CGMath

https://docs.rs/cgmath/0.18.0
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### from_value() Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Array.html

Example demonstrating the usage of the `from_value()` method to construct a vector from a single value.

```APIDOC
## fn from_value(value: Self::Element) -> Self

Construct a vector from a single value, replicating it.

```rust
use cgmath::prelude::*;
use cgmath::Vector3;

assert_eq!(Vector3::from_value(1),
           Vector3::new(1, 1, 1));
```
```

--------------------------------

### Relative Equality Comparison Examples

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Relative.html

Demonstrates how to use the Relative struct's default settings and how to customize epsilon and max_relative for equality checks. These examples use the `eq` method.

```rust
use std::f64;
use approx::Relative;

Relative::default().eq(&1.0, &1.0);
Relative::default().epsilon(f64::EPSILON).eq(&1.0, &1.0);
Relative::default().max_relative(1.0).eq(&1.0, &1.0);
Relative::default().epsilon(f64::EPSILON).max_relative(1.0).eq(&1.0, &1.0);
Relative::default().max_relative(1.0).epsilon(f64::EPSILON).eq(&1.0, &1.0);
```

--------------------------------

### len() Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Array.html

Example demonstrating the usage of the `len()` method to get the number of elements in a vector.

```APIDOC
## fn len() -> usize

Get the number of elements in the array type

```rust
use cgmath::prelude::*;
use cgmath::Vector3;

assert_eq!(Vector3::<f32>::len(), 3);
```
```

--------------------------------

### Basis2 Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Basis2.html

Demonstrates how to use Basis2 for rotating a vector in a 2D plane.

```APIDOC
### Example
```rust
use cgmath::Rad;
use cgmath::Vector2;
use cgmath::{Matrix, Matrix2};
use cgmath::{Rotation, Rotation2, Basis2};
use cgmath::UlpsEq;
use std::f64;

// For simplicity, we will rotate the unit x vector to the unit y vector --
// so the angle is 90 degrees, or π/2.
let unit_x: Vector2<f64> = Vector2::unit_x();
let rot: Basis2<f64> = Rotation2::from_angle(Rad(0.5f64 * f64::consts::PI));

// Rotate the vector using the two-dimensional rotation matrix:
let unit_y = rot.rotate_vector(unit_x);

// Since sin(π/2) may not be exactly zero due to rounding errors, we can
// use approx's assert_ulps_eq!() feature to show that it is close enough.
// assert_ulps_eq!(&unit_y, &Vector2::unit_y()); // TODO: Figure out how to use this

// This is exactly equivalent to using the raw matrix itself:
let unit_y2: Matrix2<_> = rot.into();
let unit_y2 = unit_y2 * unit_x;
assert_eq!(unit_y2, unit_y);

// Note that we can also concatenate rotations:
let rot_half: Basis2<f64> = Rotation2::from_angle(Rad(0.25f64 * f64::consts::PI));
let unit_y3 = (rot_half * rot_half).rotate_vector(unit_x);
// assert_ulps_eq!(&unit_y3, &unit_y2); // TODO: Figure out how to use this
```
```

--------------------------------

### Vector Addition Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.VectorSpace.html

Demonstrates vector addition, subtraction, and negation using the Add, Sub, and Neg traits.

```APIDOC
## Vector Addition

Vectors can be added, subtracted, or negated via the following traits:
  * `Add<Output = Self>`
  * `Sub<Output = Self>`
  * `Neg<Output = Self>`

```rust
use cgmath::Vector3;

let velocity0 = Vector3::new(1, 2, 0);
let velocity1 = Vector3::new(1, 1, 0);

let total_velocity = velocity0 + velocity1;
let velocity_diff = velocity1 - velocity0;
let reversed_velocity0 = -velocity0;
```

Vector spaces are also required to implement the additive identity trait, `Zero`. Adding this to another vector should have no effect:

```rust
use cgmath::prelude::*
use cgmath::Vector2;

let v = Vector2::new(1, 2);
assert_eq!(v + Vector2::zero(), v);
```
```

--------------------------------

### Ulps comparison examples

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Ulps.html

Demonstrates how to use the Ulps struct with default and customized epsilon and max_ulps values for equality checks. Requires importing Ulps and f64::EPSILON.

```rust
use std::f64;
use approx::Ulps;

Ulps::default().eq(&1.0, &1.0);
Ulps::default().epsilon(f64::EPSILON).eq(&1.0, &1.0);
Ulps::default().max_ulps(4).eq(&1.0, &1.0);
Ulps::default().epsilon(f64::EPSILON).max_ulps(4).eq(&1.0, &1.0);
Ulps::default().max_ulps(4).epsilon(f64::EPSILON).eq(&1.0, &1.0);
```

--------------------------------

### AbsDiff Example Usage

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.AbsDiff.html

Demonstrates how to use the AbsDiff struct for approximate equality checks.

```APIDOC
## §Example

```
use std::f64;
use approx::AbsDiff;

AbsDiff::default().eq(&1.0, &1.0);
AbsDiff::default().epsilon(f64::EPSILON).eq(&1.0, &1.0);
```
```

