Struct PluckerTransform

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pub struct PluckerTransform {
    pub rotation: PlukerRotation,
    pub translation: Vec3,
}

Expand description

A spatial transform using Plücker coordinates.

Fields§

§rotation: PlukerRotation

The rotation component of the spatial transform (E).

This is a 3×3 rotation matrix that transforms angular components from the parent/reference frame to the child/local frame.

§translation: Vec3

The translation component of the spatial transform (r).

This is a 3D vector representing the position of the child frame origin relative to the parent frame origin, expressed in parent frame coordinates.

Implementations§

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impl PluckerTransform

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pub fn identity() -> Self

Create an identity PluckerTransform.

Returns a transform with no rotation or translation.

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pub fn from_pose(pose: Pose) -> Self

Create a plucker transform from a pose. The returned transform converts from parent to local.

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pub fn any_nan(&self) -> bool

Check if the transform contains any NaN values.

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pub fn mul_transform(&self, rhs: &PluckerTransform) -> PluckerTransform

Multiply this transform by another transform.

Computes the composition of two transforms: result = self * rhs where rhs is applied first, then self.

The formula is: X1 * X2 = plx(E1E2, r2 + E2^T r1)

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pub fn inverse(&self) -> PluckerTransform

Compute the inverse of the transform.

Returns a transform that undoes this transform when applied.

The formula is: X^-1 = plx(E^T, -Er)

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pub fn transform_motion_vec( &self, v: SpatialMotionVector, ) -> SpatialMotionVector

Transform a spatial motion vector from parent frame to child frame.

Transforms a 6D motion vector containing angular and linear velocity components. The formula is: X * v^ = mv(Ew, E(v - r x w))

§Arguments

v - Spatial motion vector in parent frame coordinates

§Returns

Spatial motion vector in child frame coordinates

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pub fn inverse_transform_motion_vec( &self, v: SpatialMotionVector, ) -> SpatialMotionVector

Transform a spatial motion vector from child frame to parent frame.

This is the inverse operation of transform_motion_vec. The formula is: X^-1 * v^ = mv(E^T w, E^T v + r x E^T w)

§Arguments

v - Spatial motion vector in child frame coordinates

§Returns

Spatial motion vector in parent frame coordinates

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pub fn transform_force_vec(&self, f: SpatialForceVector) -> SpatialForceVector

Transform a spatial force vector from parent frame to child frame.

Transforms a 6D force vector containing moment (torque) and force components. The formula is: X * f = fv(E(n - r x f), Ef)

§Arguments

f - Spatial force vector in parent frame coordinates

§Returns

Spatial force vector in child frame coordinates

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pub fn inverse_transform_force_vec( &self, f: SpatialForceVector, ) -> SpatialForceVector

Transform a spatial force vector from child frame to parent frame.

This is the inverse operation of transform_force_vec. The formula is: X^-1 * f = fv(E^T n + r x E^T f, E^T f)

§Arguments

f - Spatial force vector in child frame coordinates

§Returns

Spatial force vector in parent frame coordinates

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pub fn transform_point(&self, point: Vec3) -> Vec3

Transform a point from reference frame to local

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pub fn transform_vec3(&self, vec3: Vec3) -> Vec3

Transform a 3D vector from reference frame to local frame.

Applies only the rotation component of the transform, ignoring translation. This is appropriate for transforming directions and vectors that represent

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pub fn inverse_transform_point(&self, point: Vec3) -> Vec3

Transform a point from local frame to reference frame

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pub fn inverse_transform_vec3(&self, vec3: Vec3) -> Vec3

Transform a 3D vector from local frame to reference frame.

Applies only the inverse rotation component of the transform, ignoring translation. This is the inverse operation of transform_vec3.

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pub fn inverse_transform_unitvec3(&self, vec3: UnitVec3) -> UnitVec3

Transform a unit vector from local frame to reference frame.

Applies only the inverse rotation component of the transform, ignoring translation. The input vector is assumed to be normalized and will remain normalized.

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pub fn transform_articulated_inertia( &self, inertia: &ArticulatedBodyInertia, ) -> ArticulatedBodyInertia

Transform an articulated body inertia from parent frame to child frame.

Transforms a 6×6 articulated body inertia matrix using the similarity transform: I_child = X * I_parent * Xᵀ

The formula involves three components:

Mass matrix: M = E * M * Eᵀ
Coriolis matrix: H = E * (H - r * M) * Eᵀ
Rotational inertia: I = E * (I - r×Hᵀ + (H - r×M)r×) * Eᵀ

§Arguments

inertia - Articulated body inertia in parent frame coordinates

§Returns

Articulated body inertia in child frame coordinates

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pub fn matrix(&self) -> SMatrix<6, 6>

Convert the Plücker transform to a 6×6 matrix representation.

Returns the full 6×6 spatial transform matrix:

    | E   0 |
X = |       |
    | -E×r E |

where E is the 3×3 rotation matrix and r is the translation vector. This matrix can be used for direct multiplication with 6D vectors.

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pub fn dual_matrix(&self) -> SMatrix<6, 6>

Convert the Plücker transform to its dual matrix representation.

Returns the dual transform matrix where the translation component appears in the top-right block instead of the bottom-left block:

    | E  -E×r |
X* = |        |
    | 0    E  |

The dual matrix is the transpose inverse of the regular matrix. This representation is useful for transforming certain spatial quantities.

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pub fn is_near_identity(&self, epsilon: Real) -> bool

Check whether the transform is close to identity. Check whether the transform is close to identity.

Returns true if both the rotation angle and translation magnitude are below the given epsilon threshold.

§Arguments

epsilon - Maximum allowed deviation from identity

§Returns

True if the transform is approximately identity

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impl PluckerTransform

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pub fn pose(&self) -> Pose

Convert the Plücker transform to a pose.

Returns a pose that represents the same transformation but with the rotation component inverted to match pose conventions. This is because poses typically represent the transformation from local to world space, while Plücker transforms represent the transformation from parent to child frame.