#### Describing rotation and translation in 3D

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We learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.

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We learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.

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We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure.

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For a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.

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Image warping allows us to shrink (or expand) an image by any scale factor, as well as to translate and rotate it. Let’s look at how image warping works.

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Image warping allows us to shrink (or expand) an image by any scale factor, as well as to translate and rotate it. Let’s look at how image warping works.

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A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.

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We consider a robot with four joints that moves its end-effector in 3D space.

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We recap the important points from this lecture.

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We summarise the important points from this lecture.

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We summarise the important points from this lecture.