Struct TwoPolynomials 

pub struct TwoPolynomials<T, P>
where
    P: Generic1DPoly<T>,
    T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T>,
{ /* private fields */ }

T is the type being used to represent the real numbers have two polynomials which can be used as functions from T to T so used for an R -> R^2 curve

Implementations

impl<const N: usize, T> TwoPolynomials<T, SymmetricalBasisPolynomial<N, T>>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign<T> + PartialEq,

pub fn pretty_format( &self, variable: &str, zero_pred: &impl Fn(&T) -> bool, ) -> String

where T: Debug,

impl<T, P> TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

pub fn differentiate(self) -> Result<Self, DifferentiateError>

differentiate each component

Errors

the subspace for the components does not have to be closed under d/dx operator

pub fn evaluate_at(&self, t: T) -> (T, T)

pub fn evaluate_at_many<const POINT_COUNT: usize>( &self, ts: [T; POINT_COUNT], ) -> [(T, T); POINT_COUNT]

pub fn evaluate_at_zero(&self) -> (T, T)

pub fn evaluate_at_one(&self) -> (T, T)

pub fn evaluate_at_neg_one(&self) -> (T, T)

pub fn linear_approx_poly( self, around_here: PointSpecifier<T>, ) -> Result<Self, Result<DifferentiateError, MonomialError>>

first order approximation around the given point

Errors

it might fail because the subspace for each component does not have to be closed under d/dx operator another possibility is that the subspace does not include the linear function x that should be very unusual, because we typically truncate by degree and 1 is too low of a degree to fall to the chopping block

pub fn apply_matrix(self, two_d_matrix: [[T; 2]; 2]) -> Self

where P: Clone,

A B x C D y

pub fn reflect_y(self) -> Self

pub fn reflect_x(self) -> Self

pub fn swap_axes(self) -> Self

impl<T, P> TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign + DivAssign<T>, P: Generic1DPoly<T> + Clone + FundamentalTheorem<T>,

pub fn normals_to_point( self, point: (T, T), zero_pred: &impl Fn(&T) -> bool, my_sqrt: &impl Fn(&T) -> Option<T>, my_cube_root: &impl Fn(&T) -> (Option<T>, Option<T>), ) -> Result<Vec<(T, usize)>, NormalTangentError>

given a parameterized curve in the plane find the values of the parameter where the tangent at that point is perpendicular to the displacement vector pointing between the given point and the curve

Errors

• one of the errors associated with differentiate
• a dot product was not in the subspace
• a polynomial was not exactly solvable

pub fn tangents_to_points( self, point: (T, T), zero_pred: &impl Fn(&T) -> bool, my_sqrt: &impl Fn(&T) -> Option<T>, my_cube_root: &impl Fn(&T) -> (Option<T>, Option<T>), ) -> Result<Vec<(T, usize)>, NormalTangentError>

given a parameterized curve in the plane find the values of the parameter where the tangent at that point is in the same direction as the displacement vector pointing between the given point and the curve

Errors

• one of the errors associated with differentiate
• a cross product was not in the subspace
• a polynomial was not exactly solvable

pub fn collision_curve( self, other: Self, zero_pred: &impl Fn(&T) -> bool, my_sqrt: &impl Fn(&T) -> Option<T>, my_cube_root: &impl Fn(&T) -> (Option<T>, Option<T>), ) -> Result<Vec<(T, usize)>, NormalTangentError>

given two parameterized curves in the plane find the values of the parameter where the distance between the two curves becomes 0

Errors

• a norm squared was not in the subspace
• a polynomial was not exactly solvable

pub fn signed_curvature_times_speed_cubed_and_speed_squared( self, zero_pred: &impl Fn(&T) -> bool, ) -> Result<(P, P), NormalTangentError>

for the curvature kappa, take the absolute value of the first output polynomial (in P) then divide by the speed cubed the speed squared is the second output we can’t do it purely within this level of generality with P because you can’t take the square root nor can we divide

Errors

• one of the errors associated with differentiate
• a dot product was not in the subspace
• a cross product was not in the subspace

pub fn speed_squared( self, zero_pred: &impl Fn(&T) -> bool, ) -> Result<P, NormalTangentError>

speed squared

Errors

• one of the errors associated with differentiate
• a dot product was not in the subspace

Trait Implementations

impl<T, P> Add<(T, T)> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the + operator.

fn add(self, rhs: (T, T)) -> Self::Output

Performs the + operation.

impl<T, P> Add for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<T, P> AddAssign<(T, T)> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

fn add_assign(&mut self, rhs: (T, T))

Performs the += operation.

impl<T, P> AddAssign for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<T, P> Clone for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T> + Clone,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T, P> Mul<T> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<T, P> MulAssign<T> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T, P> Neg for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T, P> Sub<(T, T)> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the - operator.

fn sub(self, rhs: (T, T)) -> Self::Output

Performs the - operation.

impl<T, P> Sub for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

type Output = TwoPolynomials<T, P>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<T, P> SubAssign<(T, T)> for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

fn sub_assign(&mut self, rhs: (T, T))

Performs the -= operation.

impl<T, P> SubAssign for TwoPolynomials<T, P>

where T: Clone + Neg<Output = T> + AddAssign + Add<Output = T> + Mul<Output = T> + MulAssign + From<SmallIntegers> + Sub<Output = T> + SubAssign, P: Generic1DPoly<T>,

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.