We show that human observers strongly underestimate a linear or circular trajectory that a luminous spot follows in the dark. At slow speeds, observers are relatively accurate, but, as the speed increases, the size of the path is progressively underestimated, by up to 35%. The underestimation imposes little memory load and does not require tracking of the trajectory. Most importantly, we found that underestimation occurred only when successive motion vectors changed in direction. This suggests a perceptual rather than representational origin of the illusion, related to vector-sum integration over time of neural motion signals in different directions. (Contains 3 footnotes and 9 figures.)