A new approach for indexing multigrain diffraction data is presented. It is based on the use of a monochromatic beam simultaneously illuminating all grains. By operating in sub-volumes of Rodrigues space, a powerful vertex-finding algorithm can be applied, with a running time that is compatible with online analysis. The resulting program, GrainSpotter, is sufficiently fast to enable online analysis during synchrotron sessions. The program applies outlier rejection schemes, leading to more robust and accurate data. By simulations it is shown that several thousand grains can be retrieved. A new method to derive partial symmetries, called pseudo-twins, is introduced. Uniquely, GrainSpotter includes an analysis of pseudo-twins, which is shown to be critical to avoid erroneous grains resulting from the indexing.