#### Angle-axis representation of rotation in 3D

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The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

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The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

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When it comes to describing a blob we can do more than just area, centroid position and bounding box. By looking at second order moments we can compute an ellipse that has the same moments of inertia as the blob, and we can use its aspect ratio and orientation to describe the shape and orientation […]

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We discuss the structure of a right-handed 3D coordinate frame and the spatial relationship between its axes which is encoded in the right-hand rule.

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When a camera moves in the world, points in the image move in a very specific way. The image plane or pixel velocity is a function of the camera’s motion and the position of the points in the world. This is known as optical flow. Let’s explore the link between camera and image motion.

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The relationship between world coordinates, image coordinates and camera spatial velocity has some interesting ramifications. Some very different camera motions cause identical motion of points in the image, and some camera motions leads to no change in the image at all in some parts of the image. Let’s explore at these phenomena and how we […]

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We start by looking at a number of different types of robot arm with particular focus on serial-link robot manipulators.

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We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.

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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 learn how to use information from three magnetometers to determine the direction of the Earth’s north magnetic pole.