Lloyd relaxation is widely employed to generate point distribution for a variety of applications in computer graphics, computer vision, and image processing. However, Lloyd relaxation has several known issues that could harm distribution quality, among which the tendency to settle into semi-regular structures being the most severe. Recently, Balzer et al. addressed this issue via a variation of Lloyd relaxation, termed capacity constraint Voronoi tessellation (CCVT). CCVT has superior quality than Lloyd relaxation, but could run orders of magnitude slower. Given the importance of Lloyd relaxation, CCVT has the potential to become a widely adopted replacement, but its slow computation could be a hindrance. In this paper, we present fast CCVT, an accelerated version of the original CCVT method. Our acceleration is composed of different methods ranging from high level parallelization and complexity reduction to low level speed optimizations. Our aggregated accelerations are orders of magnitude faster than the original method proposed by Balzer et al. (and 10 times faster than a previous accelerated implementation of the same technique) while maintaining excellent distribution quality and scaling very well as the number of points increase. We provide additional analysis for the properties of CCVT.