Struct heron::rapier_plugin::rapier2d::prelude::nalgebra::Quaternion

source · 
pub struct Quaternion<T> {
    pub coords: Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>,
}
Expand description

A quaternion. See the type alias UnitQuaternion = Unit<Quaternion> for a quaternion that may be used as a rotation.

Fields

coords: Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>

This quaternion as a 4D vector of coordinates in the [ x, y, z, w ] storage order.

Implementations

👎Deprecated: This method is a no-op and will be removed in a future release.

Moves this unit quaternion into one that owns its data.

👎Deprecated: This method is a no-op and will be removed in a future release.

Clones this unit quaternion into one that owns its data.

Normalizes this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let q_normalized = q.normalize();
relative_eq!(q_normalized.norm(), 1.0);

The imaginary part of this quaternion.

The conjugate of this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let conj = q.conjugate();
assert!(conj.i == -2.0 && conj.j == -3.0 && conj.k == -4.0 && conj.w == 1.0);

Linear interpolation between two quaternion.

Computes self * (1 - t) + other * t.

Example
let q1 = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let q2 = Quaternion::new(10.0, 20.0, 30.0, 40.0);

assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(1.9, 3.8, 5.7, 7.6));

The vector part (i, j, k) of this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(q.vector()[0], 2.0);
assert_eq!(q.vector()[1], 3.0);
assert_eq!(q.vector()[2], 4.0);

The scalar part w of this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(q.scalar(), 1.0);

Reinterprets this quaternion as a 4D vector.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
// Recall that the quaternion is stored internally as (i, j, k, w)
// while the crate::new constructor takes the arguments as (w, i, j, k).
assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

The norm of this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_relative_eq!(q.norm(), 5.47722557, epsilon = 1.0e-6);

A synonym for the norm of this quaternion.

Aka the length. This is the same as .norm()

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_relative_eq!(q.magnitude(), 5.47722557, epsilon = 1.0e-6);

The squared norm of this quaternion.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(q.magnitude_squared(), 30.0);

A synonym for the squared norm of this quaternion.

Aka the squared length. This is the same as .norm_squared()

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(q.magnitude_squared(), 30.0);

The dot product of two quaternions.

Example
let q1 = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let q2 = Quaternion::new(5.0, 6.0, 7.0, 8.0);
assert_eq!(q1.dot(&q2), 70.0);

Inverts this quaternion if it is not zero.

This method also does not works with SIMD components (see simd_try_inverse instead).

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let inv_q = q.try_inverse();

assert!(inv_q.is_some());
assert_relative_eq!(inv_q.unwrap() * q, Quaternion::identity());

//Non-invertible case
let q = Quaternion::new(0.0, 0.0, 0.0, 0.0);
let inv_q = q.try_inverse();

assert!(inv_q.is_none());

Attempt to inverse this quaternion.

This method also works with SIMD components.

Calculates the inner product (also known as the dot product). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.89.

Example
let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
let expected = Quaternion::new(-20.0, 0.0, 0.0, 0.0);
let result = a.inner(&b);
assert_relative_eq!(expected, result, epsilon = 1.0e-5);

Calculates the outer product (also known as the wedge product). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.89.

Example
let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
let expected = Quaternion::new(0.0, -5.0, 18.0, -11.0);
let result = a.outer(&b);
assert_relative_eq!(expected, result, epsilon = 1.0e-5);

Calculates the projection of self onto other (also known as the parallel). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.94.

Example
let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
let expected = Quaternion::new(0.0, 3.333333333333333, 1.3333333333333333, 0.6666666666666666);
let result = a.project(&b).unwrap();
assert_relative_eq!(expected, result, epsilon = 1.0e-5);

Calculates the rejection of self from other (also known as the perpendicular). See “Foundations of Game Engine Development, Volume 1: Mathematics” by Lengyel Formula 4.94.

Example
let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
let expected = Quaternion::new(0.0, -1.3333333333333333, 1.6666666666666665, 3.3333333333333335);
let result = a.reject(&b).unwrap();
assert_relative_eq!(expected, result, epsilon = 1.0e-5);

The polar decomposition of this quaternion.

Returns, from left to right: the quaternion norm, the half rotation angle, the rotation axis. If the rotation angle is zero, the rotation axis is set to None.

Example
let q = Quaternion::new(0.0, 5.0, 0.0, 0.0);
let (norm, half_ang, axis) = q.polar_decomposition();
assert_eq!(norm, 5.0);
assert_eq!(half_ang, f32::consts::FRAC_PI_2);
assert_eq!(axis, Some(Vector3::x_axis()));

Compute the natural logarithm of a quaternion.

Example
let q = Quaternion::new(2.0, 5.0, 0.0, 0.0);
assert_relative_eq!(q.ln(), Quaternion::new(1.683647, 1.190289, 0.0, 0.0), epsilon = 1.0e-6)

Compute the exponential of a quaternion.

Example
let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
assert_relative_eq!(q.exp(), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5)

Compute the exponential of a quaternion. Returns the identity if the vector part of this quaternion has a norm smaller than eps.

