Struct Spherical 

pub struct Spherical<const N: usize> { /* private fields */ }

Point on the surface of a sphere.

Spherical is a point on a unit N-sphere embedded in (N+1)-dimensional euclidean space. Explicitly, the N-sphere is defined by the set of (N+1)-dimensional points whose components satisfy

x_1^2 + x_2^2 + \cdots + x_{N+1}^1 = 1.0

Note that the radius is fixed to be 1.0.

Implementations

impl<const N: usize> Spherical<N>

pub fn coordinates(&self) -> &[f64; N]

Get the coordinates of the point

pub fn point(&self) -> &Cartesian<N>

Get the point of the sphere

pub fn from_cartesian_coordinates(point: Cartesian<N>) -> Spherical<N>

Construct a Sphere given a Cartesian vector and a radius.

Panics

Panics when the point is not sufficiently close to the sphere’s surface.

pub fn stereographic_projection(&self) -> Vec<f64>

Implements a stereographic projection from the N-sphere to an N-dimensional plane.

Example

use hoomd_manifold::Spherical;
use hoomd_vector::Cartesian;

let x = Cartesian::from([0.5_f64.sqrt(), 0.0, -(0.5_f64.sqrt())]);
let projection =
    Spherical::from_cartesian_coordinates(x).stereographic_projection();
assert_eq!(
    [1.0 / (2.0_f64.sqrt() + 1.0), 0.0],
    [projection[0], projection[1]]
);

impl Spherical<3>

pub fn from_polar_coordinates(theta: f64, phi: f64) -> Spherical<3>

Create a 2-sphere from spherical coordinates

impl Spherical<4>

pub fn from_polar_coordinates( theta: f64, phi_1: f64, phi_2: f64, ) -> Spherical<4>

Create a 3-sphere from spherical coordinates

Trait Implementations

impl<const N: usize> AbsDiffEq for Spherical<N>

type Epsilon = <Cartesian<N> as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximimate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of [AbsDiffEq::abs_diff_eq].

impl<const N: usize> Clone for Spherical<N>

fn clone(&self) -> Spherical<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> Debug for Spherical<N>

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

Formats the value using the given formatter.

impl<const N: usize> Default for Spherical<N>

fn default() -> Self

Returns the “default value” for a type.

impl<'de, const N: usize> Deserialize<'de> for Spherical<N>

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Distribution<Spherical<3>> for SphericalDisk

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Spherical<3>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl Metric for Spherical<3>

fn distance(&self, other: &Self) -> f64

The distance between two Spherical<3> points.

Explicitly, the metric for two points $\vec{u}$ and $\vec{v}$ on a 2-sphere with radius $R$ is given by

d_{S_2}(\vec{u}, \vec{v}) = R \arccos\left[\frac{1}{R^2}(u_1v_1 + u_2v_2 + u_3v_3)\right]

This choice of metric furnishes a representation of 2-dimensional spherical space with Gaussian curvature $K = 1/R^2$.

fn distance_squared(&self, other: &Self) -> f64

Compute the squared distance between two vectors belonging to a metric space.

fn n_dimensions(&self) -> usize

Return the number of dimensions in this vector space.

impl Metric for Spherical<4>

fn distance(&self, other: &Self) -> f64

The distance between two Spherical<4> points.

Explicitly, the metric for two points $\vec{u}$ and $\vec{v}$ on a 3-sphere with radius $R$ is given by

d_{S_3}(\vec{u}, \vec{v}) = R \arccos\left[\frac{1}{R^2}(u_1v_1 + u_2v_2 + u_3v_3 + u_4v_4)\right]

This choice of metric furnishes a representation of 3-dimensional spherical space with Gaussian curvature $K = 1/R^2$.

fn distance_squared(&self, other: &Self) -> f64

Compute the squared distance between two vectors belonging to a metric space.

fn n_dimensions(&self) -> usize

Return the number of dimensions in this vector space.

impl<const N: usize> PartialEq for Spherical<N>

fn eq(&self, other: &Spherical<N>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<const N: usize> RelativeEq for Spherical<N>

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of [RelativeEq::relative_eq].

impl<const N: usize> Serialize for Spherical<N>

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<const N: usize> Copy for Spherical<N>

impl<const N: usize> StructuralPartialEq for Spherical<N>