Struct S1Angle 

#[repr(C)]
pub struct S1Angle {
    pub radians: f64,
}

This class represents a one-dimensional angle (as opposed to a two-dimensional solid angle). It has methods for converting angles to or from radians, degrees, and the E5/E6/E7 representations (i.e. degrees multiplied by 1e5/1e6/1e7 and rounded to the nearest integer).

The internal representation is a double-precision value in radians, so conversion to and from radians is exact. Conversions between E5, E6, E7, and Degrees are not always exact; for example, Degrees(3.1) is different from E6(3100000) or E7(310000000). However, the following properties are guaranteed for any integer “n”, provided that “n” is in the input range of both functions:

$$ Degrees(n) == E6(1000000 * n) $$ $$ Degrees(n) == E7(10000000 * n) $$ $$ E6(n) == E7(10 * n) $$

The corresponding properties are not true for E5, so if you use E5 then don’t test for exact equality when comparing to other formats such as Degrees or E7.

The following conversions between degrees and radians are exact:

$$ Degrees(180) == Radians(M_PI); $$ $$ Degrees(45 * k) == Radians(k * M_PI / 4) for k == 0..8 $$

These identities also hold when the arguments are scaled up or down by any power of 2. Some similar identities are also true, for example, Degrees(60) == Radians(M_PI / 3), but be aware that this type of identity does not hold in general. For example, Degrees(3) != Radians(M_PI / 60).

Similarly, the conversion to radians means that Angle::Degrees(x).degrees() does not always equal “x”. For example,

$$ S1Angle::Degrees(45 * k).degrees() == 45 * k for k == 0..8 $$ but $$ S1Angle::Degrees(60).degrees() != 60. $$

This means that when testing for equality, you should allow for numerical errors (EXPECT_DOUBLE_EQ) or convert to discrete E5/E6/E7 values first.

CAVEAT: All of the above properties depend on “double” being the usual 64-bit IEEE 754 type (which is true on almost all modern platforms).

This class is intended to be copied by value as desired. It uses the default copy constructor and assignment operator.

Usage

Methods that are available:

• S1Angle::new: Create an angle
• S1Angle::infinity: Return an angle representing infinity
• S1Angle::from_degrees: Convert an angle in degrees to an angle in radians
• S1Angle::to_degrees: Convert an angle in radians to an angle in degrees
• S1Angle::to_e5: Convert an angle in radians to an angle in degrees
• S1Angle::to_e6: Convert an angle in radians to an angle in degrees
• S1Angle::to_e7: Convert an angle in radians to an angle in degrees
• S1Angle::from_s2points: Convert two S2Point points to an angle
• S1Angle::from_lon_lat: Convert two S2LatLng points to an angle
• S1Angle::to_meters: Convert an angle in radians to an angle in meters
• S1Angle::from_meters: Convert an angle in meters to an angle in radians
• S1Angle::to_km: Convert an angle in radians to an angle in kilometers
• S1Angle::from_km: Convert an angle in kilometers to an angle in radians
• S1Angle::e5: Build an angle in E5 format.
• S1Angle::e6: Build an angle in E6 format.
• S1Angle::e7: Build an angle in E7 format.
• S1Angle::normalize: Normalize this angle to the range (-180, 180] degrees.
• S1Angle::modulo: Returns the remainder when dividing by modulus

Fields

radians: f64

Angle in radians

Implementations

impl S1Angle

pub fn new(radians: f64) -> Self

Creates an S1Angle from a value in radians.

pub fn infinity() -> Self

Creates an S1Angle with an infinite value.

pub fn from_degrees(degrees: f64) -> Self

Creates an S1Angle from a value in degrees, converting it to radians.

pub fn to_degrees(&self) -> f64

Returns the angle in degrees.

pub fn to_e5(e5_: f64) -> Self

build an angle in E5 format.

pub fn to_e6(e6_: f64) -> Self

build an angle in E6 format.

pub fn to_e7(e7_: f64) -> Self

build an angle in E7 format.

pub fn from_s2points(a: &S2Point, b: &S2Point) -> Self

Return the angle between two points, which is also equal to the distance between these points on the unit sphere. The points do not need to be normalized. This function has a maximum error of 3.25 * DBL_EPSILON (or 2.5 * DBL_EPSILON for angles up to 1 radian). If either point is zero-length (e.g. an uninitialized S2Point), or almost zero-length, the resulting angle will be zero.

pub fn from_lon_lat<M1: MValueCompatible, M2: MValueCompatible>( a: &LonLat<M1>, b: &LonLat<M2>, ) -> Self

Like the constructor above, but return the angle (i.e., distance) between two S2LatLng points. This function has about 15 digits of accuracy for small distances but only about 8 digits of accuracy as the distance approaches 180 degrees (i.e., nearly-antipodal points).

pub fn to_meters(&self, radius: Option<f64>) -> f64

Convert an angle in radians to an angle in meters If no radius is specified, the Earth’s radius is used.

pub fn from_meters(angle: f64, radius: Option<f64>) -> Self

Convert an angle in meters to an angle in radians If no radius is specified, the Earth’s radius is used.

pub fn to_km(&self, radius: Option<f64>) -> f64

Convert an angle in radians to an angle in kilometers If no radius is specified, the Earth’s radius is used.