Example
let q = Quaternion::new(1.683647, 1.190289, 0.0, 0.0);
assert_relative_eq!(q.exp_eps(1.0e-6), Quaternion::new(2.0, 5.0, 0.0, 0.0), epsilon = 1.0e-5);

// Singular case.
let q = Quaternion::new(0.0000001, 0.0, 0.0, 0.0);
assert_eq!(q.exp_eps(1.0e-6), Quaternion::identity());

Raise the quaternion to a given floating power.

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert_relative_eq!(q.powf(1.5), Quaternion::new( -6.2576659, 4.1549037, 6.2323556, 8.3098075), epsilon = 1.0e-6);

Transforms this quaternion into its 4D vector form (Vector part, Scalar part).

Example
let mut q = Quaternion::identity();
*q.as_vector_mut() = Vector4::new(1.0, 2.0, 3.0, 4.0);
assert!(q.i == 1.0 && q.j == 2.0 && q.k == 3.0 && q.w == 4.0);

The mutable vector part (i, j, k) of this quaternion.

Example
let mut q = Quaternion::identity();
{
    let mut v = q.vector_mut();
    v[0] = 2.0;
    v[1] = 3.0;
    v[2] = 4.0;
}
assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);

Replaces this quaternion by its conjugate.

Example
let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
q.conjugate_mut();
assert!(q.i == -2.0 && q.j == -3.0 && q.k == -4.0 && q.w == 1.0);

Inverts this quaternion in-place if it is not zero.

Example
let mut q = Quaternion::new(1.0f32, 2.0, 3.0, 4.0);

assert!(q.try_inverse_mut());
assert_relative_eq!(q * Quaternion::new(1.0, 2.0, 3.0, 4.0), Quaternion::identity());

//Non-invertible case
let mut q = Quaternion::new(0.0f32, 0.0, 0.0, 0.0);
assert!(!q.try_inverse_mut());

Normalizes this quaternion.

Example
let mut q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
q.normalize_mut();
assert_relative_eq!(q.norm(), 1.0);

Calculates square of a quaternion.

Divides quaternion into two.

Calculates square root.

Check if the quaternion is pure.

A quaternion is pure if it has no real part (self.w == 0.0).

Convert quaternion to pure quaternion.

Left quaternionic division.

Calculates B-1 * A where A = self, B = other.

Right quaternionic division.

Calculates A * B-1 where A = self, B = other.

Example
let a = Quaternion::new(0.0, 1.0, 2.0, 3.0);
let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
let result = a.right_div(&b).unwrap();
let expected = Quaternion::new(0.4, 0.13333333333333336, -0.4666666666666667, 0.26666666666666666);
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the quaternionic cosinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(58.93364616794395, -34.086183690465596, -51.1292755356984, -68.17236738093119);
let result = input.cos();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the quaternionic arccosinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let result = input.cos().acos();
assert_relative_eq!(input, result, epsilon = 1.0e-7);

Calculates the quaternionic sinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(91.78371578403467, 21.886486853029176, 32.82973027954377, 43.77297370605835);
let result = input.sin();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the quaternionic arcsinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let result = input.sin().asin();
assert_relative_eq!(input, result, epsilon = 1.0e-7);

Calculates the quaternionic tangent.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.00003821631725009489, 0.3713971716439371, 0.5570957574659058, 0.7427943432878743);
let result = input.tan();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the quaternionic arctangent.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let result = input.tan().atan();
assert_relative_eq!(input, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic sinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.7323376060463428, -0.4482074499805421, -0.6723111749708133, -0.8964148999610843);
let result = input.sinh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic arcsinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(2.385889902585242, 0.514052600662788, 0.7710789009941821, 1.028105201325576);
let result = input.asinh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic cosinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.9615851176369566, -0.3413521745610167, -0.5120282618415251, -0.6827043491220334);
let result = input.cosh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic arccosinus.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(2.4014472020074007, 0.5162761016176176, 0.7744141524264264, 1.0325522032352352);
let result = input.acosh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic tangent.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(1.0248695360556623, -0.10229568178876419, -0.1534435226831464, -0.20459136357752844);
let result = input.tanh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Calculates the hyperbolic quaternionic arctangent.

Example
let input = Quaternion::new(1.0, 2.0, 3.0, 4.0);
let expected = Quaternion::new(0.03230293287000163, 0.5173453683196951, 0.7760180524795426, 1.0346907366393903);
let result = input.atanh();
assert_relative_eq!(expected, result, epsilon = 1.0e-7);

Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the w vector component.

Creates a new quaternion from its individual components. Note that the arguments order does not follow the storage order.

The storage order is [ i, j, k, w ] while the arguments for this functions are in the order (w, i, j, k).

Example
let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

Cast the components of self to another type.

Example
let q = Quaternion::new(1.0f64, 2.0, 3.0, 4.0);
let q2 = q.cast::<f32>();
assert_eq!(q2, Quaternion::new(1.0f32, 2.0, 3.0, 4.0));

Constructs a pure quaternion.

Creates a new quaternion from its scalar and vector parts. Note that the arguments order does not follow the storage order.