--------------------------------

### Scalar Multiplication Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.VectorSpace.html

Illustrates scalar multiplication and division of vectors using the Mul and Div traits.

```APIDOC
## Scalar Multiplication

Vectors can be multiplied or divided by their associated scalars via the following traits:
  * `Mul<Self::Scalar, Output = Self>`
  * `Div<Self::Scalar, Output = Self>`
  * `Rem<Self::Scalar, Output = Self>`

```rust
use cgmath::Vector2;

let translation = Vector2::new(3.0, 4.0);
let scale_factor = 2.0;

let upscaled_translation = translation * scale_factor;
let downscaled_translation = translation / scale_factor;
```
```

--------------------------------

### Point3 as_ref() to Array and Tuple

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/point.rs.html

Demonstrates using as_ref() to get references to an array and a tuple from a Point3.

```rust
let p = POINT3;
{
    let p: &[i32; 3] = p.as_ref();
    assert_eq!(p, &[1, 2, 3]);
}
{
    let p: &(i32, i32, i32) = p.as_ref();
    assert_eq!(p, &(1, 2, 3));
}
```

--------------------------------

### Point3 Slicing and Length

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/point.rs.html

Demonstrates how to access slices of a Point3 and get their lengths.

```rust
assert_eq!(&POINT3[2..], &[3]);
assert_eq!(&POINT3[1..], &[2, 3]);
assert_eq!(POINT3[2..].len(), 1);
assert_eq!(POINT3[1..].len(), 2);
assert_eq!(&POINT3[..], &[1, 2, 3]);
assert_eq!(POINT3[..].len(), 3);
```

--------------------------------

### EuclideanSpace for Point3<S>

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point3.html

Provides methods for Euclidean space operations on Point3, such as getting the origin, converting to/from vectors, and calculating midpoints.

```APIDOC
## EuclideanSpace for Point3<S>

### Description
Provides methods for Euclidean space operations on Point3, such as getting the origin, converting to/from vectors, and calculating midpoints.

### Associated Types
- **Scalar**: The associated scalar over which the space is defined.
- **Diff**: The associated space of displacement vectors.

### Methods
- **origin() -> Point3<S>**
  The point at the origin of the Euclidean space.
- **from_vec(v: Vector3<S>) -> Point3<S>**
  Convert a displacement vector to a point.
- **to_vec(self) -> Vector3<S>**
  Convert a point to a displacement vector.
- **dot(self, v: Vector3<S>) -> S**
  This is a weird one, but its useful for plane calculations.
- **midpoint(self, other: Self) -> Self**
  Returns the middle point between two other points.
- **centroid(points: &[Self]) -> Self**
  Returns the average position of all points in the slice.
```

--------------------------------

### Scalar Multiplication Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/trait.VectorSpace.html

Illustrates scalar multiplication and division of vectors using the Mul, Div, and Rem traits.

```APIDOC
## Scalar multiplication

Vectors can be multiplied or divided by their associated scalars via the following traits:
  * `Mul<Self::Scalar, Output = Self>`
  * `Div<Self::Scalar, Output = Self>`
  * `Rem<Self::Scalar, Output = Self>`

```rust
use cgmath::Vector2;

let translation = Vector2::new(3.0, 4.0);
let scale_factor = 2.0;

let upscaled_translation = translation * scale_factor;
let downscaled_translation = translation / scale_factor;
```
```

--------------------------------

### AbsDiff Usage Example

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.AbsDiff.html

Demonstrates basic usage of the AbsDiff struct for equality checks. The `default()` method creates an AbsDiff with a default epsilon, while `epsilon()` allows specifying a custom tolerance.

```rust
use std::f64;
use approx::AbsDiff;

AbsDiff::default().eq(&1.0, &1.0);
AbsDiff::default().epsilon(f64::EPSILON).eq(&1.0, &1.0);
```

--------------------------------

### Test Quaternion Slerp Start

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/quaternion.rs.html

Tests the slerp function with an interpolation factor of 0.0. The result should be the starting quaternion.

```rust
    #[test]
    fn test_slerp_start() {
        let q = Quaternion::from([0.5f64.sqrt(), 0.0, 0.5f64.sqrt(), 0.0]);
        let r = Quaternion::from([0.5, 0.5, 0.5, 0.5]);
        assert_ulps_eq!(q, q.slerp(r, 0.0));
    }
```

--------------------------------

### from

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Creates a new instance from a given value.

```APIDOC
## from

### Description
Returns the argument unchanged.

### Signature
`fn from(t: T) -> T`
```

--------------------------------

### Test Quaternion Nlerp Start

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/quaternion.rs.html

Tests the nlerp function with an interpolation factor of 0.0. The result should be the starting quaternion.

```rust
    #[test]
    fn test_nlerp_start() {
        let q = Quaternion::from([0.5f64.sqrt(), 0.0, 0.5f64.sqrt(), 0.0]);
        let r = Quaternion::from([0.5, 0.5, 0.5, 0.5]);
        assert_ulps_eq!(q, q.nlerp(r, 0.0));
    }
```

