Soft Maximum vs Hard Maximum

The other day i stumbled on an interesting concept called a “Soft Maximum”.

If you think of the normal maximum, you might have something like this:

float maxValue = max(valueA, valueB);

if valueA and valueB come from functions, there’s usually going to be a sharp bend in the graph of the above where the maximum value changes from valueA to valueB or vice versa.

Sometimes, instead of a sharp bend, you would like a smooth transition between the two values – like when using this for graphics or advanced mathematics.

Here’s the formula for soft max:

double SoftMaximum(double x, double y)
{
	double maximum = max(x, y);
	double minimum = min(x, y);
	return maximum + log( 1.0 + exp(minimum - maximum) );
}

Here are 2 really interesting links on computing and using soft max:

Soft Maximum

How to Compute the Soft Maximum

Check out the images below for an example of when you might use this. This is from a shadertoy shader The Popular Shader. The first image is with using normal max, and the second image uses soft max.

softminOFF

softminON

Converting RGB to Grayscale

If you were converting an RGB pixel to grayscale, you might be like me and be tempted to just add the red, green and blue components together and divide by 3 to get the grayscale equivalent of the color.

That’s close, but not quite correct!

Red, green and blue are not equal brightness, so doing a straight average gives you biased results.

There’s a wikipedia page on this topic here, but the equation to use is below:
grayScale = red * 0.3f + green * 0.59f + blue * 0.11f;

Here are some sample images to show you the difference.

Color:
color

Average:
avg

Weighted Average Equation:
good

Why?

You might be wondering “why the heck would i want to convert RGB to grayscale?”

Well… if you render a scene once, convert it to grayscale and shove it into the red channel, then render the scene again slightly offset to the side, convert that to grayscale and shove it into the blue channel, you can get some neat images like the below. Red/Blue 3d glasses required, click the images to view the full size versions (;

redblu3d1

redblue3d2