Struct Intrinsic2

pub struct Intrinsic2 {
    pub start: Frame2,
    pub curvature: CurvatureLaw,
    pub length: Scalar,
}

A plane curve given by its natural equation: a curvature law anchored to a start frame and run for a finite arc length.

The frame supplies the rigid motion that k(s) alone cannot: its origin is the curve start, and its x axis is the start tangent direction.

Like every other value in this crate, dirty imported data stays representable – a non-positive length is storable, and naming it is the job of a validator, not of the type.

Fields

start: Frame2

Start frame: origin at the curve start, x along the start tangent.

curvature: CurvatureLaw

Curvature as a function of arc length from start.

length: Scalar

Arc length the law is defined over.

Implementations

impl Intrinsic2

pub const fn new(start: Frame2, curvature: CurvatureLaw, length: Scalar) -> Self

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

pub fn is_straight(&self) -> bool

Whether the curve is a straight segment.

pub fn heading_at(&self, s: Scalar) -> Option<Scalar>

Tangent heading at arc length s from the start, in radians.

The integral of k over [0, s], which every law in the family has in closed form – so the heading is exact even though the POSITION is not and has to be quadratured. Measured from the start tangent, so the absolute heading is this plus the start frame’s rotation.

Returns None when s is not finite or a piecewise law does not tile [0, s], matching Self::total_turning.

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

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

This is the integral of k(s) over [0, length] – exact for every law in the family, because each one has an elementary antiderivative. It is the angle that integrates in closed form; position does not, which is why this method exists and an evaluate does not.

Returns None when the length is not finite, since the integral is then undefined rather than merely large.

pub fn turning_variation_bound(&self, s: Scalar) -> Option<Scalar>

Upper bound on the total variation of heading over [0, s], in radians.

total_turning is the SIGNED integral of k; over a zero-mean oscillation it is zero however violently the curve wiggles. A quadrature budget derived from it would then spend one panel on a curve that needs many, so this returns the integral of |k| instead – or a bound on it.

Exact for Constant. For the other families an exact total variation needs the sign changes of k, so this returns a cheap upper bound from the triangle inequality: a bound is what a panel budget wants, and overestimating costs panels while underestimating costs correctness.

None when s is not finite, matching heading_at.

Trait Implementations

impl Clone for Intrinsic2

fn clone(&self) -> Intrinsic2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Intrinsic2

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

Formats the value using the given formatter.

impl PartialEq for Intrinsic2

fn eq(&self, other: &Intrinsic2) -> 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 Intrinsic2