Converting Scalars to RGB Colormap

Posted on March 4th, 2014
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We can visualize variation of mesh-based scalars by converting each scalar to a color with the help of some colormap. A commonly used system maps the lowest value to blue, the highest to red, and the intermediate values to shades of green, yellow, and orange. This gives a “short” rainbow gradation. An alternate maps the lowest value to purple, which then gives us the full rainbow. In this article I’ll show you how to convert a scalar to the corresponding RGB pair to obtain few different colormaps:grayscale, short rainbow, long rainbow, and yellow to red. You can see an interactive demo in the follow up article on a 2D data plotter.

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Figure 1. Comparison of several different colormaps. This image is generated by your browser, using HTML5 canvas (source).


The first step is to normalize our scalar value s to the range [0:1]. This can be done using \(f=(s-s_{min})/(s_{max}-s_{min})\). We next convert to grayscale by simply multiplying this value by 255 and casting to int, g=(int)f*255. The color value is then simply RGB(g,g,g). In the above demo, I am using a for loop to iterate over the width of the canvas. The code to plot the grayscale bar is:

for (var i=0;i<w;i++)
    var f=i/w;	//convert to [0,1]
    /*plot grayscale*/
    var g=Math.round(f*255);
    ctx.fillStyle = "rgb("+g+","+g+","+g+")";
/*add legend*/
ctx.font="10px serif";

Short Rainbow

My motivation for the short rainbow algorithm was the Wikipedia article on converting HSL to RGB. To convert a scalar to a rainbow, we divide the scalar into four groups. Then based on which group we are in, we perform one of the following linear interpolations:

This ordering follows the image in the Wikipedia article. One downside of this approach is that it will vary from red to blue as f varies from 0 to 1. Typically, we want the opposite, with 0 mapping to blue and 1 to red. So we simply invert the scalar as a=1-f. There are many nifty ways to implement the mapping but I went for simplicity and just used a case. The code is shown below.

/*plot short rainbow RGB*/
var a=(1-f)/0.25;	//invert and group
var X=Math.floor(a);	//this is the integer part
var Y=Math.floor(255*(a-X)); //fractional part from 0 to 255
    case 0: r=255;g=Y;b=0;break;
    case 1: r=255-Y;g=255;b=0;break;
    case 2: r=0;g=255;b=Y;break;
    case 3: r=0;g=255-Y;b=255;break;
    case 4: r=0;g=0;b=255;break;
ctx.fillStyle = "rgb("+r+","+g+","+b+")";

Long Rainbow

The long rainbow is similar to the short rainbow, except that we divide into 5 groups, with the final one consisting of blue at maximum, green at zero, and red increasing linearly from 0 to 255. The code is below

/*convert to long rainbow RGB*/
var a=(1-f)/0.2;
var X=Math.floor(a);
var Y=Math.floor(255*(a-X));
    case 0: r=255;g=Y;b=0;break;
    case 1: r=255-Y;g=255;b=0;break;
    case 2: r=0;g=255;b=Y;break;
    case 3: r=0;g=255-Y;b=255;break;
    case 4: r=Y;g=0;b=255;break;
    case 5: r=255;g=0;b=255;break;
ctx.fillStyle = "rgb("+r+","+g+","+b+")";

Yellow to Red

Finally, the yellow to red map is basically a colored variant of the grayscale map. Its advantage over the rainbow is that it avoids gradient artifacts. We simply keep red at maximum, and vary yellow from 0 to 255, as shown below

/*convert to yellow to red*/
var a=(1-f);
var Y=Math.floor(255*a);
ctx.fillStyle = "rgb("+r+","+g+","+b+")";

3 comments to “Converting Scalars to RGB Colormap”

  1. November 3, 2017 at 1:11 pm

    It seems to me that case “5” for long rainbow is wrong, because the text says red increases linearly but the code just make red=255 not red=255-Y
    And what is weirdest is that I have been given a colormap generated by some people I do not directly know, and I do not know what software they use, but coincidently the last part of their long rainbow color scale is a static pink, not actually changing in the intensity of red nor anything.

    • November 3, 2017 at 1:42 pm

      now I got it, the final group is the case 4. the case 5 is just a final color, not a final group

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