Struct Parabola3D 

pub struct Parabola3D { /* private fields */ }

A 3D parabola defined by vertex, axis direction, and focal length.

Parameterized as P(t) = vertex + (t²/(4f)) * axis_dir + t * u_axis where f is the focal length and u_axis is perpendicular to the axis in the parabola plane.

The parameter t ranges over all reals; t = 0 is the vertex.

Implementations

impl Parabola3D

pub fn new( vertex: Point3, axis_dir: Vec3, focal_length: f64, ) -> Result<Self, MathError>

Creates a new parabola.

axis_dir is the direction from vertex toward the interior of the parabola (the axis of symmetry). focal_length is the distance from vertex to focus.

Errors

Returns an error if focal_length is not positive or axis_dir is zero.

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

Evaluates the parabola at parameter t.

At t = 0 this returns the vertex.

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

Returns the tangent vector at parameter t.

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

Returns the curvature at parameter t.

pub const fn vertex(&self) -> Point3

Returns the vertex.

pub const fn focal_length(&self) -> f64

Returns the focal length.

pub const fn axis_dir(&self) -> Vec3

Returns the axis direction (normalized).

pub const fn u_axis(&self) -> Vec3

Returns the in-plane u-axis (perpendicular to axis_dir). At parameter t, the parabola is offset by t * u_axis from the symmetry axis.

pub fn focus(&self) -> Point3

Returns the focus point.

Trait Implementations

impl Clone for Parabola3D

fn clone(&self) -> Parabola3D

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Parabola3D

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

Formats the value using the given formatter.