Opportunity knocked for SHoP Architects on July 2, 2009. On that Thursday, Bruce C. Ratner, the beleaguered developer of the controversial Atlantic Yards sports village planned for Brooklyn, N.Y., made an offer that any architect would be crazy to turn down but almost as crazy to accept.

Ratner wanted SHoP to put a better face on a critically panned redesign for his $825-million Barclays Center arena—the centerpiece of the 22-acre transit-oriented development. And he wanted a sketch from SHoP in only five days.