--------------------------------

### Get Array Length

Source: https://docs.rs/cgmath/0.18.0/cgmath/trait.Array.html

Demonstrates how to get the number of elements in an array type using the `len` method. This is a required method for the `Array` trait.

```rust
use cgmath::prelude::*
use cgmath::Vector3;

assert_eq!(Vector3::<f32>::len(), 3);
```

--------------------------------

### Get Array Length

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Array.html

Demonstrates how to get the number of elements in an array type using the `len` method. Requires importing `cgmath::prelude::*`.

```rust
use cgmath::prelude::*;
use cgmath::Vector3;

assert_eq!(Vector3::<f32>::len(), 3);
```

--------------------------------

### Construct Array from Value

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Array.html

Shows how to create an array where all elements are initialized to a single provided value using `from_value`. Requires importing `cgmath::prelude::*`.

```rust
use cgmath::prelude::*;
use cgmath::Vector3;

assert_eq!(Vector3::from_value(1),
           Vector3::new(1, 1, 1));
```

--------------------------------

### Bounded Trait Definition

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Bounded.html

The Bounded trait requires two methods: `min_value()` to get the smallest value and `max_value()` to get the largest value a type can represent.

```APIDOC
## Trait Bounded

Numbers which have upper and lower bounds.

### Required Methods

#### fn min_value() -> Self
Returns the smallest finite number this type can represent.

#### fn max_value() -> Self
Returns the largest finite number this type can represent.
```

--------------------------------

### Import cgmath Prelude

Source: https://docs.rs/cgmath/0.18.0/cgmath/index.html

Import the main traits from the cgmath prelude to avoid importing each trait individually. This allows for convenient access to common linear algebra operations.

```rust
use cgmath::prelude::*;
```

--------------------------------

### point1

Source: https://docs.rs/cgmath/0.18.0/cgmath/fn.point1.html

The short constructor for Point1.

```APIDOC
## point1

### Description
The short constructor.

### Signature
```rust
pub const fn point1<S>(x: S) -> Point1<S>
```

### Parameters
* `x`: The value for the single component of the Point1.
```

--------------------------------

### type_id

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix3.html

Gets the TypeId of the matrix.

```APIDOC
#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
Source
```

--------------------------------

### CloneToUninit Implementation (Nightly)

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.PerspectiveFov.html

Nightly-only experimental API for performing copy-assignment from self to an uninitialized destination. Use with caution.

```rust
unsafe fn clone_to_uninit(&self, dest: *mut u8)
```

--------------------------------

### Any::type_id

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix2.html

Gets the `TypeId` of `self`.

```APIDOC
## fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
```

--------------------------------

### Conversions to Vector2

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Demonstrates how to convert various types into a Vector2.

```APIDOC
## From<&'a (S, S)> for &'a Vector2<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: &'a (S, S) - The input tuple reference.

### Returns
- &'a Vector2<S> - A reference to the created Vector2.
```

```APIDOC
## From<&'a mut [S; 2]> for &'a mut Vector2<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: &'a mut [S; 2] - The mutable input array reference.

### Returns
- &'a mut Vector2<S> - A mutable reference to the created Vector2.
```

```APIDOC
## From<&'a mut (S, S)> for &'a mut Vector2<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: &'a mut (S, S) - The mutable input tuple reference.

### Returns
- &'a mut Vector2<S> - A mutable reference to the created Vector2.
```

```APIDOC
## From<[S; 2]> for Vector2<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: [S; 2] - The input array.

### Returns
- Vector2<S> - The created Vector2.
```

```APIDOC
## From<(S, S)> for Vector2<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: (S, S) - The input tuple.

### Returns
- Vector2<S> - The created Vector2.
```

--------------------------------

### type_id

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point1.html

Gets the TypeId of the Point1 instance.

```APIDOC
## fn type_id(&self) -> TypeId

### Description
Gets the `TypeId` of `self`.

### Signature
```rust
fn type_id(&self) -> TypeId
```
```

--------------------------------

### Any: type_id

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point3.html

Provides a method to get the TypeId of a type.

```APIDOC
## fn type_id(&self) -> TypeId

### Description
Gets the `TypeId` of `self`.

### Method
`type_id`

### Returns
- TypeId - The TypeId of the object.
```

--------------------------------

### Vector Constructors and Methods

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Provides details on the `new` and `map` methods for constructing and transforming vectors, as well as the `zip` method for element-wise operations between vectors.

```APIDOC
## Vector Methods

### `new`

Construct a new vector, using the provided values.

#### Signature

```rust
pub const fn new(field1: S, field2: S, ...) -> VectorN<S>
```

### `map`

Perform the given operation on each field in the vector, returning a new point constructed from the operations.

#### Signature

```rust
pub fn map<U, F>(self, mut f: F) -> VectorN<U>
where
    F: FnMut(S) -> U
```

### `zip`

Construct a new vector where each component is the result of applying the given operation to each pair of components of the given vectors.

#### Signature

```rust
pub fn zip<S2, S3, F>(self, v2: VectorN<S2>, mut f: F) -> VectorN<S3>
where
    F: FnMut(S, S2) -> S3
```
```

