On a recent hard-hat tour of the Whitney Museum of American Art’s new building in Downtown Manhattan’s Meatpacking District, the project’s architect Renzo Piano emphasized the way it will connect to its surroundings. “I love making places that contribute to city life,” said Piano. The 9-story museum, which is half-way through construction, stands at the southern end of the High Line with a series of outdoor terraces stepping down on its city side and great glass walls that will look out to the Hudson River on its other side. The $422-million building will offer the Whitney three times the amount of exhibition space as its current home in a Marcel Breuer structure on 75th Street, as well as a 170-seat theater, an education center, a conservation lab, and a ground-floor restaurant run by Danny Meyer. For the first time, the Whitney will be able to display on a permanent basis a significant portion of its collection. It will also boast the largest column-free museum gallery in New York City: 18,000 square feet on its fifth floor. The Metropolitan Museum of Art will take over the Whitney’s Breuer building when the Piano building opens in 2015.