Tokugawa Ieyasu fought a deadly battle with Shingen and Katsuyori - why he later placed former Takeda retainers in high esteem

Whenever the drama of Tokugawa Ieyasu is depicted, there is always a terrifying army standing before him - that would be the Takeda clan led by Shingen and Katsuyori. In particular, at the Battle of Mikatagahara, Ieyasu was driven into a desperate situation, only to narrowly escape death. So did that mean Ieyasu hated the Takeda clan? On the contrary, he respected the Takeda clan's vassals, who boasted of their bravery, and in fact this relation…