CP is your life's blood in crafting. Control helps, as does Craftsmanship, but when you run out of CP you are effectively done with that craft, regardless of your Craftsmanship or Control.

If you do not have enough CP, then you need the CP food/melds. If you have enough CP, and enough Craft/Control to meet the minimum required for the item you are crafting, then you have the choice of foods.