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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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.
The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.
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 […]
If we apply a sequence of 3D rotations to an objects we see that the order in which they are applied affects the final result.
This is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.
We revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.
In order to determine the size and distance of objects in the scene our brain uses a number of highly evolved tricks. Let’s look at some of these.
We revisit the important points from this masterclass.
We combine what we’ve learnt about smoothly varying position and orientation to create smoothly varying pose, often called Cartesian interpolation.