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Detecting Singularities in a Graph

Asked 2010-03-07T19:06:42.993
10

I am creating a graphing calculator in Java as a project for my programming class. There are two main components to this calculator: the graph itself, which draws the line(s), and the equation evaluator, which takes in an equation as a String and... well, evaluates it.

To create the line, I create a Path2D.Double instance, and loop through the points on the line. To do this, I calculate as many points as the graph is wide (e.g. if the graph itself is 500px wide, I calculate 500 points), and then scale it to the window of the graph.

Now, this works perfectly for most any line. However, it does not when dealing with singularities.

If, when calculating points, the graph encounters a domain error (such as 1/0), the graph closes the shape in the Path2D.Double instance and starts a new line, so that the line looks mathematically correct. Example:

Good Asymptote
(source: imagesocket.com)

However, because of the way it scales, sometimes it is rendered correctly, sometimes it isn't. When it isn't, the actual asymptotic line is shown, because within those 500 points, it skipped over x = 2.0 in the equation 1 / (x-2), and only did x = 1.98 and x = 2.04, which are perfectly valid in that equation. Example:

Bag Asymptote
(source: imagesocket.com)

In that case, I increased the wind

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1 Answer

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I finally figured out a way to have singularities graphed properly.

Essentially what I do is for every point on the graph, I check to see if it is inside the visible graphing clip. If I hit a point on the graph that is outside the visible clip, I graph that first point outside the clip, and then stop graphing any invisible points after that.

I keep calculating points and checking if they are inside the visible clip, not graphing ones that are outside the clip. Once I hit a point that is inside the clip again, I graph the point before that point, and then graph the current point.

I keep doing this until I've graphed the entire line. This creates the illusion that the entire line is begin drawn, when only the visible parts are.

This won't work if the window is large and the actual graph size in pixels is small, but it does suffice for me.

answered 2010-04-05T02:30:33.550

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