average Color objects when adding them together

[jason]

This would make it easy to create purple, for example, as red+blue.

Related tickets:

• #5601 - predefine colors in Sage.
• #5602 - make .lighter() and .darker() methods for Sage Color objects.
• #5603 - make a .mix() method for Sage color objects.
• #5604 - average Color objects when adding them together.
• #5605 - Construct Color objects using hsl and hsv values.

[jason]

This is done now:

sage: sage.plot.colors.red+sage.plot.colors.blue
RGB color (0.5, 0.0, 0.5)

So this ticket should be closed.

[mvngu]

This looks like fixed, but the averaging operator "+" is binary:

[mvngu@sage ~]$ sage
----------------------------------------------------------------------
| Sage Version 4.4.1, Release Date: 2010-05-02                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: r = sage.plot.colors.red
sage: g = sage.plot.colors.green
sage: b = sage.plot.colors.blue
sage: r; g; b
RGB color (1.0, 0.0, 0.0)
RGB color (0.0, 0.50196078431372548, 0.0)
RGB color (0.0, 0.0, 1.0)
sage: r + g; r + b
RGB color (0.5, 0.25098039215686274, 0.0)
RGB color (0.5, 0.0, 0.5)
sage: (r + g) + b; r + g + b
RGB color (0.25, 0.12549019607843137, 0.5)
RGB color (0.25, 0.12549019607843137, 0.5)
sage: (r + b) + g; r + b + g
RGB color (0.25, 0.25098039215686274, 0.25)
RGB color (0.25, 0.25098039215686274, 0.25)
sage: (g + b) + r; g + b + r
RGB color (0.5, 0.12549019607843137, 0.25)
RGB color (0.5, 0.12549019607843137, 0.25)

For more than two operands, I thought that "+" would average over the number of operands. Instead, "+" averages the first two, then average the result with the last operand.

[jason]

That's because the blending is not associative. We are just providing a simple way to blend colors together. That's a limitation of the method---is there a reason why we should insist on the addition being associative?

Mixing colors and color theory in general is a very involved topic; we are just scratching the surface here with suboptimal, but still useful, methods and shortcuts.

[mvngu]

Replying to jason:

That's because the blending is not associative. We are just providing a simple way to blend colors together. That's a limitation of the method---is there a reason why we should insist on the addition being associative?

No reason I can think of. My surprise as expressed above has more to do with my lack of understanding.