The 3D modeling user interface (UI) method provides a 2D scalable grid on a computer screen that allows a user to extrude a 3D shape therefrom. The 3D shape is then presented on the display screen, which also shows the grid that the shape was extruded from. In addition to 2D grids, the UI allows the user to define 2D concentric circular patterns on a surface of the 3D shape, from which the user can extrude a 3D projection of the concentric circular patterns. A previously defined grid can be extended or bent into an arcuate or curvy grid according to manipulations by the user. Moreover a grid can be folded back on itself by the user. Additionally the UI provides groups of user-defined wavy splines that can be extruded from a displayed surface.