How does Shakespeare transform the myth of Phoebus and Daphne to dramatize this theme?

The original myth of Apollo (Phoebus) and Daphne has been one told throughout the histories of both the ancient Greeks and Romans. It is the story of a god, Apollo, who constantly chases after the nymph, Daphne, out of uncontrollable lust that is born from him being shot in revenge by the god of love and eroticism, Eros (Cupid). This story, written by Roman poet Plubius Ovidius Naso during the reign of Augustus, makes part of the larger literary work by this author, Metamorphoses. It was centuries later that William Shakespeare takes on the story of Apollo and Daphne and transforms it into the story of Helena and Demetrius in A Midsummer's Night Dream. The main difference between the two stories is that while in Ovid's story the man chases after the woman for her affections, Shakespeare changes the expected gender roles of man chasing woman and turns it into woman chasing man, something that had been unheard of up until then. All the other elements were maintained by Shakespeare in his Midsummer's Night Dream.

Shakespeare uses Helena instead of Daphne. He transforms a man into a woman. Helena is in love with Demetrious, but he in turn loves another lady. Shakespeare changes a male to a female character. In Midsummer night's Dream it is a woman who chases a man and the myth is different because there is love and not lust in the chase.