In a laminar flow in a mixing vessel, the velocity distribution is decided deterministically. When a blade rotates at a constant speed in a vessel, the velocity has perfect time-periodicity. In this convective mixing, there are definite rules controlling the fluid motion, and they are repeatedly applied. This mixing process is considered to be a deterministic process for which templates exist, and by the repeated use of them the mixing pattern is gradually develops. These templates are the time-invariant streaklines and the streak surface made by their assembly. The various forms of mixing blades and the use of baffles determine the curvature of the streaklines and the undulation of the streak surface as their assembly. Their deformations enhance fluid mixing in various manners. This study focuses on the geometry and the deformation of streaklines and the streak surface are focused. Through this, the mechanism of laminar fluid mixing in a mixing vessel and its enhancement effects on fluid mixing are clarified.