--------------------------------

### Mint Crate Conversions (Into/From)

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/matrix.rs.html

Implementations for converting cgmath matrices to and from mint crate types. Requires the 'mint' feature to be enabled.

```Rust
impl<S: Clone> Into<mint::$MintN<S>> for $MatrixN<S> {
    #[inline]
    fn into(self) -> mint::$MintN<S> {
        mint::$MintN { $($field: self.$field.into()),+ }
    }
}

impl<S> From<mint::$MintN<S>> for $MatrixN<S> {
    #[inline]
    fn from(m: mint::$MintN<S>) -> Self {
        $MatrixN { $($field: m.$field.into()),+ }
    }
}
```

--------------------------------

### as_ptr

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Gets a raw pointer to the first element of the vector.

```APIDOC
## fn as_ptr(&self) -> *const Self::Element

### Description
Get the pointer to the first element of the array.

### Returns
- *const Self::Element: A constant pointer to the first element.
```

--------------------------------

### Converting between Points and Vectors

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/structure.rs.html

Explains how to convert between points and displacement vectors using `EuclideanSpace::{from_vec, to_vec}`.

```APIDOC
## Converting between points and vectors

Points can be converted to and from displacement vectors using the `EuclideanSpace::{from_vec, to_vec}` methods. These are inlined type conversions with no performance implications.
```

--------------------------------

### into

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Converts the current instance into another type.

```APIDOC
## into

### Description
Calls `U::from(self)`. That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

### Signature
`fn into(self) -> U`
```

--------------------------------

### UpperBounded Trait

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Rad.html

Provides functionality to get the maximum value representable by a type.

```APIDOC
### impl<T> UpperBounded for T
where T: Bounded,
#### fn max_value() -> T
Returns the largest finite number this type can represent
```

--------------------------------

### Any::type_id

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Euler.html

Gets the `TypeId` of `self`. This is a fundamental method for runtime type identification.

```APIDOC
## fn type_id(&self) -> TypeId

### Description
Gets the `TypeId` of `self`.

### Returns
A `TypeId` representing the type of `self`.
```

--------------------------------

### Matrix2 Constructors

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/matrix.rs.html

Provides methods for creating Matrix2 instances.

```APIDOC
## Matrix2::new

### Description
Creates a new Matrix2 by specifying each element.

### Signature
`pub const fn new(c0r0: S, c0r1: S, c1r0: S, c1r1: S) -> Matrix2<S>`

## Matrix2::from_cols

### Description
Creates a new Matrix2 from two column vectors.

### Signature
`pub const fn from_cols(c0: Vector2<S>, c1: Vector2<S>) -> Matrix2<S>`
```

--------------------------------

### Product Calculation (`Product`)

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix3.html

Enables calculating the product of multiple Matrix3 instances.

```APIDOC
## Product Calculation (`Product`)

Calculates the product of elements in an iterator.

### `product<I: Iterator<Item = &Matrix3<S>>>(iter: I) -> Matrix3<S>`
Takes an iterator of matrix references and returns their product.

### `product<I: Iterator<Item = Matrix3<S>>>(iter: I) -> Matrix3<S>`
Takes an iterator of matrices and returns their product.
```

--------------------------------

### Bounded Properties

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector4.html

Provides methods to get the minimum and maximum representable values for Vector4.

```APIDOC
## fn min_value() -> Vector4<S>

### Description
Returns the smallest finite number this type can represent.

### Method
`min_value`
```

```APIDOC
## fn max_value() -> Vector4<S>

### Description
Returns the largest finite number this type can represent.

### Method
`max_value`
```

--------------------------------

### Conversions from Vector2

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Demonstrates how to convert a Vector2 into other types.

```APIDOC
## Into<[S; 2]> for Vector2<S>

### Description
Converts this type into an array of two elements.

### Method
`into`

### Returns
- `[S; 2]` - The array representation of the vector.
```

```APIDOC
## Into<(S, S)> for Vector2<S>

### Description
Converts this type into a tuple of two elements.

### Method
`into`

### Returns
- `(S, S)` - The tuple representation of the vector.
```

--------------------------------

### UpperBounded for T

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector1.html

Implementation of the UpperBounded trait, providing a method to get the maximum value a type can represent.

```APIDOC
## impl<T> UpperBounded for T
where T: Bounded

### Methods
#### fn max_value() -> T
```

--------------------------------

### Matrix3 Constructors

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/matrix.rs.html

Provides methods for creating Matrix3 instances.

```APIDOC
## Matrix3::new

### Description
Creates a new Matrix3 by specifying each element.

### Signature
`pub const fn new(c0r0: S, c0r1: S, c0r2: S, c1r0: S, c1r1: S, c1r2: S, c2r0: S, c2r1: S, c2r2: S) -> Matrix3<S>`

## Matrix3::from_cols

### Description
Creates a new Matrix3 from three column vectors.

### Signature
`pub const fn from_cols(c0: Vector3<S>, c1: Vector3<S>, c2: Vector3<S>) -> Matrix3<S>`
```

