JSXGraph - challenge plots

These graphs are for comparison with the ASVG plots which involve the same functions, but are more successfully rendered there (albeit with a massive loss in generality).

You'll observe quite a few problems with the following JSXGraph plots as you zoom out, and/or if you zoom in when x is very large (say around 10,000), or has a large negative value (say around −10,000).

Also, when animating, these JSXGraph curves work very hard (in some cases calculating and plotting 65,000 data points), so things tend to crawl to a standstill, often giving a frames-per-second rate of less than 10.

Here are the same functions plotted using Desmos and Wolfram|Alpha. Desmos also has problems for larger domain values, and it was not possible to even perform the same animations as you see here on this JSXGraph page or the ASVG page. It's a similar story for Wolfram|Alpha.

1. Graph of y = a tan(qx)

Like all the examples on this page, the animation starts reasonably smoothly, but as the domain increases, the number of points goes up, and things slow down considerably.

Current graph: y = a tan(ax)

Animate:

2. Graph of y = a tan(qx2)

The number of points for this one goes up to about 55,000, so the animation is quite slow and janky.

Current graph: y = a tan(ax2)

Animate:

3. Graph of y = a sin(qx)

In this case, the number of points grows to about 20,00, so the animation is a bit smoother than the other examples.

Current graph: y = a sin(qx)

Animate:

4. Graph of y = ax sin(qx2)

In this example, as x gets larger the number of points grows rapidly - to almost 70,000 before it falls over completely. The animation suffers accordingly.

Current graph: y = ax sin(qx2)

Animate:

5. Graph of $ y = \frac{1}{a \sin(qx) + \cos(qx\sqrt{3})} $

Like the other graphs here, there are issues for large values of x, and the animations is very slow.

Current graph:

$$ y = \frac{1}{a \sin(qx) + \cos(qx\sqrt{3})} $$

Animate:

6. Graph of a Fourier series

Very strange things happen for large values of x (try the region near 1 million, for example). The animation is very slow, mostly due to the huge number of points JSXGraph attempts to use.

Current graph:

$$ y = \frac{10}{\pi} \sum_{i=1}^{100}\frac{1}{2i-1}\sin\left(\frac{(2i-1)\pi}{4}\right) $$

Animate:

Other versions

Once again, here are the same graphs as rendered by other function graphers:

  1. ASVG challenge plots (with smooth animations)
  2. Desmos challenge plots (no animations) and you can see Wolfram|Alpha's attempts there as well.