Murti Shapes

One question reagrding the shapes of various deities that a young mind would ask, is: 

• How did current shape of various deity evolve and is consistent across the world?

This one is tough question and I could not find any good answer anywhere. GaneshaSpeaks link provides references of Murti Pooja in Vedic Scriptures, Sri Ratnakar Sadasyula Ji provides some background to origin of the shapes in Quora. 

Our understanding is as follows: 

• Inital / Main Form by Rishi during Meditation: Various Rishis saw these deities in various forms in their meditation. They gave shapes to these deities and over time these were standardized.
• Additional Shapes and Weapons to Fulfill Their Roles: Various aspects of the shapes [number of hands, heads, weapons, posture, body shape] might have evolved overtime to enable these deities to fullfill their role as imagined by Rishis. For example: 
  • Lord Ganesh: All non-Sanaatani must be intrigued by Murti of Ganesh. This site explains various origins of Ganesh Ji, symbolism in his form and meaning of his many names.
  • Lord Shiv: Shiv is one of the main deity in Sanaatan Society. There are many sites explainig various aspects of his forms. Some of these sites are: Art of Living; Isha; etc.
• Additional Shapes, Forms to Assimilate Various Groups: Various aspects of these forms also suggest an effort on part of our Rishies to assimilate various tribes [community] into Sanaatan Society by accepting their form of deity into main forms of Sanaatan Deity, e.g. say a Tribe worships Snakes [even today there are tribes that worship snake and snakes don't bite anyone in that tribe; look here for an example village.]; Rishis added a story that our Lord Shiv has snakes around his neck and Lord Vishnu sleeps on Sheshnaag etc.  Some other tribe might be worshipping moon and moon is placed on the head of Shiv and so on.