--------------------------------

### From Conversions for Point1

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point1.html

Shows how to convert various types into Point1.

```APIDOC
## From Conversions for Point1

This section outlines the `From` trait implementations for creating `Point1` instances.

### `impl<'a, S> From<&'a [S; 1]> for &'a Point1<S>`
- **Function**: `from(v: &'a [S; 1]) -> &'a Point1<S>`
- **Description**: Converts a reference to a 1-element array into a reference to `Point1<S>`.

### `impl<'a, S> From<&'a (S,)> for &'a Point1<S>`
- **Function**: `from(v: &'a (S,)) -> &'a Point1<S>`
- **Description**: Converts a reference to a tuple of one element into a reference to `Point1<S>`.

### `impl<'a, S> From<&'a mut [S; 1]> for &'a mut Point1<S>`
- **Function**: `from(v: &'a mut [S; 1]) -> &'a mut Point1<S>`
- **Description**: Converts a mutable reference to a 1-element array into a mutable reference to `Point1<S>`.

### `impl<'a, S> From<&'a mut (S,)> for &'a mut Point1<S>`
- **Function**: `from(v: &'a mut (S,)) -> &'a mut Point1<S>`
- **Description**: Converts a mutable reference to a tuple of one element into a mutable reference to `Point1<S>`.

### `impl<S: Clone> From<[S; 1]> for Point1<S>`
- **Function**: `from(v: [S; 1]) -> Point1<S>`
- **Description**: Converts a 1-element array into `Point1<S>`.

### `impl<S> From<(S,)> for Point1<S>`
- **Function**: `from(v: (S,)) -> Point1<S>`
- **Description**: Converts a tuple of one element into `Point1<S>`.
```

--------------------------------

### Conversions from Slices and Tuples

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector3.html

Demonstrates various ways to create a Vector3 from slices and tuples, including mutable and immutable references.

```APIDOC
## From<&'a [S; 3]> for &'a Vector3<S>
Converts to this type from the input type.

### fn from(v: &'a [S; 3]) -> &'a Vector3<S>

## From<&'a (S, S, S)> for &'a Vector3<S>
Converts to this type from the input type.

### fn from(v: &'a (S, S, S)) -> &'a Vector3<S>

## From<&'a mut [S; 3]> for &'a mut Vector3<S>
Converts to this type from the input type.

### fn from(v: &'a mut [S; 3]) -> &'a mut Vector3<S>

## From<&'a mut (S, S, S)> for &'a mut Vector3<S>
Converts to this type from the input type.

### fn from(v: &'a mut (S, S, S)) -> &'a mut Vector3<S>

## From<[S; 3]> for Vector3<S>
Converts to this type from the input type.

### fn from(v: [S; 3]) -> Vector3<S>

## From<(S, S, S)> for Vector3<S>
Converts to this type from the input type.

### fn from(v: (S, S, S)) -> Vector3<S>
```

--------------------------------

### CloneToUninit: clone_to_uninit

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point3.html

Provides an experimental method for cloning data to uninitialized memory.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

### Description
Performs copy-assignment from `self` to `dest`. This is a nightly-only experimental API.

### Method
`clone_to_uninit`

### Parameters
- **dest** (*mut u8) - A mutable pointer to the destination memory.
```

--------------------------------

### AsRef<[[S; 3]; 3]> for Matrix3<S>

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix3.html

Provides a way to get a reference to a 3x3 array representation of the Matrix3.

```APIDOC
## fn as_ref(&self) -> &[[S; 3]; 3]

Converts this type into a shared reference of the (usually inferred) input type.
```

--------------------------------

### Compute tangent of an angle

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/structure.rs.html

Computes the tangent of the angle, returning a unitless ratio. Example usage with Rad type.

```rust
    /// ```rust
    /// use cgmath::prelude::*;
    /// use cgmath::Rad;
    ///
    /// let angle = Rad(35.0);
    /// let ratio: f32 = Rad::tan(angle);
    /// ```
    fn tan(self) -> Self::Unitless;
```

--------------------------------

### Short Constructor

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

A concise constructor function for creating vectors.

```APIDOC
## Short Constructor

### `constructor_name`

The short constructor.

#### Signature

```rust
pub const fn constructor_name<S>(field1: S, field2: S, ...) -> VectorN<S>
```
```

--------------------------------

### PartialEq Implementation for Perspective

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Perspective.html

Enables comparison of two Perspective projections for equality. Use this to check if two projection configurations are identical.

```rust
impl<S: PartialEq> PartialEq for Perspective<S>
fn eq(&self, other: &Perspective<S>) -> bool
```

--------------------------------

### Compute cosine of an angle

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/structure.rs.html

Computes the cosine of the angle, returning a unitless ratio. Example usage with Rad type.

```rust
    /// ```rust
    /// use cgmath::prelude::*;
    /// use cgmath::Rad;
    ///
    /// let angle = Rad(35.0);
    /// let ratio: f32 = Rad::cos(angle);
    /// ```
    fn cos(self) -> Self::Unitless;
```

--------------------------------

### Compute sine of an angle

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/structure.rs.html

Computes the sine of the angle, returning a unitless ratio. Example usage with Rad type.

