Embodiments relate to systems and methods for touch-based two-stage text input. The linear tool slide has an elongated construction including an elongated positioning block against which blind broaches are laterally positioned, and an electric servomotor drives the linear tool slide to provide indexing thereof between broaching movements of the broaching ram. The method includes receiving, by the client device, a list of objects of the class of objects requested, the list of objects including an interface attribute, the interface attribute configured to direct the client device to a set of display properties for each object of the list of objects. A parametric patch, such as a Bernstein-Bezier triangular patch or Heron patch, is used to determine how to divide each triangle into smaller non-planar triangles.