Can't get a simple graph to work.

Unity Engine
1

I have a screenfader that fades the screen in and out in a linear manner. I wanted to apply a curve to it and decided on the graph of y = x ^ 1/2.
If you remember, it is supposed to look like this:

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1484345--82409--$squarex_zpsf7a86c99.jpg
1484345--82409--$squarex_zpsf7a86c99.jpg824×366 13.5 KB

So I wrote a method and applied it to the fade and it didn’t work the way I expected. To figure out why, I took a look at what data is being output:

void Fade()
	{
		float count = 0;
		float change = 0;
		float fadeAlpha = 0;
		while(fadeAlpha < 1)
		{
			change = Mathf.Pow(count, 1f/2f);
			fadeAlpha += change;
			Debug.Log("fadeAlpha is "+fadeAlpha);
			Debug.Log("the change is "+change);
			count += 0.001f;
		}
	}

Of course 1/2 could have been written as 0.5, or I could have done sqrt(count) instead, but they all give the same results.

The numbers I was seeing didn’t make sense. The graph starts out with a steep curve and this curve becomes less and less the more we go along the x axis. So this means the value of the variable change should at first be larger numbers and then smaller numbers near the end. But in reality it was the opposite. I even took the data and plotted a graph and got this:

1024×780 103 KB

1484345--82410--$graph_zps85525352.jpg
1484345--82410--$graph_zps85525352.jpg1024×780 101 KB

Which is the inverse of what I’m supposed to get!
I have spent a lot of time trying to figure out where I have screwed up but have not been able to figure it out. I am using the equation

y = x ^ 1/2

but am instead getting a graph that looks more like

y = x ^ 2

I would appreciate if anyone could help me figure out what I’m doing wrong?

2

It’s been a while so maybe you figured it out already, but your problem is that you are adding the value from your function each step. Set fadeAlpha to sqrt(count) directly if that’s the shape you want your curve.

When you keep adding it, your fadeAlpha will approximate the integral of sqrt(count)–which is (2/3)*(x^1.5). That is what you’re seeing (with some error because you are numerically integrating it).

3

Yes, of course! /facepalm
This is exactly where I was screwing it up, how could I be so stupid? I can’t even remember why I decided to add it to itself.
Thank you very much! Sometimes you really need someone else to point out your obvious stupid mistakes to you.

4

Don’t feel bad… I was never good and graphing functions so I still find it impressive :wink: