Based on the gear engagement theory, the mathematical model of the planar enveloping hourglass worm gears was established. By combination with engineering practice, the geometrical features of worm and gear are analyzed. Taking the secondary contact zone of worm gears in typical design as an example, reconfiguration methods of curved surface composed of unequally distribute data points are researched. Result shows that the required precision of the space surface can be achieved and the surface can be built easily through programming, when principal curves are planer curve and the cross ones are Non-Uniform Rational B-Splines(NURBS) curve. On UG-GRIP platform, three-dimensional model building system of planar enveloping hourglass worm drives is developed. The accuracy of the solid model is validated by example, that the max error of the data points is 4.7 μm