Abstract The known rotation problem refers to a special case of structure-from-motion where the absolute orientations of the cameras are known. When formulated as a minimax (ℓ∞) problem on reprojection errors, the problem is an instance of pseudo-convex programming. Though theoretically tractable, solving the known rotation problem on large-scale data (1,000’s of views, 10,000’s scene points) using existing methods can be very time-consuming. In this paper, we devise a fast algorithm for the known rotation problem. Our approach alternates between pose estimation and triangulation (i.e., resection-intersection) to break the problem into multiple simpler instances of pseudo-convex programming. The key to the vastly superior performance of our method lies in using a novel minimum enclosing ball (MEB) technique for the calculation of updating steps, which obviates the need for convex optimisation routines and greatly reduces memory footprint. We demonstrate the practicality of our method on large-scale problem instances which easily overwhelm current state-of-the-art algorithms</