Struct Hyperbola3D 

pub struct Hyperbola3D { /* private fields */ }

A 3D hyperbola defined by center, axis, and two semi-axis lengths.

Parameterized as P(t) = center + a * cosh(t) * u_axis + b * sinh(t) * v_axis.

The parameter t ranges over all reals; t = 0 gives the vertex closest to center on the positive branch.

Implementations

impl Hyperbola3D

pub fn new( center: Point3, normal: Vec3, semi_major: f64, semi_minor: f64, ) -> Result<Self, MathError>

Creates a new hyperbola.

semi_major is the real semi-axis (distance from center to vertex), semi_minor is the imaginary semi-axis.

Errors

Returns an error if either semi-axis is non-positive.

pub fn evaluate(&self, t: f64) -> Point3

Evaluates the hyperbola at parameter t.

pub fn tangent(&self, t: f64) -> Vec3

Returns the tangent vector at parameter t.

pub const fn center(&self) -> Point3

Returns the center.

pub const fn semi_major(&self) -> f64

Returns the semi-major axis (real axis).

pub const fn semi_minor(&self) -> f64

Returns the semi-minor axis (imaginary axis).

pub const fn normal(&self) -> Vec3

Returns the normal (axis perpendicular to the hyperbola plane).

pub const fn u_axis(&self) -> Vec3

Returns the in-plane u-axis (real semi-axis direction). At parameter t, the hyperbola is at offset semi_major * cosh(t) * u_axis + semi_minor * sinh(t) * v_axis from the center.

pub const fn v_axis(&self) -> Vec3

Returns the in-plane v-axis (imaginary semi-axis direction).

pub fn eccentricity(&self) -> f64

Returns the eccentricity: e = sqrt(1 + (b/a)²).

pub fn foci(&self) -> (Point3, Point3)

Returns the two foci.

Trait Implementations

impl Clone for Hyperbola3D

fn clone(&self) -> Hyperbola3D

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Hyperbola3D

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

Formats the value using the given formatter.