#### Summary of 2D geometry and pose

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We summarise the important points from this lecture.

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We summarise the important points from this lecture.

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We extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.

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We combine what we’ve learnt about smoothly varying position and orientation to create smoothly varying pose, often called Cartesian interpolation.

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We consider multiple objects each with its own coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our algebraic notation to ease the manipulation of relative poses.

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We consider multiple objects each with their own 3D coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our previous 2D algebraic notation to 3D and look again at pose graphs.

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The pose of an object can be considered in two parts, the position of the object and the orientation of the object.

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To fully describe an object on the plane we need to not only describe its position, but also which direction it is pointing. This combination is referred to as pose.

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We recap the important points from this lecture.

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We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

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The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).