Struct Sphere

Source

pub struct Sphere { /* private fields */ }

Expand description

A sphere in 3D: a Frame3D (origin plus local x/y/z directions) and a radius, evaluated as Rcv = r*cos(v), origin + Rcv*cos(u)*x_dir + Rcv*sin(u)*y_dir + r*sin(v)*z_dir.

§Examples

use geomcore::{Sphere, Point3D};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
assert_eq!(sphere.eval_point(0.0, 0.0), Point3D::new(3.0, 0.0, 0.0));

Implementations§

Source §

impl Sphere

Source

pub fn new( center: Point3D, radius: f64, ) -> Result<Sphere, SphereConstructionError>

Creates a sphere from a center and a radius, using a world-aligned frame (x/y/z directions matching Vector3D::X/Vector3D::Y/ Vector3D::Z) at center.

§Errors

Returns SphereConstructionError::NegativeRadius if radius < 0.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::new(1.0, 2.0, 3.0), 2.0).unwrap();
assert_eq!(sphere.center(), Point3D::new(1.0, 2.0, 3.0));

Source

pub fn from_frame( frame: Frame3D, radius: f64, ) -> Result<Sphere, SphereConstructionError>

Creates a sphere from a frame and a radius directly.

§Errors

Returns SphereConstructionError::NegativeRadius if radius < 0.

§Examples

use geomcore::{Frame3D, Sphere};
let sphere = Sphere::from_frame(Frame3D::WORLD, 2.0).unwrap();
assert_eq!(sphere.frame(), Frame3D::WORLD);

Source

pub fn center(&self) -> Point3D

Returns the center of the sphere.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::new(1.0, 2.0, 3.0), 2.0).unwrap();
assert_eq!(sphere.center(), Point3D::new(1.0, 2.0, 3.0));

Source

pub fn frame(&self) -> Frame3D

Returns the sphere’s frame.

§Examples

use geomcore::{Frame3D, Sphere};
let sphere = Sphere::from_frame(Frame3D::WORLD, 2.0).unwrap();
assert_eq!(sphere.frame(), Frame3D::WORLD);

Source

pub fn radius(&self) -> f64

Returns the sphere’s radius.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::ORIGIN, 2.0).unwrap();
assert_eq!(sphere.radius(), 2.0);

Source

pub fn eval_point(&self, u: f64, v: f64) -> Point3D

Evaluates the point on the sphere at (u, v). See the type-level docs for the formula.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
assert_eq!(sphere.eval_point(0.0, 0.0), Point3D::new(3.0, 0.0, 0.0));

Source

pub fn eval_points(&self, uvs: &[(f64, f64)]) -> Vec<Point3D>

Evaluates the points on the sphere at each (u, v) in uvs.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
let points = sphere.eval_points(&[(0.0, 0.0)]);
assert_eq!(points[0], Point3D::new(3.0, 0.0, 0.0));

Source

pub fn eval_derivative(&self, u: f64, v: f64, du: u32, dv: u32) -> Vector3D

Evaluates the derivative of order (du, dv) at (u, v). See surface_math::analytic::sphere_derivative for the formulas.

§Panics

Panics if du + dv == 0 (use Sphere::eval_point for the position itself) or if du + dv > 2.

§Examples

use geomcore::{Point3D, Sphere, Vector3D};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
assert_eq!(sphere.eval_derivative(0.0, 0.0, 0, 1), Vector3D::Z * 3.0);

Source

pub fn parameters_of(&self, point: Point3D) -> (f64, f64)

Recovers (u, v) of a point on (or near) the sphere. See surface_math::analytic::sphere_parameters for the formula, including the pole handling.

§Examples

use geomcore::{Point3D, Sphere};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
let (u, v) = sphere.parameters_of(Point3D::new(3.0, 0.0, 0.0));
assert_eq!((u, v), (0.0, 0.0));

Source

pub fn contains(&self, point: Point3D, tol: Tolerance) -> bool

Returns whether point lies on the sphere: the inverse parameters are recovered with Sphere::parameters_of and re-evaluated, and the point counts as contained when the re-evaluated point is within tol.confusion of it.

§Examples

use geomcore::{Point3D, Sphere, Tolerance};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
let tol = Tolerance::DEFAULT;
assert!(sphere.contains(Point3D::new(3.0, 0.0, 0.0), tol));
assert!(!sphere.contains(Point3D::ORIGIN, tol));

Source

pub fn project_point(&self, point: Point3D, tol: Tolerance) -> SurfaceProjection

Projects point onto the sphere, returning the (u, v) parameters of the closest point and its distance. Distances within tol.confusion snap to 0.0, matching Sphere::contains.

§Examples

use geomcore::{Point3D, Sphere, Tolerance};
let sphere = Sphere::new(Point3D::ORIGIN, 3.0).unwrap();
let proj = sphere.project_point(Point3D::new(4.0, 0.0, 0.0), Tolerance::DEFAULT);
assert_eq!((proj.u, proj.v), (0.0, 0.0));
assert_eq!(proj.distance, 1.0);

Source

pub fn project_points( &self, points: &[Point3D], tol: Tolerance, ) -> Vec<SurfaceProjection>

Projects each point in points onto the sphere.

Default-style batch wrapper over Sphere::project_point: one native call per batch, mirroring Sphere::eval_points.

Source

pub fn intersect_sphere( &self, other: &Sphere, tol: Tolerance, ) -> SphereSphereIntersection

Intersects this sphere with another sphere.

Concentric spheres (center distance within tol.confusion) are SphereSphereIntersection::Coincident when the radii agree within tolerance, else SphereSphereIntersection::Empty. Otherwise the radical plane cuts the center line at distance a = (r1^2 - r2^2 + d^2) / (2d) from this center; a negative r1^2 - a^2 (beyond tolerance) misses (SphereSphereIntersection::Empty), a near-zero one grazes in a single SphereSphereIntersection::TangentPoint, and the rest meet in a Circle3D whose axis points from this center to the other.

§Examples

use geomcore::{Point3D, Sphere, SphereSphereIntersection, Tolerance};
let s1 = Sphere::new(Point3D::ORIGIN, 2.0).unwrap();
let s2 = Sphere::new(Point3D::new(3.0, 0.0, 0.0), 2.0).unwrap();
let tol = Tolerance::DEFAULT;
match s1.intersect_sphere(&s2, tol) {
    SphereSphereIntersection::Circle(circle) => {
        assert_eq!(circle.center(), Point3D::new(1.5, 0.0, 0.0));
    }
    _ => panic!("expected a circle"),
}