The pattern of time-dependent laminar fluid mixing without molecular diffusion is uniquely determined when the velocity vectors are known. Therefore, the exact mixing pattern can, in principle, be calculated by integration of the velocity vectors with respect to time. Even if the flow is laminar, however, it is extremely difficult to recognize the mechanism of fluid mixing and the overall physical and geometrical image of a complex flow field in a three-dimensional agitated vessel. On the other hand, it is known that laminar fluid mixing in an agitated vessel proceeds following the template made by the streakline growing from the tip of a paddle blade. In this paper, we propose the new mixing model based on the streakline and the mapping on it. This mixing model provides clearer physical images than the ordinary mixing model based on pathlines and clarifies the relation between the time-invariant structure behind the mixing fluid field and the time-variable properties in the mixing pattern that change following the invariant rule.