```rust
    /// ```rust
    /// use cgmath::prelude::*;
    /// use cgmath::Rad;
    ///
    /// let angle = Rad(35.0);
    /// let ratio: f32 = Rad::sin(angle);
    /// ```
    fn sin(self) -> Self::Unitless;
```

--------------------------------

### Into<mint::Quaternion<S>> for Quaternion<S>

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/quaternion.rs.html

Converts a cgmath::Quaternion into a mint::Quaternion.

```APIDOC
## Into<mint::Quaternion<S>> for Quaternion<S>

### Description
Converts a `cgmath::Quaternion<S>` into a `mint::Quaternion<S>`. This requires the `mint` feature to be enabled and the scalar type `S` to implement `Clone`.

### Method
`into(self) -> mint::Quaternion<S>`

### Parameters
None

### Returns
A `mint::Quaternion<S>` instance.
```

--------------------------------

### CloneToUninit

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point1.html

Performs copy-assignment from self to a destination pointer. This is an experimental, nightly-only API.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

### Description
Performs copy-assignment from `self` to `dest`.

### Signature
```rust
unsafe fn clone_to_uninit(&self, dest: *mut u8)
```
```

--------------------------------

### CloneToUninit::clone_to_uninit

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix2.html

Performs copy-assignment from `self` to `dest`. This is a nightly-only experimental API.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (`clone_to_uninit`)
Performs copy-assignment from `self` to `dest`. Read more
```

--------------------------------

### Vector4 Range Indexing

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Demonstrates slicing Vector4 using range indices for both start and end, and full range.

```rust
#[test]
fn test_index_range() {
    assert_eq!(&VECTOR4[..2], &[1, 2]);
    assert_eq!(&VECTOR4[..3], &[1, 2, 3]);
    assert_eq!(VECTOR4[..2].len(), 2);
    assert_eq!(VECTOR4[..3].len(), 3);
    assert_eq!(&VECTOR4[2..], &[3, 4]);
    assert_eq!(&VECTOR4[1..], &[2, 3, 4]);
    assert_eq!(VECTOR4[2..].len(), 2);
    assert_eq!(VECTOR4[1..].len(), 3);
    assert_eq!(&VECTOR4[..], &[1, 2, 3, 4]);
    assert_eq!(VECTOR4[..].len(), 4);
}
```

--------------------------------

### Mint Crate Conversion Macro Calls

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/matrix.rs.html

Macro calls to generate mint conversions for Matrix2, Matrix3, and Matrix4.

```Rust
#[cfg(feature = "mint")]
mint_conversions!(Matrix2 { x, y }, ColumnMatrix2);
#[cfg(feature = "mint")]
mint_conversions!(Matrix3 { x, y, z }, ColumnMatrix3);
#[cfg(feature = "mint")]
mint_conversions!(Matrix4 { x, y, z, w }, ColumnMatrix4);
```

--------------------------------

### Point3 as_mut() to Array and Tuple

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/point.rs.html

Illustrates using as_mut() to get mutable references to an array and a tuple from a Point3.

```rust
let mut p = POINT3;
{
    let p: &mut [i32; 3] = p.as_mut();
    assert_eq!(p, &mut [1, 2, 3]);
}
{
    let p: &mut (i32, i32, i32) = p.as_mut();
    assert_eq!(p, &mut (1, 2, 3));
}
```

--------------------------------

### Mint Conversions for Point2

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/point.rs.html

Implements conversions between cgmath's Point2 and mint's Point2, useful for interoperability with other libraries.

```rust
#[cfg(feature = "mint")]
impl_mint_conversions!(Point2 { x, y }, Point2);
```

--------------------------------

### Bounded for PointN

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/point.rs.html

Implements the Bounded trait for PointN, providing methods to get the minimum and maximum possible values.

```rust
impl<S: Bounded> Bounded for $PointN<S> {
    #[inline]
    fn min_value() -> $PointN<S> {
        $PointN { $($field: S::min_value()),+ }
    }

    #[inline]
    fn max_value() -> $PointN<S> {
        $PointN { $($field: S::max_value()),+ }
    }
}
```

--------------------------------

### Conversions to Vector1

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector1.html

Demonstrates how to convert other types into a Vector1.

```APIDOC
## From<&'a mut (S,)> for &'a mut Vector1<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: &'a mut (S,) - The mutable tuple to convert from.

### Returns
- &'a mut Vector1<S> - A mutable reference to the created Vector1.
```

```APIDOC
## From<[S; 1]> for Vector1<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: [S; 1] - The array of size 1 to convert from.

### Returns
- Vector1<S> - The created Vector1.
```

```APIDOC
## From<(S,)> for Vector1<S>

### Description
Converts to this type from the input type.

### Method
`from`

### Parameters
- `v`: (S,) - The tuple containing a single element to convert from.

### Returns
- Vector1<S> - The created Vector1.
```

--------------------------------

### AsRef<[S; 9]> for Matrix3<S>

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Matrix3.html

Provides a way to get a reference to a flat array of 9 elements representing the Matrix3.

```APIDOC
## fn as_ref(&self) -> &[S; 9]

Converts this type into a shared reference of the (usually inferred) input type.
```

--------------------------------

### as_mut_ptr() - Get mutable pointer

Source: https://docs.rs/cgmath/0.18.0/cgmath/trait.Array.html

The `as_mut_ptr()` method returns a raw, mutable pointer to the first element of the array.

