# 3D and Contour Grapher

A graph in 3 dimensions is written in general: *z* = *f*(*x*, *y*). That is, the *z-*value is found by substituting in both an *x-*value and a *y-*value.

The first example we see below is the graph of *z* = sin(*x*) + sin(*y*). It's a function of *x* and *y*.

You can use the following applet to explore 3D graphs and even create your own, using variables *x* and *y*. You can also toggle between 3D Grapher mode and Contour mode.

## Things to do

1. Choose any of the pre-set 3D graphs using the drop down box at the top.

2. You can **enter your own function** of *x* and *y* using simple math expressions (see below the graph for acceptable syntax).

3. Select **Contour** mode using the check box. In this mode, you are looking at the 3D graph from above and the colored lines represent equal heights (it's just like a contour map in geography). The blue lines are lowest and the red ones are highest.

4. You can **vary** the *x-* and *y-* lower and upper limits using the sliders below the graph.

5. You can **vary** the *z-*scale (changing the height of each peak) and the number of **segments** (which alters the sampling rate) using the sliders below the graph.

6. **Zoom** in and out using the mouse wheel (or 2-finger pinching, if on a mobile device). Also make use of the **z-Scale slider** to see main features of the graph

7. **Pan** the whole graph left and right using the right mouse button and dragging (or 3-finger swipe on a mobile device)

This applet should work OK on mobile devices.

Choose function: OR:

Show: floor axes mesh contour

*x*-min

*x*-max

*y*-min

*y*-max

*z*-scale

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## Some graphs to try

The grapher will accept any of the following functions (use the notation shown). You can copy from the examples below if you wish.

**Planes:**(like`3x + 2y - 4`

)- Involving
**powers:**(like`x^2 + 3y^2 - 5x + 2`

) - Any of the
**trigonometric functions:**`sin(x+y), cos((x-y)/2), tan(x/y), sec(x^2/4), cot(3x)`

(several of these will go off to infinity and are a challenge to see) **Exponential**(`e^x, e^y`

) and**logarithm**(`ln(x+y)`

for natural log and`log(x+y)`

for log base 10)**Absolute value**: use "abs" like this:`abs(x+y)`

**Sign**(1 if the sign is positive, −1 if the sign of the function is negative.) For example, try`sign(sin(x))`

In fact, you can use most of the javascript math functions, including

**ceiling:**`ceil(x)`

and**round**:`round(x)`

**square root:**`sqrt(y)`

You can also use any combinations of the above, like `ln(abs(x-y))`

.

**If your graph doesn't work:** Try using brackets! For example, "tan 2x" won't work. You have to put `tan(2x)`

.

## More Information

**Credit:** The above 3D grapher is based on Lee Stemkoski's Three.js Examples.