Struct Intrinsic3

pub struct Intrinsic3 {
    pub start: Frame3,
    pub curvature: CurvatureLaw,
    pub torsion: CurvatureLaw,
    pub length: Scalar,
}

A space curve given by its natural equations.

curvature is k(s) >= 0 by the Frenet convention; a signed law is storable, because dirty imported data stays representable here as everywhere else in this crate, and naming it is a validator’s job.

torsion is tau(s), signed: positive is a right-handed screw. Torsion identically zero is a plane curve, and the plane is the one spanned by the start frame’s x and y axes.

Both laws reuse CurvatureLaw, which is the general “scalar function of arc length” in this crate: constant, polynomial, sinusoid, their sum, and piecewise combinations. Nothing about it is curvature-specific, and a second near-identical enum for torsion would be duplication with a different name.

Fields

start: Frame3

Start frame: origin at the curve start, x along the start tangent, y along the start normal, z along the start binormal.

curvature: CurvatureLaw

Curvature as a function of arc length from start.

torsion: CurvatureLaw

Torsion as a function of arc length from start.

length: Scalar

Arc length the laws are defined over.

Implementations

impl Intrinsic3

pub const fn new( start: Frame3, curvature: CurvatureLaw, torsion: CurvatureLaw, length: Scalar, ) -> Self

Anchor a curvature and a torsion law to a start frame over an arc length.

pub fn is_planar(&self) -> bool

Whether the curve is planar: torsion identically zero.

A planar space curve is exactly a 2D curve embedded in the start frame’s plane, so this is the predicate that decides whether the cheaper 2D path applies.

pub fn is_helical(&self) -> bool

Whether the curve is a helix: curvature and torsion both constant.

This is the case where the Frenet generators commute at every arc length, so the product integral collapses to a single matrix exponential and the curve has an elementary closed form. Worth naming because it is both the classical example and the exactly-solvable case.

pub fn total_turning(&self) -> Option<Scalar>

Total tangent turning over the curve, in radians, in closed form.

The integral of k – exact, as in 2D. Note this is NOT enough to recover the frame in space, only the amount the tangent has swung.

pub fn total_torsion(&self) -> Option<Scalar>

Total torsion over the curve, in radians, in closed form.

The integral of tau. For a helix this is the angle the binormal has swung about the axis.

Trait Implementations

impl Clone for Intrinsic3

fn clone(&self) -> Intrinsic3

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Intrinsic3

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

Formats the value using the given formatter.

impl PartialEq for Intrinsic3

fn eq(&self, other: &Intrinsic3) -> 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 Intrinsic3