Struct QuadraticGraph2

pub struct QuadraticGraph2 {
    pub a: Trig2,
    pub b: Trig2,
    pub c: Trig2,
    pub branch: Branch,
}

The graph of one root of a(t) v^2 + b(t) v + c(t) = 0, parameterised by its first coordinate: the point at t is (t, v(t)).

Where a vanishes the quadratic is linear and the branch that stays finite is v = -c / b; the evaluation below is the rationalised form v = 2c / (-b - sign sqrt(D)), which is finite there and free of the cancellation -b + sqrt(D) suffers when 4ac is small.

The graph is only defined where D = b^2 - 4ac >= 0. Which spans those are is decided when the graph is constructed (exactly, from the operands’ own numbers) and carried by the edge interval that uses it; evaluating outside them is refused, not extrapolated.

Fields

a: Trig2

Coefficient of v^2.

b: Trig2

Coefficient of v.

c: Trig2

Constant coefficient.

branch: Branch

Which root.

Implementations

impl QuadraticGraph2

pub fn discriminant(&self, t: Scalar) -> Scalar

The discriminant b^2 - 4ac at t.

pub fn height(&self, t: Scalar) -> Option<Scalar>

Height at t, or None where the root does not exist or diverges.

pub fn slope(&self, t: Scalar) -> Option<Scalar>

dv/dt at t, by differentiating the quadratic implicitly; None where the height is undefined or the tangent is vertical (a branch end, where 2 a v + b = 0).

pub fn bend(&self, t: Scalar) -> Option<Scalar>

d2v/dt2 at t.

pub fn is_finite(&self) -> bool

Whether every coefficient is finite.

Trait Implementations

impl Clone for QuadraticGraph2

fn clone(&self) -> QuadraticGraph2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for QuadraticGraph2

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

Formats the value using the given formatter.

impl PartialEq for QuadraticGraph2

fn eq(&self, other: &QuadraticGraph2) -> 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 Copy for QuadraticGraph2

impl StructuralPartialEq for QuadraticGraph2