Introduction to 3D geometry
In the last lecture we talked about how we described the position of objects in a two dimensional world. We used the example, for instance, a robot and we created a two dimensional co-ordinate frame.
We placed the co-ordinate frame at a reference location and we can describe the position of the robot with respect to that coordinate frame. We also talked about how we describe the orientation of the object; that is which way the robot is pointing with respect to the axes on this coordinate frame.
Now what we are going to do is to kick it up a level of complexity and introduce the third dimension. So for most robotics the third dimension is really important. The robots hand for instance, in any sort of real robot, the hand is going to move in a plane, but it is also going to be able to move up and down.
So we need to be able to describe the position and orientation of bodies in three-dimensional space. But there are also a lot of robots that move in three-dimensional space. So here I have a model airplane, or course an airplane flies through the air. It goes up and it goes down. It can move left and right, and it can also rotate in a number of interesting ways. It can pitch up and down, it can yaw like this, and it can roll like this.
So underwater robots are another example, they are a bit like this but instead of flying through the air, they are flying through the water. So these are two really important classes of robots today, robots that fly and robots that swim under the water and their motion is described in terms of three-dimensional space.
Where perhaps a simple wheeled robot like this, we could get by with just describing it’s position and it’s orientation in terms of two-dimensional space.
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.
This content assumes high school level mathematics and requires an understanding of undergraduate-level mathematics; for example, linear algebra - matrices, vectors, complex numbers, vector calculus and MATLAB programming.