我认为，可以理解现在分词短语作原因状语，来举例说明与某人相识的原因。在一个饭局上碰巧与某人同桌在先，然后came to know him. 所以分词用了完成体。如果分词用在句首，则可以用一般体 Being at the same table at a dinner party, I came to know Mr. Smith. 此时，现在分词短语可以理解为时间状语或原因状语。

又如：Tom came/got to know his girl friend by mere chance，having helped her when she was involved in a traffic accident.