Search Results for: Cartesian coordinates

Let’s recap the basics of homogeneous coordinates to represent points on a plane.

We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

We summarise the important points from this lecture.

We revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.

We revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.

We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

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.

An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

For an image stored as a variable in the MATLAB workspace let’s look at how we access the values of individual pixels in an image using their row and column coordinates. Using the MATLAB colon operator we can extract an intensity profile, extract a submatrix which is a region of the image, flip the image […]