Struct ToroidalSurface 

pub struct ToroidalSurface { /* private fields */ }

A toroidal surface.

Parameterized as P(u, v) = center + (R + r*cos(v))*(cos(u)*x + sin(u)*y) + r*sin(v)*z where R is the major radius, r is the minor radius, u ∈ [0, 2π) (around the tube) and v ∈ [0, 2π) (around the cross-section).

Implementations

impl ToroidalSurface

pub fn new( center: Point3, major_radius: f64, minor_radius: f64, ) -> Result<Self, MathError>

Creates a new toroidal surface.

Errors

Returns an error if either radius is not positive or minor_radius > major_radius.

pub fn with_axis( center: Point3, major_radius: f64, minor_radius: f64, z_axis: Vec3, ) -> Result<Self, MathError>

Creates a toroidal surface with a specified axis direction.

The axis is the central symmetry axis of the torus. The local coordinate frame is derived from it.

Errors

Returns an error if either radius is not positive or axis is zero.

pub fn with_axis_and_ref_dir( center: Point3, major_radius: f64, minor_radius: f64, z_axis: Vec3, ref_dir: Vec3, ) -> Result<Self, MathError>

Create a torus with explicit axis and reference direction.

ref_dir defines the x-axis of the local frame (projected perpendicular to z_axis). This preserves the parametric orientation from STEP AXIS2_PLACEMENT_3D.

Errors

Returns MathError::ParameterOutOfRange if either radius is non-positive, or MathError::ZeroVector if z_axis is zero.

Panics

Panics if the fallback perpendicular vector cannot be normalized (should not occur for any valid unit z_axis).

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

Evaluates the surface at parameters (u, v).

pub fn normal(&self, u: f64, v: f64) -> Vec3

Returns the outward surface normal at parameters (u, v).

pub const fn center(&self) -> Point3

Returns the center.

pub fn translated(&self, offset: Vec3) -> Self

Returns a copy of this torus with its center translated by offset.

pub fn aabb(&self) -> Aabb3

Axis-aligned bounding box of the full torus. The half-extent along each world axis sums the ring’s projection onto the plane perpendicular to the torus axis ((major+minor)·‖(x·ê, y·ê)‖) and the tube’s projection onto the axis (minor·|z·ê|); x/y/z_axis are orthonormal. A sound superset used by the boolean broad-phase — a full torus’s boundary is degenerate seam points, so a boundary-only bbox collapses to a point.

pub const fn major_radius(&self) -> f64

Returns the major radius (distance from center to tube center).

pub const fn minor_radius(&self) -> f64

Returns the minor radius (tube cross-section radius).

pub const fn x_axis(&self) -> Vec3

Returns the local X axis.

pub const fn y_axis(&self) -> Vec3

Returns the local Y axis.

pub const fn z_axis(&self) -> Vec3

Returns the torus axis direction (perpendicular to the ring plane).

pub fn project_point(&self, point: Point3) -> (f64, f64)

Project a 3D point onto the torus surface, returning (u, v) parameters.

u ∈ [0, 2π) is the angle around the major circle. v ∈ [0, 2π) is the angle around the tube cross-section.

pub fn to_nurbs(&self) -> Result<NurbsSurface, MathError>

Convert to an approximate NURBS surface.

Errors

Returns an error if NurbsSurface construction fails.

Trait Implementations

impl Clone for ToroidalSurface

fn clone(&self) -> ToroidalSurface

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ToroidalSurface

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for ToroidalSurface

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl ParametricSurface for ToroidalSurface

fn evaluate(&self, u: f64, v: f64) -> Point3

Evaluate the surface at parameters (u, v).

fn normal(&self, u: f64, v: f64) -> Vec3

Surface normal at parameters (u, v).

fn project_point(&self, point: Point3) -> (f64, f64)

Project a 3D point onto the surface, returning (u, v) parameters.

fn partial_u(&self, u: f64, v: f64) -> Vec3

Partial derivative ∂S/∂u at (u, v).

fn partial_v(&self, u: f64, v: f64) -> Vec3

Partial derivative ∂S/∂v at (u, v).

impl Serialize for ToroidalSurface

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.