Y Coordinate

Y coordinate

Y position offset

I think you're getting the hang of this.

You remember a robot operating in a plane environment has usually 3 coordinates.

Let's try this first one two comma negative three.

So this could be li.

If we want to plot points, if we call this the y axis, and we call this the x axis, and if we call this the x coordinate, or maybe more properly that the x coordinate and call this the y coordinate, then we can set up an equation here.

The desired y position in pixels

It's negative 4.

The x coordinate is 2.

Each of these red dots of which there are several thousand here is a discrete guess where the road might be.

That's our x coordinate.

This is our coordinate x naught f of x naught, and up here is our coordinate for this point, which would be, the x coordinate would be x naught plus h, and the y coordinate would be f of x naught plus h.

I want to use the cost function of 1, so each step costs you exactly 1 for now.

Which is interesting.

Part d, or coordinate d, or point d.

So it's that point there.

That's just the y coordinate up here.

Each of these small dots over here is a hypothesis where the robot might be.

This actually is the x slope.

Or b which is, remember, what was b?

So we're at 0.

Well, in y.

Where's my x, y's, and z's?

There we solved the x coordinate.

Let's do b right there. b is at the coordinate let's see, its x coordinate, and just drop down there, is 7.

Looks like a fancy term, but all it means is, look.

This angle is beta, and here is our robot car.

Well, let's use this one. This is interesting two comma zero.

You're like, gee, how do I plot this in three dimensions?

The vertical axis here is the y axis and the convention when we get an ordered pair like this is the first coordinate is the x coordinate and the second coordinate is the y coordinate

For example, we can set a position.

So the difference in y I could just say y minus k.

So the point 0, 3 is on both of these lines.

Negative 8.

And its y coordinate, it's 2 below the origin.

Whatever happens with the y and z axes won't affect the x axis value. So in the second system x will also be 10 .

And d sub 2, what's this going to be equal to?

Let me get another color.

So negative 6, that's right there.

This is really challenging to program. It's based on the math I just gave you.

You see that right there. y coordinate negative 2, as well.

So, this is the x coordinate, and this is the y coordinate.

Change in y, change in y, over change in x, is equal to we take the first y point, which is 3.