Type Definition nalgebra::geometry::UnitComplex
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type UnitComplex<N> = Unit<Complex<N>>;
A complex number with a norm equal to 1.
Methods
impl<N: Real> UnitComplex<N>
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fn angle(&self) -> N
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The rotation angle in ]-pi; pi]
of this unit complex number.
fn sin_angle(&self) -> N
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The sine of the rotation angle.
fn cos_angle(&self) -> N
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The cosine of the rotation angle.
fn scaled_axis(&self) -> Vector1<N>
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The rotation angle returned as a 1-dimensional vector.
fn complex(&self) -> &Complex<N>
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The underlying complex number.
Same as self.as_ref()
.
fn conjugate(&self) -> Self
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Compute the conjugate of this unit complex number.
fn inverse(&self) -> Self
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Inverts this complex number if it is not zero.
fn angle_to(&self, other: &Self) -> N
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The rotation angle needed to make self
and other
coincide.
fn rotation_to(&self, other: &Self) -> Self
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The unit complex number needed to make self
and other
coincide.
The result is such that: self.rotation_to(other) * self == other
.
fn conjugate_mut(&mut self)
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Compute in-place the conjugate of this unit complex number.
fn inverse_mut(&mut self)
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Inverts in-place this unit complex number.
fn powf(&self, n: N) -> Self
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Raise this unit complex number to a given floating power.
This returns the unit complex number that identifies a rotation angle equal to
self.angle() × n
.
fn to_rotation_matrix(&self) -> Rotation2<N>
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Builds the rotation matrix corresponding to this unit complex number.
fn to_homogeneous(&self) -> Matrix3<N>
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Converts this unit complex number into its equivalent homogeneous transformation matrix.
impl<N: Real> UnitComplex<N>
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fn identity() -> Self
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The unit complex number multiplicative identity.
fn new(angle: N) -> Self
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Builds the unit complex number corresponding to the rotation with the angle.
fn from_angle(angle: N) -> Self
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Builds the unit complex number corresponding to the rotation with the angle.
Same as Self::new(angle)
.
fn from_cos_sin_unchecked(cos: N, sin: N) -> Self
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Builds the unit complex number frow the sinus and cosinus of the rotation angle.
The input values are not checked.
fn from_scaled_axis<SB: Storage<N, U1, U1>>(
axisangle: Vector<N, U1, SB>
) -> Self
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axisangle: Vector<N, U1, SB>
) -> Self
Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
Equivalent to Self::new(axisangle[0])
.
fn from_complex(q: Complex<N>) -> Self
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Creates a new unit complex number from a complex number.
The input complex number will be normalized.
fn from_complex_and_get(q: Complex<N>) -> (Self, N)
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Creates a new unit complex number from a complex number.
The input complex number will be normalized. Returns the complex number norm as well.
fn from_rotation_matrix(rotmat: &Rotation<N, U2>) -> Self where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
Builds the unit complex number from the corresponding 2D rotation matrix.
fn rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>
) -> Self where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
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a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>
) -> Self where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
The unit complex needed to make a
and b
be collinear and point toward the same
direction.
fn scaled_rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N
) -> Self where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
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a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N
) -> Self where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
The smallest rotation needed to make a
and b
collinear and point toward the same
direction, raised to the power s
.
impl<N: Real> UnitComplex<N>
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fn rotate<R2: Dim, C2: Dim, S2: StorageMut<N, R2, C2>>(
&self,
rhs: &mut Matrix<N, R2, C2, S2>
) where
ShapeConstraint: DimEq<R2, U2>,
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&self,
rhs: &mut Matrix<N, R2, C2, S2>
) where
ShapeConstraint: DimEq<R2, U2>,
Performs the multiplication rhs = self * rhs
in-place.
fn rotate_rows<R2: Dim, C2: Dim, S2: StorageMut<N, R2, C2>>(
&self,
lhs: &mut Matrix<N, R2, C2, S2>
) where
ShapeConstraint: DimEq<C2, U2>,
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&self,
lhs: &mut Matrix<N, R2, C2, S2>
) where
ShapeConstraint: DimEq<C2, U2>,
Performs the multiplication lhs = lhs * self
in-place.
