You talk in your books of a “global perspective” in which a person strives to see the common humanity between the self and the offending other. If a person were to practice the global perspective with most people whom she meets on a daily basis, would this help the person to forgive when it is time to apply this perspective to someone who was cruel?

Yes, this kind of practice on those who have done nothing wrong can be good practice for the time in which there is injustice and pain and anger.  Taking the global perspective with others who are not harmful will not lead to an automatic forgiving (toward those who are unfair to you), but it could make the starting of the process easier.  It could make the cognitive understanding of the offending other easier as well.