pub fn from_km(angle: f64, radius: Option<f64>) -> Self

Convert an angle in kilometers to an angle in radians If no radius is specified, the Earth’s radius is used.

pub fn e5(&self) -> f64

Build an angle in E5 format.

pub fn e6(&self) -> f64

Build an angle in E6 format.

pub fn e7(&self) -> f64

Build an angle in E7 format.

pub fn normalize(&self) -> Self

Normalize this angle to the range (-180, 180] degrees.

pub fn modulo(&self, modulus: f64) -> Self

Returns the remainder when dividing by modulus

Methods from Deref<Target = f64>

pub const RADIX: u32 = 2u32

pub const MANTISSA_DIGITS: u32 = 53u32

pub const DIGITS: u32 = 15u32

pub const EPSILON: f64 = 2.2204460492503131E-16f64

pub const MIN: f64 = -1.7976931348623157E+308f64

pub const MIN_POSITIVE: f64 = 2.2250738585072014E-308f64

pub const MAX: f64 = 1.7976931348623157E+308f64

pub const MIN_EXP: i32 = -1_021i32

pub const MAX_EXP: i32 = 1_024i32

pub const MIN_10_EXP: i32 = -307i32

pub const MAX_10_EXP: i32 = 308i32

pub const NAN: f64 = NaN_f64

pub const INFINITY: f64 = +Inf_f64

pub const NEG_INFINITY: f64 = -Inf_f64

pub fn total_cmp(&self, other: &f64) -> Ordering

Returns the ordering between self and other.

Unlike the standard partial comparison between floating point numbers, this comparison always produces an ordering in accordance to the totalOrder predicate as defined in the IEEE 754 (2008 revision) floating point standard. The values are ordered in the following sequence:

• negative quiet NaN
• negative signaling NaN
• negative infinity
• negative numbers
• negative subnormal numbers
• negative zero
• positive zero
• positive subnormal numbers
• positive numbers
• positive infinity
• positive signaling NaN
• positive quiet NaN.

The ordering established by this function does not always agree with the PartialOrd and PartialEq implementations of f64. For example, they consider negative and positive zero equal, while total_cmp doesn’t.

The interpretation of the signaling NaN bit follows the definition in the IEEE 754 standard, which may not match the interpretation by some of the older, non-conformant (e.g. MIPS) hardware implementations.

Example

struct GoodBoy {
    name: String,
    weight: f64,
}

let mut bois = vec![
    GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
    GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
    GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
    GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
    GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
    GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
];

bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));

// `f64::NAN` could be positive or negative, which will affect the sort order.
if f64::NAN.is_sign_negative() {
    assert!(bois.into_iter().map(|b| b.weight)
        .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::INFINITY].iter())
        .all(|(a, b)| a.to_bits() == b.to_bits()))
} else {
    assert!(bois.into_iter().map(|b| b.weight)
        .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
        .all(|(a, b)| a.to_bits() == b.to_bits()))
}

Trait Implementations

impl Add<f64> for S1Angle

type Output = S1Angle

The resulting type after applying the + operator.

fn add(self, rhs: f64) -> Self

Performs the + operation.

impl Add for S1Angle

type Output = S1Angle

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl Clone for S1Angle

fn clone(&self) -> S1Angle

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for S1Angle

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

Formats the value using the given formatter.

impl Default for S1Angle

fn default() -> S1Angle

Returns the “default value” for a type.

impl Deref for S1Angle

type Target = f64

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl Div<f64> for S1Angle

type Output = S1Angle

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> Self

Performs the / operation.

impl Div for S1Angle

type Output = S1Angle

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Performs the / operation.

impl From<S1Angle> for S1ChordAngle

fn from(angle: S1Angle) -> S1ChordAngle

Converts to this type from the input type.

impl From<S1ChordAngle> for S1Angle

fn from(c_angle: S1ChordAngle) -> S1Angle

Converts to this type from the input type.

impl From<f64> for S1Angle

fn from(radians: f64) -> S1Angle

Converts to this type from the input type.

impl Mul<f64> for S1Angle

type Output = S1Angle

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> Self

Performs the * operation.

impl Mul for S1Angle

type Output = S1Angle

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl Neg for S1Angle

type Output = S1Angle

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl Ord for S1Angle

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq<f64> for S1Angle

fn eq(&self, other: &f64) -> 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 PartialEq for S1Angle

fn eq(&self, other: &Self) -> 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 PartialOrd<f64> for S1Angle

fn partial_cmp(&self, other: &f64) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialOrd for S1Angle

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Rem<f64> for S1Angle

type Output = S1Angle

The resulting type after applying the % operator.

fn rem(self, modulus: f64) -> Self::Output

Performs the % operation.

impl RemAssign<f64> for S1Angle

fn rem_assign(&mut self, modulus: f64)

Performs the %= operation.

impl Sub<f64> for S1Angle

fn sub(self, rhs: f64) -> Self

Subtracts a value from the radians of the chord angle.

type Output = S1Angle

The resulting type after applying the - operator.

impl Sub for S1Angle

type Output = S1Angle

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl Copy for S1Angle

impl Eq for S1Angle