Struct macroquad::math::Quat [−][src]
#[repr(transparent)]pub struct Quat(_);
Expand description
A quaternion representing an orientation.
This quaternion is intended to be of unit length but may denormalize due to floating point “error creep” which can occur when successive quaternion operations are applied.
This type is 16 byte aligned.
Implementations
Creates a new rotation quaternion.
This should generally not be called manually unless you know what you are doing.
Use one of the other constructors instead such as identity
or from_axis_angle
.
from_xyzw
is mostly used by unit tests and serde
deserialization.
use Quat::IDENTITY instead
Creates a rotation quaternion from an unaligned slice.
Preconditions
The resulting quaternion is expected to be of unit length.
Panics
Panics if slice
length is less than 4.
Create a quaternion for a normalized rotation axis
and angle
(in radians).
The axis must be normalized (unit-length).
Create a quaternion that rotates v.length()
radians around v.normalize()
.
from_scaled_axis(Vec3::ZERO)
results in the identity quaternion.
Creates a quaternion from the angle
(in radians) around the x axis.
Creates a quaternion from the angle
(in radians) around the y axis.
Creates a quaternion from the angle
(in radians) around the z axis.
Create a quaternion from the given yaw (around y), pitch (around x) and roll (around z) in radians.
Creates a quaternion from a 3x3 rotation matrix.
Creates a quaternion from a 3x3 rotation matrix inside a homogeneous 4x4 matrix.
Gets the minimal rotation for transforming from
to to
.
The rotation is in the plane spanned by the two vectors.
Will rotate at most 180 degrees.
The input vectors must be normalized (unit-length).
from_rotation_arc(from, to) * from ≈ to
.
For near-singular cases (from≈to and from≈-to) the current implementation
is only accurate to about 0.001 (for f32
).
Gets the minimal rotation for transforming from
to either to
or -to
.
This means that the resulting quaternion will rotate from
so that it is colinear with to
.
The rotation is in the plane spanned by the two vectors. Will rotate at most 90 degrees.
The input vectors must be normalized (unit-length).
to.dot(from_rotation_arc_colinear(from, to) * from).abs() ≈ 1
.
Returns the rotation axis and angle (in radians) of self
.
Returns the rotation axis scaled by the rotation in radians.
Returns the quaternion conjugate of self
. For a unit quaternion the
conjugate is also the inverse.
Returns the inverse of a normalized quaternion.
Typically quaternion inverse returns the conjugate of a normalized quaternion.
Because self
is assumed to already be unit length this method does not normalize
before returning the conjugate.
Computes the dot product of self
and other
. The dot product is
equal to the the cosine of the angle between two quaternion rotations.
Computes the squared length of self
.
This is generally faster than length()
as it avoids a square
root operation.
Computes 1.0 / length()
.
For valid results, self
must not be of length zero.
Returns self
normalized to length 1.0.
For valid results, self
must not be of length zero.
Returns true
if, and only if, all elements are finite.
If any element is either NaN
, positive or negative infinity, this will return false
.
Returns whether self
of length 1.0
or not.
Uses a precision threshold of 1e-6
.
Returns the angle (in radians) for the minimal rotation for transforming this quaternion into another.
Both quaternions must be normalized.
Returns true if the absolute difference of all elements between self
and other
is less than or equal to max_abs_diff
.
This can be used to compare if two quaternions contain similar elements. It works
best when comparing with a known value. The max_abs_diff
that should be used used
depends on the values being compared against.
For more see comparing floating point numbers.
Performs a linear interpolation between self
and other
based on
the value s
.
When s
is 0.0
, the result will be equal to self
. When s
is 1.0
, the result will be equal to other
.
Performs a spherical linear interpolation between self
and end
based on the value s
.
When s
is 0.0
, the result will be equal to self
. When s
is 1.0
, the result will be equal to end
.
Note that a rotation can be represented by two quaternions: q
and
-q
. The slerp path between q
and end
will be different from the
path between -q
and end
. One path will take the long way around and
one will take the short way. In order to correct for this, the dot
product between self
and end
should be positive. If the dot
product is negative, slerp between -self
and end
.
Multiplies a quaternion and a 3D vector, returning the rotated vector.
Multiplies two quaternions. If they each represent a rotation, the result will represent the combined rotation. Note that due to floating point rounding the result may not be perfectly normalized.
Multiplies a quaternion and a 3D vector, returning the rotated vector.
Trait Implementations
Adds two quaternions. The sum is not guaranteed to be normalized.
NB: Addition is not the same as combining the rotations represented by the two quaternions! That corresponds to multiplication.
Performs the *=
operation. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
Auto Trait Implementations
impl RefUnwindSafe for Quat
impl UnwindSafe for Quat
Blanket Implementations
Mutably borrows from an owned value. Read more