The Denver Botanic Gardens has spent more than $116 million revamping itself over the past decade. There’s a new science pyramid, gift shop and welcome center, a children’s garden, an outdoor bistro, a tea garden and a massive greenhouse complex. Old structures (like the glass-enclosed Boettcher Memorial Tropical Conservatory) have been refurbished, and new ones (like a green-roofed parking garage) have been built from the ground up. But none of those projects contains the potential to transform the garden and the way Denverites use it as much as the Freyer-Newman Center, the 13th and final step of its master redevelopment plan, which opened to the public last week. The center — a sprawling, 100,000-square-foot structure on the corner of York Street and 11th Avenue — is meant to serve a number of purposes.