Trait Implementations
impl<N: Real + Display> Display for UnitComplex<N>
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fn fmt(&self, f: &mut Formatter) -> Result
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Formats the value using the given formatter. Read more
impl<N: Real> ApproxEq for UnitComplex<N>
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type Epsilon = N
Used for specifying relative comparisons.
fn default_epsilon() -> Self::Epsilon
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The default tolerance to use when testing values that are close together. Read more
fn default_max_relative() -> Self::Epsilon
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The default relative tolerance for testing values that are far-apart. Read more
fn default_max_ulps() -> u32
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The default ULPs to tolerate when testing values that are far-apart. Read more
fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
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&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 ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool
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A test for equality that uses units in the last place (ULP) if the values are far apart.
fn relative_ne(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
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&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
The inverse of ApproxEq::relative_eq
.
fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool
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The inverse of ApproxEq::ulps_eq
.
impl<N: Real> One for UnitComplex<N>
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impl<N: Real + Rand> Rand for UnitComplex<N>
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fn rand<R: Rng>(rng: &mut R) -> Self
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Generates a random instance of this type using the specified source of randomness. Read more
impl<N: Real> Mul<UnitComplex<N>> for UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: UnitComplex<N>) -> UnitComplex<N>
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Performs the *
operation.
impl<'a, N: Real> Mul<UnitComplex<N>> for &'a UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: UnitComplex<N>) -> UnitComplex<N>
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b UnitComplex<N>> for UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N>
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b UnitComplex<N>> for &'a UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N>
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Performs the *
operation.
impl<N: Real> Div<UnitComplex<N>> for UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: UnitComplex<N>) -> UnitComplex<N>
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Performs the /
operation.
impl<'a, N: Real> Div<UnitComplex<N>> for &'a UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: UnitComplex<N>) -> UnitComplex<N>
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Performs the /
operation.
impl<'b, N: Real> Div<&'b UnitComplex<N>> for UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N>
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Performs the /
operation.
impl<'a, 'b, N: Real> Div<&'b UnitComplex<N>> for &'a UnitComplex<N>
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type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: &'b UnitComplex<N>) -> UnitComplex<N>
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Performs the /
operation.
impl<N: Real> Mul<Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Rotation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real> Mul<Rotation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Rotation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Rotation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b Rotation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Rotation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<N: Real> Div<Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: Rotation<N, U2>) -> Self::Output
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Performs the /
operation.
impl<'a, N: Real> Div<Rotation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: Rotation<N, U2>) -> Self::Output
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Performs the /
operation.
impl<'b, N: Real> Div<&'b Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: &'b Rotation<N, U2>) -> Self::Output
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Performs the /
operation.
impl<'a, 'b, N: Real> Div<&'b Rotation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
type Output = UnitComplex<N>
The resulting type after applying the /
operator.
fn div(self, rhs: &'b Rotation<N, U2>) -> Self::Output
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Performs the /
operation.
impl<N: Real> Mul<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Point2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Point2<N>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real> Mul<Point2<N>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Point2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Point2<N>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Point2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Point2<N>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b Point2<N>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Point2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Point2<N>) -> Self::Output
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Performs the *
operation.
impl<N: Real, S: Storage<N, U2>> Mul<Vector<N, U2, S>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Vector2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Vector<N, U2, S>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real, S: Storage<N, U2>> Mul<Vector<N, U2, S>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Vector2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: Vector<N, U2, S>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real, S: Storage<N, U2>> Mul<&'b Vector<N, U2, S>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Vector2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Vector<N, U2, S>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real, S: Storage<N, U2>> Mul<&'b Vector<N, U2, S>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Vector2<N>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Vector<N, U2, S>) -> Self::Output
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Performs the *
operation.
impl<N: Real, S: Storage<N, U2>> Mul<Unit<Vector<N, U2, S>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Unit<Vector2<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Unit<Vector<N, U2, S>>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real, S: Storage<N, U2>> Mul<Unit<Vector<N, U2, S>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Unit<Vector2<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Unit<Vector<N, U2, S>>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real, S: Storage<N, U2>> Mul<&'b Unit<Vector<N, U2, S>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Unit<Vector2<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Unit<Vector<N, U2, S>>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real, S: Storage<N, U2>> Mul<&'b Unit<Vector<N, U2, S>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Unit<Vector2<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Unit<Vector<N, U2, S>>) -> Self::Output
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Performs the *
operation.
impl<N: Real> Mul<Isometry<N, U2, UnitComplex<N>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Isometry<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real> Mul<Isometry<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Isometry<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b Isometry<N, U2, UnitComplex<N>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Isometry<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b Isometry<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Isometry<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<N: Real> Mul<Similarity<N, U2, UnitComplex<N>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Similarity<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Similarity<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real> Mul<Similarity<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Similarity<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Similarity<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b Similarity<N, U2, UnitComplex<N>>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Similarity<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Similarity<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b Similarity<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Similarity<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Similarity<N, U2, UnitComplex<N>>) -> Self::Output
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Performs the *
operation.
impl<N: Real> Mul<Translation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Translation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'a, N: Real> Mul<Translation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: Translation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'b, N: Real> Mul<&'b Translation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Translation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<'a, 'b, N: Real> Mul<&'b Translation<N, U2>> for &'a UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U1>,
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DefaultAllocator: Allocator<N, U2, U1>,
type Output = Isometry<N, U2, UnitComplex<N>>
The resulting type after applying the *
operator.
