In flow visualization, field lines are often used to convey both global and local structure and movement of the flow. One challenge is to find and classify the representative field lines. Most existing solutions follow an automatic approach that generates field lines characterizing the flow and arranges these lines into a single picture. In our work, we advocate a user-centric approach to exploring 3D vector fields. Our method allows the user to sketch 2D curves for pattern matching in 2D and field lines clustering in 3D. Specifically, a 3D field line whose view-dependent 2D projection is most similar to the user drawing will be identified and utilized to extract all similar 3D field lines. Furthermore, we employ an automatic clustering method to generate field-line templates for the user to locate subfields of interest. This semi-automatic process leverages the user's knowledge about the flow field through intuitive user interaction, resulting in a promising alternative to existing flow visualization solutions. With our sketch-based interface, the user can effectively dissect the flow field and make more structured visualization for analysis or presentation.