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Colours in Visual Basic
By James (p385) on November 4, 1998:

Here's one for the brainpans amongst us!

When coding in Visual Basic 5, trying to create a simple draw program, I came across the methods Point and PSet.

Point has the syntax OBJECT.Point (X,Y) and this returns the colour at point (X,Y) as a single integer.

PSet has the syntax OBJECT.PSet (X,Y), RGB(R, G, B) and this sets the colour at point (X,Y) using the RGB syntax.

In the PSet method the variables R, G, & B are all integers ranging form 0 to 255 and the value(V) returned in the Point method is an integer ranging from 0 (black) to 16777215 (white).

I was wondering if I could find the relationship, so after a while of trile and error I found that V = R + (256) G + (2562) B.

I also realised that R, G, and B could be worked out by a series of calculations given only V.

I put it to you to develop a proof for this. Good luck.

Yours sincerely

no. p385 (James)

By Dave (dms22) on November 7, 1998:

This seems like more of a computer science question than a maths one. I believe that your information is not quite correct, and here's the full story:

Programmers generally use hexadecimal numbers and powers of two, since they store 0s and 1s (ie 2 states). Note that 256=28. If you haven't seen hexadecimal notation, it works like this:
1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11,...
This means that you don't get to 10 after 9. There are six more 'numbers' inbetween, representing 11 to 15. To avoid confusion, we shall write an x in front of a hexadecimal number. Then, for example, x6B2 should be read as x2+xB×16+x6×(16×16) = 2+176+1536 =1714. It's a bit confusing at first, but makes programming a lot easier.

So, how does VB store colours? Each of RGB can go from 0 to 255, which is x0 to xFF. To create a large number which has all of the information in it, just put the three numbers together. For example, to have R=x55, G=x7F, B=x00 we would write
V=x557F00
Looking at the value of V in hexadecimal, we can immediately tell how much red, green and blue is in it.

If you understood how to calculate hexadecimal numbers, you might have noticed that the above can be rephrased:
V=R×(2562)+G×256+B
To get R,G,B from V we convert to hex like the above, and one way of doing this is the following:
Divide V by (2562) and look at the number before the decimal point. This is R.
Divide (V-R×(2562)) by 256 and again look at the number before the decimal point. This is G.
Finally, B=V-R×(2562)-G×256.


This only works because each of R,G,B is less than 256. Without this restriction, we could not recover them like this. Can you see why?

Many calculators/computer programs will convert numbers between decimal (normal) and hexadecimal. You might want to see what Octal and binary are like too.

Finally, the largest number you can have, which corresponds to pure white, is xFFFFFF=16777215, which makes more sense when it's in hexadecimal format.

Best of luck with your programming.

-Dave