Struct SphericalSurface 

pub struct SphericalSurface { /* private fields */ }

An infinite spherical surface (actually a sphere).

Parameterized as P(u, v) = center + radius*(cos(v)*cos(u)*x + cos(v)*sin(u)*y + sin(v)*z) where u ∈ [0, 2π) (longitude) and v ∈ [-π/2, π/2] (latitude).

Implementations

impl SphericalSurface

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

Creates a new spherical surface.

Errors

Returns an error if radius is not positive.

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

Creates a spherical surface with a custom orientation.

Errors

Returns an error if radius is not positive or the z-axis is zero.

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 normal at parameters (u, v).

pub const fn center(&self) -> Point3

Returns the center.

pub const fn radius(&self) -> f64

Returns the 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 local Z axis (pole direction).

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

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

pub fn aabb(&self) -> Aabb3

Axis-aligned bounding box of the full sphere (center ± radius on every axis). Orientation-independent and a sound superset of any spherical patch — the boolean broad-phase uses it because a face’s boundary-only bbox misses the surface bulge between its boundary edges (a hemisphere’s only boundary is its equator).

pub fn aabb_region(&self, pole: Vec3) -> Aabb3

Axis-aligned bounding box of the hemisphere on the pole-axis side — the half-ball {center + radius·d : d·pole ≥ 0}. A tight, sound superset of any spherical patch lying on that side; the boolean broad-phase uses it so that one hemisphere face’s box does not admit the other’s sections (the full-sphere aabb would). Falls back to the full sphere when pole is degenerate (side ambiguous).

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

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

u is the longitudinal angle [0, 2π), v is the latitude [-π/2, π/2].

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 SphericalSurface

fn clone(&self) -> SphericalSurface

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SphericalSurface

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for SphericalSurface

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl ParametricSurface for SphericalSurface

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 SphericalSurface

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

where __S: Serializer,

Serialize this value into the given Serde serializer.