Coordinates

 

There are many diiferent coordinates in the world!

The most common is cartesian coordinates, where we plot a point by how far along and up.

Then there are polar coordinates, which use distance and angle

But the elements of a matrix also have coordinates, but they don't relate well to cartesian coordinates, sadly.

And when programming computer graphics the coordinates are different again!

Cartesian Coordinates

Cartesian coordinates start with the concept of a number line

There is a zero point and values increase to the right.

That seems natural as we write from the left to the right (possibly so right-handed people can more easily see what they have just written, also seems be true when chiselling!)

Then the next thing we want to do is go up or down, and up seems better being positive, yes?

So we get this:

Matrix Coordinates

But matrices use a different system, we put the row number (which is the up-down direction) first, then the left-right direction. Oh help me!

And we don't start at (0,0), we start at (1,1)

So we get this:

Screen Coordinates

Screen coordinates are very similar to cartesian coordinates, but the up-down direction starts at the top and goes down.

So drawing a function graph on a computer screen can be confusing: if we want the bottom corner of the graph to be 300 px from the top of the screen, we have to use (x,300-y) to plot any point.

Angles

With polar coordinates the angle starts along th x-axis and increases counter-clockwise (opposite to how closks go)

But with compass direction we start along the y-axis and go in the clockwise direction.

(Tears are being held back at this point)

Why?

Just life I suppose.

But it is important for you to know all this, just so you don't think you are going crazy when you find your ups and downs being reversed in direction, or order!