Struct Sphere

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pub struct Sphere {
    pub radius: Real,
}

Expand description

A sphere defined by its radius.

Fields§

§radius: Real

Radius of the sphere.

Implementations§

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impl Sphere

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pub fn new(radius: Real) -> Self

Create a new sphere with the given radius.

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pub fn surface_area(&self) -> Real

Surface area: 4πr².

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pub fn volume_explicit(&self) -> Real

Volume: (4/3)πr³.

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

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

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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.

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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.

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

GJK support function: farthest point in direction.

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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).

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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.

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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.

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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).

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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.

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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.

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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.

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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.

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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.

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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.

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

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

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

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

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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).

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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].

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

Spherical cap surface area (curved part only).

Area = 2π r h.

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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|.

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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.

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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.

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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.

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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.

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