Struct Helmert 

pub struct Helmert { /* private fields */ }

Seven-parameter Helmert transformation between geocentric frames: translation, small rotation, scale.

Parameters come from EPSG, a national survey or a chart note, in one of two rotation sign conventions: position vector (rotates the point) and coordinate frame (rotates the axes; opposite sign). Each has its own constructor so parameters are entered as published.

The rotation matrix is the small-angle I + [r]× used by the definitions, not an exact rotation: the published parameters were fitted with it.

Implementations

impl Helmert

pub const IDENTITY: Self

Identity.

pub const fn translation(dx: f64, dy: f64, dz: f64) -> Self

Translation only, metres: the three-parameter form most shifts are published in.

pub fn position_vector( translation: [f64; 3], rotation: [f64; 3], scale_ppm: f64, ) -> Result<Self>

Seven parameters, position vector convention (EPSG 9606, Bursa-Wolf as used in Europe): translations in m, rotations in arc-seconds, scale in ppm.

Errors

KernelError::NotFinite for a non-finite parameter; KernelError::OutOfRange for a scale ≤ −1 000 000 ppm (collapses the frame).

pub fn coordinate_frame( translation: [f64; 3], rotation: [f64; 3], scale_ppm: f64, ) -> Result<Self>

Seven parameters, coordinate frame convention (EPSG 9607, as used in the US and Australia): as Helmert::position_vector with rotation signs reversed.

Errors

As Helmert::position_vector.

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

Translation, m.

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

Rotation, arc-seconds, position vector convention.

pub const fn scale_ppm(&self) -> f64

Scale difference, ppm.

pub fn is_identity(&self) -> bool

Whether every parameter is zero.

pub fn apply(&self, point: EcefPoint) -> EcefPoint

Forward transform: X′ = T + (1 + s) (I + [r]×) X.

pub fn apply_inverse(&self, point: EcefPoint) -> EcefPoint

Inverse transform, exact (not the usual sign-reversal approximation), so a round trip closes to rounding precision.

For M = I + [r]×, M⁻¹ = (I − [r]× + r rᵀ) / (1 + |r|²).

Trait Implementations

impl Clone for Helmert

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Helmert

impl Debug for Helmert

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

Formats the value using the given formatter.

impl PartialEq for Helmert

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Helmert