Summary: We present a heuristic search algorithm for the \(\mathbb R^d\) Manhattan shortest path problem that achieves front-to-front bidirectionality in subquadratic time. In the study of bidirectional search algorithms, front-to-front heuristic computations were thought to be prohibitively expensive (at least quadratic time complexity); our algorithm runs in \(O(n \log^d n)\) time and \(O(n \log^{d-1} n)\) space, where \(n\) is the number of visited vertices. We achieve this result by embedding the problem in \(R^{d+1}\) and identifying heuristic calculations as instances of a dynamic closest-point problem, to which we then apply methods from computational geometry.