dist

Calculate distance between transformations

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    Syntax

    distance = dist(transformation1,transformation2)
    distance = dist(transformation1,transformation2,weights)
    distance = dist(rotation1,rotation2)

    Description

    distance = dist(transformation1,transformation2) returns the distance distance between the poses represented by transformation transformation1 and transformation transformation2.

    For the homogeneous transformation object se3, the dist function calculates translational and rotational distance independently and combines them in a weighted sum. Translational distance is the Euclidean distance, and rotational distance is the angular difference between the rotation quaternions of transformation1 and transformation2.

    distance = dist(transformation1,transformation2,weights) specifies the weights weights for the translational and rotational distances for calculating the weighted sum of two homogeneous transformations.

    distance = dist(rotation1,rotation2) returns the distance distance between the poses represented by transformation rotation1 and transformation rotation2.

    For the homogeneous transformation object se3, the dist function calculates translational and rotational distance independently and combines them in a weighted sum. Translational distance is the Euclidean distance, and rotational distance is the angular difference between the rotation quaternions of rotation1 and rotation2.

    For rotation object so3, the dist function calculates the rotational distance as the angular difference between the rotation quaternions of rotation1 and rotation2.

    Input Arguments

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    First transformation, specified as a scalar se3 object or as an N-element array of transformation objects, where N is the total number of transformations. If you specify transformation1 as an array, each element must be of the same type.

    Either transformation1 or transformation2 must be a scalar transformation object of the same type. For example, if transformation1 is an array of se3 objects, transformation2 must be a scalar se3 object.

    Last transformation, specified as a scalar se3 object or as an N-element array of transformation objects, where N is the total number of transformations. If you specify transformation2 as an array, each element must be of the same type.

    Either transformation1 or transformation2 must be a scalar transformation object of the same type. For example, if transformation1 is an array of se3 objects, transformation2 must be a scalar se3 object.

    First rotation, specified as a scalar so3 object, or as an N-element array of rotation objects, where N is the total number of rotations. If you specify rotation1 as an array, each element must be of the same type.

    Either rotation1 or rotation2 must be a scalar rotation object of the same type. For example, if rotation1 is an array of so3 objects, rotation2 must be a scalar so3 object.

    Last rotation, specified as a scalar so3 object, or as an N-element array of rotation objects, where N is the total number of rotations. If you specify rotation2 as an array, each element must be of the same type.

    Either rotation1 or rotation2 must be a scalar rotation object of the same type. For example, if rotation1 is an array of se3 objects, rotation2 must be a scalar se3 object.

    Weights of the translation and rotation in the distance sum, specified as a two-element row vector in the form [WeightXYZ WeightQ]. WeightXYZ is the translational weight and WeightQ is the rotational weight. Both weights must be nonnegative numeric values.

    Data Types: single | double

    Output Arguments

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    Distance between transformations, returned as a nonnegative numeric scalar. The distance calculate changes depending on the transformation object type of transformation1 and transformation2 or rotation1 and rotation2:

    • se3 — The dist function calculates translational and rotational distance independently and combines them in a weighted sum specified by the weights argument. The translational distance is the Euclidean distance between transformation1 and transformation2. The rotational distance is the angular difference between the rotations of transformation1 and transformation2.

    • so3 — The dist function calculates the rotational distance as the angular difference between the rotations of rotation1 and rotation2.

    To calculate the rotational distance, the dist function converts the rotation matrix of transformation1 and transformation2 or rotation1 and rotation2 into quaternion objects and uses the quaternion dist function to calculate the angular distance.

    See Also

    Functions

    Objects