fn mul(self, rhs: &'b Translation<N, U2>) -> Self::Output
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Performs the *
operation.
impl<N: Real> MulAssign<UnitComplex<N>> for UnitComplex<N>
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fn mul_assign(&mut self, rhs: UnitComplex<N>)
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Performs the *=
operation.
impl<'b, N: Real> MulAssign<&'b UnitComplex<N>> for UnitComplex<N>
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fn mul_assign(&mut self, rhs: &'b UnitComplex<N>)
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Performs the *=
operation.
impl<N: Real> DivAssign<UnitComplex<N>> for UnitComplex<N>
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fn div_assign(&mut self, rhs: UnitComplex<N>)
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Performs the /=
operation.
impl<'b, N: Real> DivAssign<&'b UnitComplex<N>> for UnitComplex<N>
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fn div_assign(&mut self, rhs: &'b UnitComplex<N>)
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Performs the /=
operation.
impl<N: Real> MulAssign<Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
fn mul_assign(&mut self, rhs: Rotation<N, U2>)
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Performs the *=
operation.
impl<'b, N: Real> MulAssign<&'b Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
fn mul_assign(&mut self, rhs: &'b Rotation<N, U2>)
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Performs the *=
operation.
impl<N: Real> DivAssign<Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
fn div_assign(&mut self, rhs: Rotation<N, U2>)
[src]
Performs the /=
operation.
impl<'b, N: Real> DivAssign<&'b Rotation<N, U2>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2, U2>,
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DefaultAllocator: Allocator<N, U2, U2>,
fn div_assign(&mut self, rhs: &'b Rotation<N, U2>)
[src]
Performs the /=
operation.
impl<N: Real> Identity<Multiplicative> for UnitComplex<N>
[src]
impl<N: Real> AbstractMagma<Multiplicative> for UnitComplex<N>
[src]
fn operate(&self, rhs: &Self) -> Self
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Performs an operation.
fn op(&self, O, lhs: &Self) -> Self
[src]
Performs specific operation.
impl<N: Real> Inverse<Multiplicative> for UnitComplex<N>
[src]
fn inverse(&self) -> Self
[src]
Returns the inverse of self
, relative to the operator O
.
fn inverse_mut(&mut self)
[src]
In-place inversin of self
.
impl<N: Real> AbstractSemigroup<Multiplicative> for UnitComplex<N>
[src]
fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: ApproxEq,
[src]
Self: ApproxEq,
Returns true
if associativity holds for the given arguments. Approximate equality is used for verifications. Read more
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq,
[src]
Self: Eq,
Returns true
if associativity holds for the given arguments.
impl<N: Real> AbstractQuasigroup<Multiplicative> for UnitComplex<N>
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fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
Self: ApproxEq,
[src]
Self: ApproxEq,
Returns true
if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more
fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
Self: Eq,
[src]
Self: Eq,
Returns true
if latin squareness holds for the given arguments.
impl<N: Real> AbstractMonoid<Multiplicative> for UnitComplex<N>
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fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
Self: ApproxEq,
[src]
Self: ApproxEq,
Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more
fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
Self: Eq,
[src]
Self: Eq,
Checks whether operating with the identity element is a no-op for the given argument. Read more
impl<N: Real> AbstractLoop<Multiplicative> for UnitComplex<N>
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impl<N: Real> AbstractGroup<Multiplicative> for UnitComplex<N>
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impl<N: Real> Transformation<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
fn transform_point(&self, pt: &Point2<N>) -> Point2<N>
[src]
Applies this group's action on a point from the euclidean space.
fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N>
[src]
Applies this group's action on a vector from the euclidean space. Read more
impl<N: Real> ProjectiveTransformation<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N>
[src]
Applies this group's inverse action on a point from the euclidean space.
fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N>
[src]
Applies this group's inverse action on a vector from the euclidean space. Read more
impl<N: Real> AffineTransformation<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
type Rotation = Self
Type of the first rotation to be applied.
type NonUniformScaling = Id
Type of the non-uniform scaling to be applied.
type Translation = Id
The type of the pure translation part of this affine transformation.
fn decompose(&self) -> (Id, Self, Id, Self)
[src]
Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation. Read more
fn append_translation(&self, _: &Self::Translation) -> Self
[src]
Appends a translation to this similarity.
fn prepend_translation(&self, _: &Self::Translation) -> Self
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Prepends a translation to this similarity.
fn append_rotation(&self, r: &Self::Rotation) -> Self
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Appends a rotation to this similarity.
fn prepend_rotation(&self, r: &Self::Rotation) -> Self
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Prepends a rotation to this similarity.
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self
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Appends a scaling factor to this similarity.
