) -> Vector3D<f32, U>

Cast into an f32 vector.

pub fn to_f64(self) -> Vector3D<f64, U>

Cast into an f64 vector.

pub fn to_usize(self) -> Vector3D<usize, U>

Cast into an usize vector, truncating decimals if any.

When casting from floating vector vectors, it is worth considering whether to round(), ceil() or floor() before the cast in order to obtain the desired conversion behavior.

pub fn to_u32(self) -> Vector3D<u32, U>

Cast into an u32 vector, truncating decimals if any.

When casting from floating vector vectors, it is worth considering whether to round(), ceil() or floor() before the cast in order to obtain the desired conversion behavior.

pub fn to_i32(self) -> Vector3D<i32, U>

Cast into an i32 vector, truncating decimals if any.

When casting from floating vector vectors, it is worth considering whether to round(), ceil() or floor() before the cast in order to obtain the desired conversion behavior.

pub fn to_i64(self) -> Vector3D<i64, U>

Cast into an i64 vector, truncating decimals if any.

When casting from floating vector vectors, it is worth considering whether to round(), ceil() or floor() before the cast in order to obtain the desired conversion behavior.

Trait Implementations

impl<'a, T, U> Add<&Vector3D<T, U>> for Vector3D<T, U>

where T: 'a + Add + Copy, U: 'a,

type Output = Vector3D<<T as Add>::Output, U>

The resulting type after applying the + operator.

fn add( self, other: &Vector3D<T, U>, ) -> <Vector3D<T, U> as Add<&Vector3D<T, U>>>::Output

Performs the + operation.

impl<T, U> Add<Vector3D<T, U>> for Point3D<T, U>

where T: Add,

type Output = Point3D<<T as Add>::Output, U>

The resulting type after applying the + operator.

fn add( self, other: Vector3D<T, U>, ) -> <Point3D<T, U> as Add<Vector3D<T, U>>>::Output

Performs the + operation.

impl<T, U> Add for Vector3D<T, U>

where T: Add,

type Output = Vector3D<<T as Add>::Output, U>

The resulting type after applying the + operator.

fn add(self, other: Vector3D<T, U>) -> <Vector3D<T, U> as Add>::Output

Performs the + operation.

impl<T, U> AddAssign<Vector3D<T, U>> for Point3D<T, U>

where T: Copy + Add<Output = T>,

fn add_assign(&mut self, other: Vector3D<T, U>)

Performs the += operation.

impl<T, U> AddAssign for Vector3D<T, U>

where T: Copy + Add<Output = T>,

fn add_assign(&mut self, other: Vector3D<T, U>)

Performs the += operation.

impl<T, U> ApproxEq<Vector3D<T, U>> for Vector3D<T, U>

where T: ApproxEq<T>,

fn approx_epsilon() -> Vector3D<T, U>

Default epsilon value

fn approx_eq_eps(&self, other: &Vector3D<T, U>, eps: &Vector3D<T, U>) -> bool

Returns true if this object is approximately equal to the other one, using a provided epsilon value.

fn approx_eq(&self, other: &Self) -> bool

Returns true if this object is approximately equal to the other one, using the approx_epsilon epsilon value.

impl<T, U> Ceil for Vector3D<T, U>

where T: Ceil,

fn ceil(self) -> Vector3D<T, U>

See Vector3D::ceil.

impl<T, U> Clone for Vector3D<T, U>

where T: Clone,

fn clone(&self) -> Vector3D<T, U>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T, U> Debug for Vector3D<T, U>

where T: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T, U> Default for Vector3D<T, U>

where T: Default,

fn default() -> Vector3D<T, U>

Returns the “default value” for a type.

impl<T, U1, U2> Div<Scale<T, U1, U2>> for Vector3D<T, U2>

where T: Copy + Div,

type Output = Vector3D<<T as Div>::Output, U1>

The resulting type after applying the / operator.

fn div( self, scale: Scale<T, U1, U2>, ) -> <Vector3D<T, U2> as Div<Scale<T, U1, U2>>>::Output

Performs the / operation.

impl<T, U> Div<T> for Vector3D<T, U>

where T: Copy + Div,

type Output = Vector3D<<T as Div>::Output, U>

The resulting type after applying the / operator.

fn div(self, scale: T) -> <Vector3D<T, U> as Div<T>>::Output

Performs the / operation.

impl<T, U> DivAssign<Scale<T, U, U>> for Vector3D<T, U>

where T: Copy + DivAssign,

fn div_assign(&mut self, scale: Scale<T, U, U>)

Performs the /= operation.

impl<T, U> DivAssign<T> for Vector3D<T, U>

where T: Copy + Div<Output = T>,

fn div_assign(&mut self, scale: T)

Performs the /= operation.

impl<T, U> Floor for Vector3D<T, U>

where T: Floor,

fn floor(self) -> Vector3D<T, U>

See Vector3D::floor.

impl<T, U> From<[T; 3]> for Vector3D<T, U>

fn from(_: [T; 3]) -> Vector3D<T, U>

Converts to this type from the input type.

