1. A computer-implemented method for automatic construction of an arch form for a patient's teeth, the method comprising the following steps performed by a computer: receiving three dimensional data for the patient's teeth; detecting facial axis points for the teeth; creating a plurality of pairs of corresponding teeth; calculating a mid-point for each created pair of teeth; calculating a line that approximates the calculated mid-points; utilizing the calculated line as a y-axis of a coordinate frame of the arch form; utilizing a normal of an occlusal plane as a z-axis of the coordinate frame of the arch form; determining an origin of the coordinate frame of the arch form; determining an x-axis of the coordinate frame by calculating a cross product of the y-axis and z-axis of the coordinate frame of the arch form; transforming each of the detected facial axis points into the calculated coordinate frame of the arch form; and constructing control points of a Bezier spline curve from the transformed facial axis points.