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self
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Prepends a scaling factor to this similarity.
fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>
[src]
Appends to this similarity a rotation centered at the point p
, i.e., this point is left invariant. Read more
impl<N: Real> Similarity<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
type Scaling = Id
The type of the pure (uniform) scaling part of this similarity transformation.
fn translation(&self) -> Id
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The pure translational component of this similarity transformation.
fn rotation(&self) -> Self
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The pure rotational component of this similarity transformation.
fn scaling(&self) -> Id
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The pure scaling component of this similarity transformation.
fn translate_point(&self, pt: &E) -> E
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Applies this transformation's pure translational part to a point.
fn rotate_point(&self, pt: &E) -> E
[src]
Applies this transformation's pure rotational part to a point.
fn scale_point(&self, pt: &E) -> E
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Applies this transformation's pure scaling part to a point.
fn rotate_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
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&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
Applies this transformation's pure rotational part to a vector.
fn scale_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
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&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
Applies this transformation's pure scaling part to a vector.
fn inverse_translate_point(&self, pt: &E) -> E
[src]
Applies this transformation inverse's pure translational part to a point.
fn inverse_rotate_point(&self, pt: &E) -> E
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Applies this transformation inverse's pure rotational part to a point.
fn inverse_scale_point(&self, pt: &E) -> E
[src]
Applies this transformation inverse's pure scaling part to a point.
fn inverse_rotate_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
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&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
Applies this transformation inverse's pure rotational part to a vector.
fn inverse_scale_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
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&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
Applies this transformation inverse's pure scaling part to a vector.
impl<N: Real> Isometry<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
impl<N: Real> DirectIsometry<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
impl<N: Real> OrthogonalTransformation<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
impl<N: Real> Rotation<Point2<N>> for UnitComplex<N> where
DefaultAllocator: Allocator<N, U2>,
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DefaultAllocator: Allocator<N, U2>,
fn powf(&self, n: N) -> Option<Self>
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Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n
. Read more
fn rotation_between(a: &Vector2<N>, b: &Vector2<N>) -> Option<Self>
[src]
Computes a simple rotation that makes the angle between a
and b
equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0
. If a
and b
are collinear, the computed rotation may not be unique. Returns None
if no such simple rotation exists in the subgroup represented by Self
. Read more
fn scaled_rotation_between(a: &Vector2<N>, b: &Vector2<N>, s: N) -> Option<Self>
[src]
Computes the rotation between a
and b
and raises it to the power n
. Read more
impl<N1, N2> SubsetOf<UnitComplex<N2>> for UnitComplex<N1> where
N1: Real,
N2: Real + SupersetOf<N1>,
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N1: Real,
N2: Real + SupersetOf<N1>,
fn to_superset(&self) -> UnitComplex<N2>
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The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(uq: &UnitComplex<N2>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(uq: &UnitComplex<N2>) -> Self
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Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more
impl<N1, N2> SubsetOf<Rotation2<N2>> for UnitComplex<N1> where
N1: Real,
N2: Real + SupersetOf<N1>,
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N1: Real,
N2: Real + SupersetOf<N1>,
fn to_superset(&self) -> Rotation2<N2>
[src]
The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(rot: &Rotation2<N2>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(rot: &Rotation2<N2>) -> Self
[src]
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more
impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1> where
N1: Real,
N2: Real + SupersetOf<N1>,
R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
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N1: Real,
N2: Real + SupersetOf<N1>,
R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
fn to_superset(&self) -> Isometry<N2, U2, R>
[src]
The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(iso: &Isometry<N2, U2, R>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> Self
[src]
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more
impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1> where
N1: Real,
N2: Real + SupersetOf<N1>,
R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
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N1: Real,
N2: Real + SupersetOf<N1>,
R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,
fn to_superset(&self) -> Similarity<N2, U2, R>
[src]
The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(sim: &Similarity<N2, U2, R>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Self
[src]
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more
impl<N1, N2, C> SubsetOf<Transform<N2, U2, C>> for UnitComplex<N1> where
N1: Real,
N2: Real + SupersetOf<N1>,
C: SuperTCategoryOf<TAffine>,
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N1: Real,
N2: Real + SupersetOf<N1>,
C: SuperTCategoryOf<TAffine>,
fn to_superset(&self) -> Transform<N2, U2, C>
[src]
The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(t: &Transform<N2, U2, C>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Self
[src]
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more
impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for UnitComplex<N1>
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fn to_superset(&self) -> Matrix3<N2>
[src]
The inclusion map: converts self
to the equivalent element of its superset.
fn is_in_subset(m: &Matrix3<N2>) -> bool
[src]
Checks if element
is actually part of the subset Self
(and can be converted to it).
unsafe fn from_superset_unchecked(m: &Matrix3<N2>) -> Self
[src]
Use with care! Same as self.to_superset
but without any property checks. Always succeeds.
fn from_superset(element: &T) -> Option<Self>
[src]
The inverse inclusion map: attempts to construct self
from the equivalent element of its superset. Read more