impl<T, U> From<(T, T, T)> for Vector3D<T, U>

fn from(tuple: (T, T, T)) -> Vector3D<T, U>

Converts to this type from the input type.

impl<T, Src, Dst> From<Translation3D<T, Src, Dst>> for Vector3D<T, Src>

fn from(t: Translation3D<T, Src, Dst>) -> Vector3D<T, Src>

Converts to this type from the input type.

impl<T, Src, Dst> From<Vector3D<T, Dst>> for RigidTransform3D<T, Src, Dst>

where T: Real + ApproxEq<T>,

fn from(t: Vector3D<T, Dst>) -> RigidTransform3D<T, Src, Dst>

Converts to this type from the input type.

impl<T, Src, Dst> From<Vector3D<T, Src>> for Translation3D<T, Src, Dst>

fn from(v: Vector3D<T, Src>) -> Translation3D<T, Src, Dst>

Converts to this type from the input type.

impl<T, U> From<Vector3D<T, U>> for HomogeneousVector<T, U>

where T: Zero,

fn from(v: Vector3D<T, U>) -> HomogeneousVector<T, U>

Converts to this type from the input type.

impl<T, U> From<Vector3D<T, U>> for Size3D<T, U>

fn from(v: Vector3D<T, U>) -> Size3D<T, U>

Converts to this type from the input type.

impl<T, U> Hash for Vector3D<T, U>

where T: Hash,

fn hash<H>(&self, h: &mut H)

where H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T, U1, U2> Mul<Scale<T, U1, U2>> for Vector3D<T, U1>

where T: Copy + Mul,

type Output = Vector3D<<T as Mul>::Output, U2>

The resulting type after applying the * operator.

fn mul( self, scale: Scale<T, U1, U2>, ) -> <Vector3D<T, U1> as Mul<Scale<T, U1, U2>>>::Output

Performs the * operation.

impl<T, U> Mul<T> for Vector3D<T, U>

where T: Copy + Mul,

type Output = Vector3D<<T as Mul>::Output, U>

The resulting type after applying the * operator.

fn mul(self, scale: T) -> <Vector3D<T, U> as Mul<T>>::Output

Performs the * operation.

impl<T, U> MulAssign<Scale<T, U, U>> for Vector3D<T, U>

where T: Copy + MulAssign,

fn mul_assign(&mut self, scale: Scale<T, U, U>)

Performs the *= operation.

impl<T, U> MulAssign<T> for Vector3D<T, U>

where T: Copy + Mul<Output = T>,

fn mul_assign(&mut self, scale: T)

Performs the *= operation.

impl<T, U> Neg for Vector3D<T, U>

where T: Neg,

type Output = Vector3D<<T as Neg>::Output, U>

The resulting type after applying the - operator.

fn neg(self) -> <Vector3D<T, U> as Neg>::Output

Performs the unary - operation.

impl<T, U> PartialEq for Vector3D<T, U>

where T: PartialEq,

fn eq(&self, other: &Vector3D<T, U>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T, U> Round for Vector3D<T, U>

where T: Round,

fn round(self) -> Vector3D<T, U>

See Vector3D::round.

impl<T, U> Sub<Vector3D<T, U>> for Point3D<T, U>

where T: Sub,

type Output = Point3D<<T as Sub>::Output, U>

The resulting type after applying the - operator.

fn sub( self, other: Vector3D<T, U>, ) -> <Point3D<T, U> as Sub<Vector3D<T, U>>>::Output

Performs the - operation.

impl<T, U> Sub for Vector3D<T, U>

where T: Sub,

type Output = Vector3D<<T as Sub>::Output, U>

The resulting type after applying the - operator.

fn sub(self, other: Vector3D<T, U>) -> <Vector3D<T, U> as Sub>::Output

Performs the - operation.

impl<T, U> SubAssign<Vector3D<T, U>> for Point3D<T, U>

where T: Copy + Sub<Output = T>,

fn sub_assign(&mut self, other: Vector3D<T, U>)

Performs the -= operation.

impl<T, U> SubAssign for Vector3D<T, U>

where T: Copy + Sub<Output = T>,

fn sub_assign(&mut self, other: Vector3D<T, U>)

Performs the -= operation.

impl<'a, T, U> Sum<&'a Vector3D<T, U>> for Vector3D<T, U>

where T: 'a + Add<Output = T> + Copy + Zero, U: 'a,

fn sum<I>(iter: I) -> Vector3D<T, U>

where I: Iterator<Item = &'a Vector3D<T, U>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, U> Sum for Vector3D<T, U>

where T: Add<Output = T> + Zero,

fn sum<I>(iter: I) -> Vector3D<T, U>

where I: Iterator<Item = Vector3D<T, U>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, U> Zero for Vector3D<T, U>

where T: Zero,

fn zero() -> Vector3D<T, U>

Constructor, setting all components to zero.

impl<T, U> Copy for Vector3D<T, U>

where T: Copy,

impl<T, U> Eq for Vector3D<T, U>

where T: Eq,