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I have two points and would like a metric that tells me how close those points are to each other. Each point is described by both a 3D position and a 3D orientation.

I can determine the distance between the positions of these points using the euclidean distance, and I can find the angular distance of their orientaions.

Is there a metric that encompasses both the distance and orientation as a single value?

I could combine the rotation and translation into a 4x4 transformation matrix, but I don't see how that that would help me get to a single value metric.

Morgoth
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    A 3D orientation is a 3D vector, so are you working with 6D vectors? The (6D) euclidean distance is a metric, but idk if it is suitable for your needs. – dcolazin May 12 '19 at 15:22

1 Answers1

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You can add the Euclidean distance between the points to the angular distance (after scaling to unit length) as in the linked question.

If you want to weight the distances differently, use any linear combination with positive coefficients.

Whether this construction works for you depends on the application you want it for.

Ethan Bolker
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