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I plan to write a painting program based on linear combinations of xy plane points (0,1), (1,0) and (0,0). Such system works identically to RGB, except that the primaries are not within the gamut but at the corners of a triangle that encloses the entire gamut. I have seen the three points being referred to as X, Y and Z (upper case) somewhere, but I cannot find the page anymore (I marked them to the picture myself).

My pixel format stores the intensity of each of those three components the same way as RGB does, together with alpha value. This allows using pretty much any image manipulation operation designed for RGBA without modifying the code.

What is my format called? Is it XYZA, RGBA or something else? Google doesn't seem to know of XYZA. RGBA will get confused with sRGB + alpha (which I also need to use in the same program).

Notice that the primaries X, Y and Z and their intensities have little to do with the x, y and z coordinates (lower case) that are more commonly used.

A: 

Are you storing a float between 0.0 and 1.0 for each XYX and A intensity and then mapping that to the RGBA space?

You just have a custom format. It's not called anything special. (I don't believe that it really is a pixel format, it is in fact a color space or color coordinate in a color space being mapped to a certain pixel format.)

I am storing floats for X, Y and Z (which I suppose you meant instead of coordinates x, y and z) and alpha. I can map those values to any color space, the most popular of which is sRGB with alpha.
Tronic
A: 

http://en.wikipedia.org/wiki/RGB_color_space has the answer:

The CIE 1931 color space standard defines both the CIE RGB space, which is an RGB color space with monochromatic primaries, and the CIE XYZ color space, which works like an RGB color space except that it has non-physical primaries that can not be said to be red, green, and blue.

From this I interpret that XYZA is the correct way to call it.

Tronic