Additive blending of RGB colors representing light

Question

I have a RGB color that represents light. I am looking for an algorithm to draw this over an arbitrary background (could be, for example, an image) in a way that simulates (or resembles) lighting.

Some examples:

• RGB=#888888 represents white light at 50% intensity

  • Painting this over white (#ffffff) background pixels would do nothing
  • Painting this over black (#000000) background pixels would paint as #888888
  • Painting this over red (#ff0000) background pixels would result in a "lighter red"

• RGB=#ff0000 represents red light at 100% intensity

  • Painting this over white (#ffffff) background pixels should result in a "light red" (mix of red and white)
  • Painting this over black (#000000) background pixels would paint as #880000

• RGB=#000000 represents no light. Painting this over any background should have no effect.

I was hoping that I would be able to translate the original RGB color in (a set of) RGBA color(s) that I could paint over the background. I have been looking for an algorithm for this and playing around with HSL, HSB, alpha, etc. but cannot find a generic way to accomplish this.

Is there a generic algorithm to achieve what I want?

Update: I am aware of this question, but I don't think this is a duplicate (despite the similar names). The accepted answer to that question describes a behaviour (Red + Black = Dark red) that does not match this sceneario (lighting). I am specifically looking for an algorithm to simulate (colored) lighting.

Answer 1

If you view the values as decimal you have values that range 0-255. You could sum the two colours and then rescale them back to the range.

FF0000 + FFFFFF 
= 255,0,0 + 255,255,255 
= 510,255,255

Then scale this by 255/510 to

510 * 255/510, 255 * 255/510, 255 * 255/510
= 255, 127, 127

A light red as required.