Search Results for: dimension

We summarise the important points from this lecture.

An image is a two dimensional projection of a three dimensional world. The big problem with this projection is that big distant objects appear the same size as small close objects. For people, and robots, it’s important to distinguish these different situations. Let’s look at how humans and robots can determine the scale of objects […]

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.

How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]

How is an image formed? The real world has three dimensions but an image has only two: how does this happen and what are the consequences? We can use simple geometry to understand what’s going on.

As the illumination level changes so do the red, green and blue tristimulus values, but they are linearly related. We can separate brightness from chromaticity which is a two dimensional representation of color. We discuss briefly the effect of gamma encoding on the color reproduction process.

We introduce serial-link robot manipulators, the sort of robot arms you might have seen working in factories doing tasks like welding, spray painting or material transfer. We will learn how we can compute the pose of the robot’s end-effector given knowledge of the robot’s joint angles and the dimensions of its links.

The workspace of a robot arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm.

We will learn about inverse kinematics, that is, how to compute the robot’s joint angles given the desired pose of their end-effector and knowledge about the dimensions of its links. We will also learn about how to generate paths that lead to smooth coordinated motion of the end-effector.

We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.