The storage order is [ vector, scalar ].

Example
let w = 1.0;
let ijk = Vector3::new(2.0, 3.0, 4.0);
let q = Quaternion::from_parts(w, ijk);
assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));

Constructs a real quaternion.

The quaternion multiplicative identity.

Example
let q = Quaternion::identity();
let q2 = Quaternion::new(1.0, 2.0, 3.0, 4.0);

assert_eq!(q * q2, q2);
assert_eq!(q2 * q, q2);

Creates a new quaternion from its polar decomposition.

Note that axis is assumed to be a unit vector.

Trait Implementations

Used for specifying relative comparisons.
The default tolerance to use when testing values that are close together. Read more
A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
The inverse of [AbsDiffEq::abs_diff_eq].
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
Performs the += operation. Read more
Performs the += operation. Read more
Returns a copy of the value. Read more
Performs copy-assignment from source. Read more
Formats the value using the given formatter. Read more
Returns the “default value” for a type. Read more
The resulting type after dereferencing.
Dereferences the value.
Mutably dereferences the value.
Formats the value using the given formatter. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
Performs the /= operation. Read more
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Converts to this type from the input type.
Feeds this value into the given Hasher. Read more
Feeds a slice of this type into the given Hasher. Read more
The returned type after indexing.
Performs the indexing (container[index]) operation. Read more
Performs the mutable indexing (container[index]) operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
The resulting type after applying the - operator.
Performs the unary - operation. Read more
The resulting type after applying the - operator.
Performs the unary - operation. Read more
The type of the norm.
Computes the norm.
Computes the squared norm.
Multiply self by n.
Divides self by n.
Returns the multiplicative identity element of Self, 1. Read more
Sets self to the multiplicative identity element of Self, 1.
Returns true if self is equal to the multiplicative identity. Read more
This method tests for self and other values to be equal, and is used by ==. Read more
This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
The default relative tolerance for testing values that are far-apart. Read more
A test for equality that uses a relative comparison if the values are far apart.
The inverse of [RelativeEq::relative_eq].
The type of the elements of each lane of this SIMD value.
Type of the result of comparing two SIMD values like self.
The number of lanes of this SIMD value.
Initializes an SIMD value with each lanes set to val.
Extracts the i-th lane of self. Read more
Extracts the i-th lane of self without bound-checking.
Replaces the i-th lane of self by val. Read more
Replaces the i-th lane of self by val without bound-checking.
Merges self and other depending on the lanes of cond. Read more
Applies a function to each lane of self. Read more
Applies a function to each lane of self paired with the corresponding lane of b. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
Performs the -= operation. Read more
Performs the -= operation. Read more
The inclusion map: converts self to the equivalent element of its superset.
Checks if element is actually part of the subset Self (and can be converted to it).
Use with care! Same as self.to_superset but without any property checks. Always succeeds.
The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
The default ULPs to tolerate when testing values that are far-apart. Read more
A test for equality that uses units in the last place (ULP) if the values are far apart.
The inverse of [UlpsEq::ulps_eq].
Returns the additive identity element of Self, 0. Read more
Returns true if self is equal to the additive identity.
Sets self to the additive identity element of Self, 0.

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more
Return the T [ShaderType] for self. When used in [AsBindGroup] derives, it is safe to assume that all images in self exist. Read more
Immutably borrows from an owned value. Read more
Mutably borrows from an owned value. Read more
Convert Box<dyn Trait> (where Trait: Downcast) to Box<dyn Any>. Box<dyn Any> can then be further downcast into Box<ConcreteType> where ConcreteType implements Trait. Read more
Convert Rc<Trait> (where Trait: Downcast) to Rc<Any>. Rc<Any> can then be further downcast into Rc<ConcreteType> where ConcreteType implements Trait. Read more
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Convert Arc<Trait> (where Trait: Downcast) to Arc<Any>. Arc<Any> can then be further downcast into Arc<ConcreteType> where ConcreteType implements Trait. Read more
Compare self to key and return true if they are equal.

Returns the argument unchanged.

Creates Self using data from the given [World]
Instruments this type with the provided Span, returning an Instrumented wrapper. Read more
Instruments this type with the current Span, returning an Instrumented wrapper. Read more

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

The alignment of pointer.
The type for initializers.
Initializes a with the given initializer. Read more
Dereferences the given pointer. Read more
Mutably dereferences the given pointer. Read more
Drops the object pointed to by the given pointer. Read more
Should always be Self
The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
Checks if self is actually part of its subset T (and can be converted to it).
Use with care! Same as self.to_subset but without any property checks. Always succeeds.
The inclusion map: converts self to the equivalent element of its superset.
The resulting type after obtaining ownership.
Creates owned data from borrowed data, usually by cloning. Read more
Uses borrowed data to replace owned data, usually by cloning. Read more
Converts the given value to a String. Read more
The type returned in the event of a conversion error.
Performs the conversion.
The type returned in the event of a conversion error.
Performs the conversion.
Attaches the provided Subscriber to this type, returning a WithDispatch wrapper. Read more
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