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So we have learned the first way on how to plot three dimensional data.

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But of course, we can also generate a real 3D plot.

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So for this, we just take the same arrays that we have to find here.

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So the X values to Y values and the corresponding Z values that we have plotted here in terms of their

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color.

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But now we're going to plot them by their actual height.

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And to do this, we must use these so-called Contour 3D plots.

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And this is a bit tricky, I would say, because I mean, our PC screen is, of course, two dimensional

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and we want to plot it in three dimensions.

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So we need some kind of projection and some viewpoints, and this is exactly is exactly what we are

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going to do first.

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We will have to define the commands called Peltier.

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So it's again enough plot lib commands and then axes.

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Projection

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is 3D.

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So this enables us to do 3D plots.

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And now I must give this one also a name.

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So this will be our 3D plot.

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So, yeah, I don't know.

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Maybe it's called it's.

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Lots.

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Or projection, maybe a bit a bad name, but yeah, it doesn't really matter what we call it, just

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have to remember.

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And then we just write plot projection.

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Don't contour 3D at now, here comes the actual plot.

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So I mean, you probably guessed already what's going to come next?

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The X components, the Y components, because the components, then we need some kind of know quality.

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No.

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And then we can also provide some color map.

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And for example, we could use binary.

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And this will be a plot, so you can also control the viewpoint by writing down lots of projection,

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which is our name, and then the option will leave you in it and you can then provide the vector from

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which you are watching.

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For example, I tested this one, so now it looks a bit different.

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I told you that this number controls the quality of the plots.

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So for example, if you decrease it, you see basically we just add some lines here, and if we just

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have 10 and we just have 10 lines.

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And so, yeah, these are basically these lines.

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And you can also see here it's a one to one correspondence.

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So we just have one that just looks like this.

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So obviously, the more lines we have to smooth out the plot looks, but also the longer it takes to

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calculate it and the higher the storage capacity or the memory will be than for a simple binary like

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you check what happens if we do it like this.

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So then we get this colorful plot.

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Maybe you like this better, but here you can provide a color map and you can Google.

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The different color maps binary would be a black and white method.

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All right, so we have now plotted this data in a three dimensional fashion.

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Now, of course, we can also do is just to make some line and scatter plots, as we have done before,

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in two dimensions.

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So let me show you how this works.

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It's, of course, pretty similar, but this will be the last example for the plotting that I'm going

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to show you.

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So since it's pretty similar to the last one, let me just go straight ahead.

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I write T dot axes.

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Once again, projection is 3D to enable the three dimensional plotting and this one, maybe I come up

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with a better name.

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Peltier three.

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And all right, so now what we can do is we can we have to specify new values and maybe just go ahead

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and show you what I have in mind here.

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So this time I will start with the Z coordinate, which may look a bit unusual, but you hopefully will

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see soon why I do this.

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So in 3D, all the dimensions are have the same rights.

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So to say so you don't have to define first X and Y and calculate Z.

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You can also first define Z and then calculate X and Y, for example.

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And this is what we're going to do here.

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So once again, we have to define sound in space.

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Some are basically.

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And I go from zero to 30.

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I tested this before.

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That works quite well.

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And I use 301 points then from here.

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So so this is basically just a list which goes from zero down to zero point one zero point two until

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it reaches 30.

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Now from here, I calculate the X coordinate and the Y coordinate.

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Sorry, like this.

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So the X coordinate will just be a sign function

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and the Y coordinate will be a cosine function.

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So you see, this one is something like a circle.

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But at the same time, the C coordinate that will increase linearly.

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So if we can do now is we can write Patti 3D, which is our name from the for the plot.

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And then just as previously we write or we wrote Contour 3D.

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This time we write Plot 3D, and now we have to provide the lists for the variables.

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But here we have to make sure to give them in the right order.

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Otherwise, yeah, we will project in a different way.

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So you see, we have to circle in the X Y plane, but in the Z direction, we have a linear dependence,

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so we get this type of spiral.

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So now we can play a bit with the data.

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For example, I told you what happens if we choose the wrong order, then our spiral will go along to

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different direction, of course.

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So it's also possible.

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What do you have to be careful to really get the correct thing that you want to get?

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And we can also scale this, for example, to make it not a circle, but an ellipse.

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So like this, and you see it still looks like a circle.

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But when you look at the axes, this axis goes from minus one to one, and this from from minus two

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to two.

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Still, in the plots, they have the same length.

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So if you want to make them really their actual length, you have to explicitly define the limits of

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the plot.

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So this you can do by writing down plots, dots x limb and then also plot toward the y limb.

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And now we must provide the same numbers here, and I take two.

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Now you see, it's an ellipse, so there's oval shape instead of the round circular shape that we have

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before.

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So now let me show you another thing that's possible.

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Let me just copy this.

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And this time, instead of using plot three d, we use Scatter 3D.

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So this is really the same thing as we did in two dimensions, but this one gave us a smooth line as

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here.

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And this one gave us individual data points.

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So here you see all of these points, and especially if I decrease the number or the range, and you

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will see that it's not actual smooth, but they are really individual points that you can plot.

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And as always, you can combine several plots so you could combine this one and this one.

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All right.

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So in our plotting lecture, we have started from two dimensional data where we have created a scatterplot

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which are individual data points.

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Then we have created these line plots, which you can do by writing down field dot plots.

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Then we have come to three dimensional data, which you can visualize using density or contour plots,

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where the third dimension is basically encoded by the color as hero here.

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Or you can go to real three dimensional plots where you have such a surface three dimensional space.

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Or you can even have some like parametric plots where you have a line or even individual data points

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in three dimensional space.