#### Introduction to 3D geometry

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We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.

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We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.

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We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.

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We summarise the important points from this lecture.

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We will learn how to create coordinate frames that have smoothly changing position and orientation over time.

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A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]

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The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

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Most computers today have a built-in camera. Let’s look at how we can grab images directly from such a camera and put them in the MATLAB workspace.

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We store movies in files, typically in an MPEG format. Let’s look at what’s inside one of those movie files, and how we can grab a frame from a movie as an image and put it into the MATLAB workspace.

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If we want to process images the first thing we need to do is to read an image into MATLAB as a variable in the workspace. What kind of variable is an image? How can we see the image inside a variable? How do we refer to to individual pixels within an image.

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Since an image in MATLAB is just a matrix of numbers, we could write code to fill in the elements of the matrix. Let’s look at some simple examples such as squares, circles and lines and more complex images formed by pasting these shapes together.