Struct Sphere 

pub struct Sphere {
    pub radius: Real,
}

A sphere defined by its radius.

Fields

radius: Real

Radius of the sphere.

Implementations

impl Sphere

pub fn new(radius: Real) -> Self

Create a new sphere with the given radius.

pub fn surface_area(&self) -> Real

Surface area: 4πr².

pub fn volume_explicit(&self) -> Real

Volume: (4/3)πr³.

pub fn inertia_tensor_array(&self, mass: f64) -> [[f64; 3]; 3]

Inertia tensor as [[f64;3\];3] row-major: (2/5)mr² × identity.

pub fn ray_cast_array( &self, origin: [f64; 3], direction: [f64; 3], max_toi: f64, ) -> Option<(f64, [f64; 3])>

Ray cast returning (t, normal) as plain arrays.

pub fn closest_point(&self, p: [f64; 3]) -> [f64; 3]

Closest point on the sphere surface to p. If p is the origin, returns a point on the +X side.

pub fn support(&self, direction: [f64; 3]) -> [f64; 3]

GJK support function: farthest point in direction.

pub fn support_with_center( &self, center: [f64; 3], direction: [f64; 3], ) -> [f64; 3]

GJK support point with a center offset. Returns center + radius * normalize(direction).

pub fn minkowski_sum_support( &self, other: &Sphere, direction: [f64; 3], ) -> [f64; 3]

Minkowski sum support: support(A) + support(B) in the given direction. Both spheres are centered at the origin.

pub fn minkowski_diff_support( &self, other: &Sphere, direction: [f64; 3], ) -> [f64; 3]

Minkowski difference support: support_A(d) - support_B(-d). Both spheres centered at origin.

pub fn bounding_sphere_from_points(points: &[[f64; 3]]) -> ([f64; 3], f64)

Compute bounding sphere from a set of points (Ritter’s algorithm). Returns (center, radius).

pub fn intersects_sphere( &self, center_a: [f64; 3], other: &Sphere, center_b: [f64; 3], ) -> bool

Sphere-sphere intersection test. Returns true if two spheres (at given centers) overlap.

pub fn sphere_intersection_circle( &self, center_a: [f64; 3], other: &Sphere, center_b: [f64; 3], ) -> Option<([f64; 3], [f64; 3], f64)>

Sphere-sphere intersection circle. Returns Some((center, normal, circle_radius)) if the spheres intersect in a circle, None if they don’t intersect or are concentric.

pub fn closest_point_to_line( &self, line_point: [f64; 3], line_dir: [f64; 3], ) -> [f64; 3]

Closest point on the sphere surface to a line defined by point and direction. Returns the closest point on the sphere surface.

pub fn closest_point_to_plane(&self, normal: [f64; 3], d: f64) -> [f64; 3]

Closest point on the sphere surface to a plane defined by normal (unit) and d where normal · x = d.

pub fn sphere_sweep( &self, start: [f64; 3], velocity: [f64; 3], target_center: [f64; 3], target_radius: f64, max_t: f64, ) -> Option<f64>

Sphere sweep (moving sphere): test if a sphere moving from start along velocity hits a static sphere (centered at target_center with target_radius). Returns Some(t) in [0, max_t] if there is a collision.

pub fn signed_distance(&self, p: [f64; 3]) -> f64

Signed distance from a point to the sphere surface. Negative if inside the sphere, positive if outside.

pub fn contains_point(&self, p: [f64; 3]) -> bool

Returns true if the point is inside (or on) the sphere.

pub fn project_inside(&self, p: [f64; 3]) -> [f64; 3]

Project a point onto the sphere interior (clamp to sphere if outside).

pub fn geodesic_icosphere( &self, subdivisions: u32, ) -> (Vec<[f64; 3]>, Vec<[usize; 3]>)

Generate a geodesic icosphere by subdividing an icosahedron.

Returns (vertices, triangles) where each vertex is a unit-sphere point scaled to self.radius, and triangles are [usize; 3] index triples. subdivisions = 0 gives the base icosahedron (20 faces, 12 verts).

pub fn spherical_cap_volume(&self, h: f64) -> f64

Spherical cap volume.

Returns the volume of a spherical cap of height h cut from this sphere. h must be in [0, 2r].

pub fn spherical_cap_area(&self, h: f64) -> f64

Spherical cap surface area (curved part only).

Area = 2π r h.

pub fn spherical_zone_area(&self, h1: f64, h2: f64) -> f64

Spherical zone area between two parallel planes.

For planes at heights h1 and h2 (measured from the bottom of the sphere), returns the surface area of the zone. Area = 2π r |h2 - h1|.

pub fn hemisphere_cosine_sample(&self, n: usize, seed: u64) -> Vec<[f64; 3]>

Sample points on the hemisphere (z ≥ 0) using cosine-weighted sampling.

Uses a deterministic xorshift PRNG seeded with seed. Each point lies on the unit hemisphere surface projected to self.radius.

pub fn hemisphere_uniform_sample(&self, n: usize, seed: u64) -> Vec<[f64; 3]>

Uniform hemisphere sampling (z ≥ 0).

Each sample is uniformly distributed on the upper hemisphere.

pub fn fibonacci_sphere(&self, n: usize) -> Vec<[f64; 3]>

3-D Fibonacci sphere packing.

Generates n nearly uniformly distributed points on the sphere surface using the golden-angle Fibonacci lattice method.

pub fn stereographic_project(&self, p: [f64; 3]) -> Option<[f64; 2]>

Stereographic projection from the sphere to the plane.

Projects a point p on the sphere to the stereographic plane using the south pole as the projection center. The north pole maps to infinity; the south pole is undefined.

Returns (x_plane, y_plane) or None if p is at (or near) the south pole.

pub fn stereographic_unproject(&self, uv: [f64; 2]) -> [f64; 3]

Inverse stereographic projection from the plane to the sphere.

Maps (x_plane, y_plane) back to a point on the sphere. Uses the formula: X = 4r²x/D, Y = 4r²y/D, Z = r(D - 4r²)/D where D = x² + y² + 4r².

pub fn sh_l3(m: i32, theta: f64, phi: f64) -> f64

Spherical harmonic (l=3) coefficient Y_3^m(theta, phi).

Extends spherical_harmonic to degree 3.

pub fn cap_solid_angle(&self, h: f64) -> f64

Compute the solid angle subtended by a spherical cap of height h.

Ω = 2π(1 - cos θ) where cos θ = 1 - h/r.

pub fn lon_lat(&self, p: [f64; 3]) -> (f64, f64)

Longitude/latitude (geographic) coordinates for a point on the sphere.

Returns (longitude, latitude) in radians. Longitude in (-π, π], latitude in [-π/2, π/2].

Trait Implementations

impl Clone for Sphere

fn clone(&self) -> Sphere

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Sphere

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

Formats the value using the given formatter.

impl Shape for Sphere

fn bounding_box(&self) -> Aabb

Compute the axis-aligned bounding box of this shape (in local space).

fn support_point(&self, direction: &Vec3) -> Vec3

Compute the support point in the given direction (for GJK).

fn volume(&self) -> Real

Compute the volume of this shape.

fn center_of_mass(&self) -> Vec3

Compute the center of mass in local space.

fn inertia_tensor(&self, mass: Real) -> Mat3

Compute the inertia tensor for the given mass.

fn ray_cast( &self, ray_origin: &Vec3, ray_direction: &Vec3, max_toi: Real, ) -> Option<RayHit>

Cast a ray against this shape (in local space). Returns the first intersection within max_toi.

fn mass_properties(&self, density: Real) -> MassProperties

Compute full mass properties for a given density.