Struct Cone 

pub struct Cone {
    pub radius: Real,
    pub half_height: Real,
}

A cone defined by radius and half-height along the Y axis. Base is at y = -half_height, apex at y = +half_height.

Fields

radius: Real

Radius of the base.

half_height: Real

Half-height along the Y axis.

Implementations

impl Cone

pub fn new(radius: Real, half_height: Real) -> Self

Create a new cone.

pub fn volume_explicit(&self) -> Real

Volume: πr²h/3 (h = full height = 2*half_height).

pub fn surface_area(&self) -> Real

Surface area: base disk + lateral surface = πr² + πr*slant. slant = sqrt(r² + h²) where h = full height.

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

Inertia tensor as [[f64;3\];3] row-major.

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 (or inside) the cone to point p.

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

GJK support function using plain arrays. Returns the farthest point on the cone in the given direction.

pub fn slant_height(&self) -> f64

Slant height of the cone: sqrt(r² + h²).

pub fn half_angle(&self) -> f64

Half angle of the cone in radians: atan(r / h).

pub fn lateral_surface_area(&self) -> f64

Lateral (side) surface area only: πr * slant.

pub fn base_area(&self) -> f64

Base area: πr².

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

Returns true if p is inside the cone.

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

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

pub fn radius_at_y(&self, y: f64) -> f64

Radius at a given y coordinate (clamped to cone range).

pub fn truncated_cone(&self, cut_ratio: f64) -> (f64, f64, f64)

Create a truncated cone (frustum) by cutting at a given height ratio. cut_ratio is in [0, 1] where 0 = base, 1 = apex. Returns (top_radius, bottom_radius, half_height).

pub fn truncated_cone_volume(&self, cut_ratio: f64) -> f64

Volume of a truncated cone (frustum). cut_ratio is in [0, 1].

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

Ray cast against only the base cap at y = -half_height.

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

Closest point on the cone’s lateral surface to a point. This projects onto the side surface only (ignoring base cap).

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

Analytic ray-cone intersection (same as ray_cast but returns plain arrays). Identical to ray_cast_array but additionally returns a boolean indicating whether the hit is on the lateral surface (true) or base cap (false).

pub fn intersects_plane(&self, plane_normal: [f64; 3], plane_d: f64) -> bool

Cone-plane intersection.

Tests whether the cone intersects a plane defined by plane_normal (unit) and plane_d (signed distance from origin: dot(n, x) = plane_d).

Returns true if any part of the cone (including base disk) is on or crosses the plane.

pub fn frustum_from_cone(&self, y_bottom: f64, y_top: f64) -> (f64, f64, f64)

Compute a frustum (truncated cone) from this cone.

Cuts the cone at heights y_bottom and y_top (in cone-local space, where -half_height ≤ y_bottom < y_top ≤ half_height).

Returns (bottom_radius, top_radius, frustum_half_height).

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

Cone SDF (Signed Distance Function).

Returns negative inside the cone, positive outside. Same as signed_distance but exposed under the SDF naming convention.

pub fn intersects_sphere( &self, sphere_center: [f64; 3], sphere_radius: f64, ) -> bool

Cone-sphere intersection test.

Returns true if the sphere (center + radius) overlaps the cone. Uses the closest-point approach: if the closest point on the cone to the sphere center is within sphere_radius, they intersect.

pub fn frustum_lateral_area(&self, y_bottom: f64, y_top: f64) -> f64

Lateral surface area of a frustum derived from this cone.

y_bottom and y_top are in cone-local Y coordinates. Lateral area = π * (r_bottom + r_top) * slant_height_frustum.

pub fn apex_angle(&self) -> f64

Apex angle of the cone (full angle at the apex), in radians.

The full apex angle is 2 * atan(r / h) where h is the full height.

pub fn double_cone_params(&self) -> (f64, f64)

Create a double cone (bicone) by reflecting this cone across its base.

Returns the parameters of the upper half (this cone) and the lower half (same dimensions, mirrored). Both have apex at ±half_height.

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

Returns true if p is inside the double cone (both upper and lower).

The double cone is symmetric about y=0. Upper half: apex at +half_height, lower half: apex at -half_height.

pub fn unfold_lateral(&self, u: f64, t_slant: f64) -> [f64; 2]

Lateral surface unfolding: convert (u, t) to a point in the unrolled lateral surface plane.

In the unrolled sector the slant height becomes the radial distance and the azimuth u is scaled by sin(half_angle). Returns (x_unrolled, y_unrolled).

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

Bounding cone for a set of points: returns the smallest half-angle cone with its apex at the origin and axis along +Y that contains all points.

Returns (axis_half_angle_radians, axis_elevation) where the axis is fixed to +Y.

pub fn volume_swept(&self, delta: [f64; 3]) -> f64

Volume swept when the cone translates by vector delta.

Approximate: V_cone + base_area * |delta|.

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

Cone SDF gradient (approximate unit normal direction).

Returns the gradient of the SDF at p, suitable as the collision normal.

pub fn ray_intersection_count( &self, origin: [f64; 3], direction: [f64; 3], max_toi: f64, ) -> usize

Ray-cone intersection count (lateral + base cap).

Returns the number of valid positive-t intersections within [0, max_toi].

pub fn solid_angle(&self) -> f64

Compute the solid angle subtended by the cone at the apex.

For a cone with half-angle α, the solid angle is 2π(1 - cos α).

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

Generate points on the base circle of the cone.

Returns n equally-spaced points on the base rim at y = -half_height.

pub fn sphere_inside_cone(&self, center: [f64; 3], sphere_radius: f64) -> bool

Test whether a sphere at center with sphere_radius is entirely inside the cone (a stricter test than intersects_sphere).

pub fn random_lateral_surface_point(&self, seed: u64) -> [f64; 3]

Sample a random point on the cone’s lateral surface using a deterministic PRNG.

Trait Implementations

impl Clone for Cone

fn clone(&self) -> Cone

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Cone

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

Formats the value using the given formatter.

impl Shape for Cone

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.