Struct Vector 

pub struct Vector {
    pub x: f64,
    pub y: f64,
    pub z: f64,
}

A free vector in space.

Fields

x: f64

X component.

y: f64

Y component.

z: f64

Z component.

Implementations

impl Vector

pub const ZERO: Self

The zero vector.

pub const X: Self

Unit vector along +X.

pub const Y: Self

Unit vector along +Y.

pub const Z: Self

Unit vector along +Z.

pub const fn new(x: f64, y: f64, z: f64) -> Self

A vector from components.

pub const fn splat(v: f64) -> Self

A vector with all components equal.

pub const fn to_array(self) -> [f64; 3]

Components as an array.

pub const fn from_array([x, y, z]: [f64; 3]) -> Self

A vector from an array.

pub fn coord(self, index: usize) -> OgeomResult<f64>

Component by index, 0..3.

Errors

OgeomError::Range if index >= 3.

pub fn dot(self, other: Self) -> f64

Dot product.

pub fn cross(self, other: Self) -> Self

Cross product. Right-handed: X.cross(Y) == Z.

Each component is a two-term difference ab - cd, evaluated without a fused multiply-add on purpose. An FMA rounds one product and not the other, which destroys the exact cancellation that makes the cross product of collinear vectors come out at exactly zero.

pub fn triple(self, a: Self, b: Self) -> f64

Scalar triple product self · (a × b): the signed volume of the parallelepiped the three vectors span.

pub fn square_magnitude(self) -> f64

Squared magnitude. Prefer this to Vector::magnitude when comparing lengths: it avoids a square root and the rounding that comes with it.

pub fn magnitude(self) -> f64

Magnitude.

pub fn normalized(self, tol: Tolerances) -> OgeomResult<Self>

This vector scaled to unit length.

Errors

OgeomError::Construction if the magnitude is below tol.confusion(), or if any component is non-finite. Normalizing a near-zero vector amplifies whatever noise it holds into an arbitrary direction, so it is refused rather than approximated.

pub fn is_finite(self) -> bool

Whether every component is finite.

pub fn is_zero(self, tol: Tolerances) -> bool

Whether the magnitude is within tol.confusion() of zero.

pub fn is_equal(self, other: Self, tol: Tolerances) -> bool

Whether two vectors agree component-wise within tol.confusion().

pub fn angle(self, other: Self, tol: Tolerances) -> OgeomResult<f64>

Angle to other, in [0, π].

Uses atan2 of the cross and dot products rather than acos of the normalized dot product: acos loses most of its precision for nearly parallel or nearly antiparallel vectors, which is exactly where angle tests matter.

Errors

OgeomError::Construction if either vector is degenerate.

pub fn signed_angle( self, other: Self, reference: Self, tol: Tolerances, ) -> OgeomResult<f64>

Angle to other measured about reference, in (-π, π].

Positive when self turns towards other counter-clockwise as seen from the tip of reference.

Errors

OgeomError::Construction if any vector is degenerate, or if reference is not perpendicular to both within tol.angular().

pub fn is_parallel(self, other: Self, tol: Tolerances) -> bool

Whether self and other point the same way, within tol.angular().

pub fn is_collinear(self, other: Self, tol: Tolerances) -> bool

Whether self and other are parallel, ignoring sense.

pub fn is_normal(self, other: Self, tol: Tolerances) -> bool

Whether self and other are perpendicular, within tol.angular().

pub fn projected_onto(self, other: Self, tol: Tolerances) -> OgeomResult<Self>

Component of self along other.

Errors

OgeomError::Construction if other is degenerate.

pub fn lerp(self, other: Self, t: f64) -> Self

Linear interpolation, t = 0 giving self.

pub fn min(self, other: Self) -> Self

Component-wise minimum.

pub fn max(self, other: Self) -> Self

Component-wise maximum.

pub const fn xy(self) -> Vector2

The 2D vector formed by dropping the Z component.

Trait Implementations

impl Add for Vector

type Output = Vector

The resulting type after applying the + operator.

fn add(self, o: Self) -> Self

Performs the + operation.

impl Add<Vector> for Point

type Output = Point

The resulting type after applying the + operator.

fn add(self, v: Vector) -> Self

Performs the + operation.

impl AddAssign for Vector

fn add_assign(&mut self, o: Self)

Performs the += operation.

impl AddAssign<Vector> for Point

fn add_assign(&mut self, v: Vector)

Performs the += operation.

impl Blend for Vector

fn zero() -> Self

The additive identity.

fn scale(self, k: f64) -> Self

Scale by a factor.

fn add(self, other: Self) -> Self

Add another value.

fn lerp(self, other: Self, t: f64) -> Self

self * (1 - t) + other * t.

fn sub(self, other: Self) -> Self

Subtract, via scaling by -1.

impl Clone for Vector

fn clone(&self) -> Vector

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Vector

impl Debug for Vector

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

Formats the value using the given formatter.

impl Default for Vector

fn default() -> Vector

Returns the “default value” for a type.

impl Div<f64> for Vector

type Output = Vector

The resulting type after applying the / operator.

fn div(self, s: f64) -> Self

Performs the / operation.

impl DivAssign<f64> for Vector

fn div_assign(&mut self, s: f64)

Performs the /= operation.

impl From<Direction> for Vector

fn from(d: Direction) -> Self

Converts to this type from the input type.

impl Mul<Vector> for Matrix3

type Output = Vector

The resulting type after applying the * operator.

fn mul(self, v: Vector) -> Vector

Performs the * operation.

impl Mul<Vector> for f64

type Output = Vector

The resulting type after applying the * operator.

fn mul(self, v: Vector) -> Vector

Performs the * operation.

impl Mul<f64> for Vector

type Output = Vector

The resulting type after applying the * operator.

fn mul(self, s: f64) -> Self

Performs the * operation.

impl MulAssign<f64> for Vector

fn mul_assign(&mut self, s: f64)

Performs the *= operation.

impl Neg for Vector

type Output = Vector

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Vector

fn eq(&self, other: &Vector) -> 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 StructuralPartialEq for Vector

impl Sub for Vector

type Output = Vector

The resulting type after applying the - operator.

fn sub(self, o: Self) -> Self

Performs the - operation.

impl Sub<Vector> for Point

type Output = Point

The resulting type after applying the - operator.

fn sub(self, v: Vector) -> Self

Performs the - operation.

impl SubAssign for Vector

fn sub_assign(&mut self, o: Self)

Performs the -= operation.

impl SubAssign<Vector> for Point

fn sub_assign(&mut self, v: Vector)

Performs the -= operation.