Abstract: A new method to visualize 3D rotation-free vector fields is presented, which tries to construct a surface in space so that the vectors on it are all orthogonal to it. Firstly, the system of partial differential equations of the surface is established, and then solved by our numerical method similar to classical fourth order Runge-Kutta method. Finally, the discrete points corresponding to the numerical solutions are triangulated to approximate the desired surface. Our numerical method for the partial differential equations borrows the idea of solving ordinary differential equations and the surface constructed reveals the continuity of the vector fields to a greater degree than point icons and line icons.

Key words: computer application, visualization, system of partial differential equations, vector fields, rotation-free