```APIDOC
## fn as_mut_ptr(&mut self) -> *mut Self::Element

Get a mutable pointer to the first element of the array.
```

--------------------------------

### Vector3 Creation from Array and Tuple

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Demonstrates creating a Vector3 from a slice or tuple, including mutable references. Ensure the input has the correct number of elements.

```rust
fn test_from() {
    assert_eq!(Vector3::from([1, 2, 3]), VECTOR3);
    {
        let v = &[1, 2, 3];
        let v: &Vector3<_> = From::from(v);
        assert_eq!(v, &VECTOR3);
    }
    {
        let v = &mut [1, 2, 3];
        let v: &mut Vector3<_> = From::from(v);
        assert_eq!(v, &VECTOR3);
    }
    assert_eq!(Vector3::from((1, 2, 3)), VECTOR3);
    {
        let v = &(1, 2, 3);
        let v: &Vector3<_> = From::from(v);
        assert_eq!(v, &VECTOR3);
    }
    {
        let v = &mut (1, 2, 3);
        let v: &mut Vector3<_> = From::from(v);
        assert_eq!(v, &VECTOR3);
    }
}
```

--------------------------------

### Conversions from Vector1

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector1.html

Demonstrates how to convert a Vector1 into other types.

```APIDOC
## Into<[S; 1]> for Vector1<S>

### Description
Converts this type into the (usually inferred) input type.

### Method
`into`

### Returns
- [S; 1] - The array of size 1 representation of the Vector1.
```

```APIDOC
## Into<(S,)> for Vector1<S>

### Description
Converts this type into the (usually inferred) input type.

### Method
`into`

### Returns
- (S,) - The tuple representation of the Vector1.
```

--------------------------------

### as_ptr() - Get immutable pointer

Source: https://docs.rs/cgmath/0.18.0/cgmath/trait.Array.html

The `as_ptr()` method returns a raw, immutable pointer to the first element of the array.

```APIDOC
## fn as_ptr(&self) -> *const Self::Element

Get the pointer to the first element of the array.
```

--------------------------------

### len() - Get array length

Source: https://docs.rs/cgmath/0.18.0/cgmath/trait.Array.html

The `len()` method returns the number of elements in the array type. This is a static method.

```APIDOC
## fn len() -> usize

Get the number of elements in the array type.

### Example
```rust
use cgmath::prelude::*
use cgmath::Vector3;

assert_eq!(Vector3::<f32>::len(), 3);
```
```

--------------------------------

### CloneToUninit for T

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Deg.html

Provides the experimental `clone_to_uninit` method for copy-assignment to uninitialized memory.

```APIDOC
## unsafe fn clone_to_uninit(&self, dest: *mut u8)

Performs copy-assignment from `self` to `dest`.
```

--------------------------------

### Vector2 Creation from Array and Tuple

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Demonstrates creating a Vector2 from a slice or tuple, including mutable references. Ensure the input has the correct number of elements.

```rust
fn test_from() {
    assert_eq!(Vector2::from([1, 2]), VECTOR2);
    {
        let v = &[1, 2];
        let v: &Vector2<_> = From::from(v);
        assert_eq!(v, &VECTOR2);
    }
    {
        let v = &mut [1, 2];
        let v: &mut Vector2<_> = From::from(v);
        assert_eq!(v, &VECTOR2);
    }
    assert_eq!(Vector2::from((1, 2)), VECTOR2);
    {
        let v = &(1, 2);
        let v: &Vector2<_> = From::from(v);
        assert_eq!(v, &VECTOR2);
    }
    {
        let v = &mut (1, 2);
        let v: &mut Vector2<_> = From::from(v);
        assert_eq!(v, &VECTOR2);
    }
}
```

--------------------------------

### Bounded Implementation

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Deg.html

Implementation of the Bounded trait for Deg<S>, providing methods to get the minimum and maximum representable values.

```APIDOC
### impl<S: Bounded> Bounded for Deg<S>

#### fn min_value() -> Deg<S>
Returns the smallest finite number this type can represent

#### fn max_value() -> Deg<S>
Returns the largest finite number this type can represent
```

--------------------------------

### Get Inverse Transformation

Source: https://docs.rs/cgmath/0.18.0/cgmath/prelude/trait.Transform.html

Computes and returns a transformation that reverses the effect of this transformation. Returns None if the transformation is not invertible.

```rust
fn inverse_transform(&self) -> Option<Self>;
```

--------------------------------

### Basis2 Product Methods

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Basis2.html

Methods for calculating the product of multiple Basis2 instances.

```APIDOC
## fn product<I: Iterator<Item = &'a Basis2<S>>>(iter: I) -> Basis2<S>

Takes an iterator and generates `Self` from the elements by multiplying the items.

### Method
`product`

### Parameters
- `iter`: An iterator over `Basis2` references.

### Returns
`Basis2<S>`: The resulting `Basis2` after multiplying all items in the iterator.
```

```APIDOC
## fn product<I: Iterator<Item = Basis2<S>>>(iter: I) -> Basis2<S>

Takes an iterator and generates `Self` from the elements by multiplying the items.

