Struct ImplicitCurve2

pub struct ImplicitCurve2 {
    pub field: Field2,
    pub cells: Vec<ImplicitCell>,
}

A stretch of a field’s zero set, in the parameters of the surface the field lives on. The parameter t runs over [0, cells.len()]: cell i covers [i, i + 1], its free parameter moving linearly from from to to.

Fields

field: Field2

The field whose zero the curve is.

cells: Vec<ImplicitCell>

The cells, each starting where the previous ends.

Implementations

impl ImplicitCurve2

pub fn end(&self) -> f64

The parameter range, [0, cells.len()].

pub fn solve_cell(&self, cell: &ImplicitCell, free: f64) -> Option<f64>

The solved value of cell at free value free.

pub fn point(&self, t: f64) -> Option<DVec2>

The point at t, or None outside [0, cells.len()].

pub fn derivative(&self, t: f64) -> Option<DVec2>

dP/dt.

pub fn second_derivative(&self, t: f64) -> Option<DVec2>

d2P/dt2.

pub fn parameter_of(&self, p: DVec2) -> Option<f64>

The parameter of a point on the curve: the cell whose box holds it, and where its free value falls in the cell.

pub fn shifted(&self, du: f64, dv: f64) -> ImplicitCurve2

The same curve moved by whole periods (du, dv) in parameters.

pub fn closure(&self, periodic_u: bool, periodic_v: bool) -> Option<DVec2>

The offset from the curve’s start to its end in parameters when it closes up to whole periods of 2 pi in the periodic parameters ((0, 0) for a loop that does not wind), or None when it is open.

pub fn sub( &self, t0: f64, t1: f64, closure: Option<DVec2>, ) -> Option<ImplicitCurve2>

The stretch from t0 to t1, as a curve of its own over [0, cells]. With t0 > t1 the stretch runs on past the end and round from the start, which needs the curve’s closure offset.

pub fn rotated(&self, t: f64, closure: DVec2) -> Option<ImplicitCurve2>

A closed curve’s whole loop, starting at t instead of at 0.

pub fn clipped(&self, lo: DVec2, hi: DVec2) -> Vec<ImplicitCurve2>

The stretches of the curve inside the box [lo, hi], each as a curve of its own. Crossings of the box’s sides are found by a scan of each cell and bisection on the distance to the box.

pub fn reversed(&self) -> ImplicitCurve2

The same curve run backwards: t becomes cells.len() - t.

pub fn turning_points(&self, lo: f64, hi: f64) -> Vec<f64>

Parameters in (lo, hi) where the curve may stop being monotone in u or v: every cell boundary, and inside each cell every point where the solved parameter turns (the field’s partial along the free parameter changes sign on the curve). Between consecutive values the curve is monotone in both parameters.

Each turning point is isolated with interval bounds of that partial over boxes that certainly hold the curve (the solved parameter moves at most max |F_free| / min |F_solved| per unit of the free one), so none is missed; a double root, where the sign does not change, is not a turn and is not reported.

pub fn is_finite(&self) -> bool

Whether every number is finite.

Trait Implementations

impl Clone for ImplicitCurve2

fn clone(&self) -> ImplicitCurve2

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for ImplicitCurve2

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

Formats the value using the given formatter.

impl PartialEq for ImplicitCurve2

fn eq(&self, other: &ImplicitCurve2) -> 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 ImplicitCurve2