3D and Heatmap.Rmd

The contour() function produces a contour plot in order to represent three-dimensional data; it is like a topographical map. It takes three arguments:

1. A vector of the x values (the first dimension),
2. A vector of the y values (the second dimension), and
3. A matrix whose elements correspond to the z value (the third dimension) for each pair of (x,y) coordinates.

As with the plot() function, there are many other inputs that can be used to fine-tune the output of the contour() function. To learn more about these, take a look at the help file by typing ?contour.

```{r}

x=seq(-pi ,pi ,length =50)
y=x
f=outer(x,y,function (x,y)cos(y)/(1+x^2))
contour (x,y,f)
contour (x,y,f,nlevels =45, add=T)
fa=(f-t(f))/2
contour (x,y,fa,nlevels =15)
```
The image() function works the same way as contour(), except that it produces a color-coded plot whose colors depend on the z value. This is known as a heatmap, and is sometimes used to plot temperature in weather forecasts. Alternatively, persp() can be used to produce a three-dimensional plot. The arguments theta and phi control the angles at which the plot is viewed.
```{r}
image(x,y,fa)
persp(x,y,fa)
persp(x,y,fa ,theta =30)
persp(x,y,fa ,theta =30, phi =20)
persp(x,y,fa ,theta =30, phi =70)
persp(x,y,fa ,theta =30, phi =40)
```