### Method
`product`

### Parameters
- `iter`: An iterator over `Basis2` instances.

### Returns
`Basis2<S>`: The resulting `Basis2` after multiplying all items in the iterator.
```

--------------------------------

### Bounded Trait Implementation

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Implements the `Bounded` trait for vectors, providing methods to get the minimum and maximum possible values.

```APIDOC
## Bounded Trait Implementation

### `min_value()`

Returns a vector with each element set to the minimum value of the scalar type `S`.

### `max_value()`

Returns a vector with each element set to the maximum value of the scalar type `S`.
```

--------------------------------

### From<Perspective<S>> for Matrix4<S> Implementation

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Perspective.html

Allows conversion from a Perspective projection to a Matrix4.

```APIDOC
### impl<S: BaseFloat> From<Perspective<S>> for Matrix4<S>

#### fn from(persp: Perspective<S>) -> Matrix4<S>
Converts to this type from the input type.
```

--------------------------------

### Array Trait for Vector2

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Vector2.html

Provides array-like functionality for Vector2, including getting the length, creating from a scalar, and summing elements.

```APIDOC
## Array Trait for Vector2

### Description
Provides array-like functionality for `Vector2`.

### Implementations
* `impl<S: Copy> Array for Vector2<S>`

### Methods
* `fn len() -> usize`: Get the number of elements in the array type.
* `fn from_value(scalar: S) -> Vector2<S>`: Construct a vector from a single value, replicating it.
* `fn sum(self) -> S`: The sum of the elements of the array.
```

--------------------------------

### Vector Constructor and Utility Methods

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/vector.rs.html

Provides a constant constructor `new` for creating vectors, a `map` method for applying a function to each component, and a `zip` method for combining two vectors element-wise using a function.

```rust
impl<S> $VectorN<S> {
    /// Construct a new vector, using the provided values.
    #[inline]
    pub const fn new($($field: S),+) -> $VectorN<S> {
        $VectorN { $($field: $field),+ }
    }

    /// Perform the given operation on each field in the vector, returning a new point
    /// constructed from the operations.
    #[inline]
    pub fn map<U, F>(self, mut f: F)
        where F: FnMut(S) -> U
    {
        $VectorN { $($field: f(self.$field)),+ }
    }

    /// Construct a new vector where each component is the result of
    /// applying the given operation to each pair of components of the
    /// given vectors.
    #[inline]
    pub fn zip<S2, S3, F>(self, v2: $VectorN<S2>, mut f: F)
        where F: FnMut(S, S2) -> S3
    {
        $VectorN { $($field: f(self.$field, v2.$field)),+ }
    }
}
```

--------------------------------

### Array for Point1<S>

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.Point1.html

Provides array-like functionality for Point1, including getting length, creating from a value, summing, and accessing elements.

```APIDOC
## impl<S: BaseNum> Array for Point1<S>

```rust
type Element = S
fn len() -> usize
fn from_value(scalar: S) -> Point1<S>
fn sum(self) -> S
fn product(self) -> S
fn is_finite(&self) -> bool
fn as_ptr(&self) -> *const Self::Element
fn as_mut_ptr(&mut self) -> *mut Self::Element
fn swap_elements(&mut self, i: usize, j: usize)
```

Get the number of elements in the array type Read more
Construct a vector from a single value, replicating it. Read more
where S: Add<Output = S>,
The sum of the elements of the array.
where S: Mul<Output = S>,
The product of the elements of the array.
where S: Float,
Whether all elements of the array are finite
Get the pointer to the first element of the array.
Get a mutable pointer to the first element of the array.
Swap the elements at indices `i` and `j` in-place.
```

--------------------------------

### From<mint::Quaternion<S>> for Quaternion<S>

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/quaternion.rs.html

Converts a mint::Quaternion into a cgmath::Quaternion.

```APIDOC
## From<mint::Quaternion<S>> for Quaternion<S>

### Description
Converts a `mint::Quaternion<S>` into a `cgmath::Quaternion<S>`. This requires the `mint` feature to be enabled.

### Method
`from(q: mint::Quaternion<S>)`

### Parameters
- **q** (mint::Quaternion<S>) - The mint quaternion to convert.

### Returns
A `Quaternion<S>` instance.
```

--------------------------------

### PartialEq Implementation for PerspectiveFov

Source: https://docs.rs/cgmath/0.18.0/cgmath/struct.PerspectiveFov.html

Allows comparison of two PerspectiveFov instances for equality. This is used to check if two projection settings are identical.

```rust
fn eq(&self, other: &PerspectiveFov<S>) -> bool
```

--------------------------------

### Compute cosecant of an angle

Source: https://docs.rs/cgmath/0.18.0/src/cgmath/structure.rs.html

Computes the cosecant of the angle. This is equivalent to calculating the reciprocal of the sine of the angle. Example usage with Rad type.

```rust
    /// ```rust
    /// use cgmath::prelude::*;
    /// use cgmath::Rad;
    ///

```
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