Abstract: The One-Sheet Hyperbolid can be formed by connecting the correponding points
of projection point ranges with two intersection lines as the basis in a space. When one line of
them is moved to a new position, the One-Sheet Hyperbolid will generate change in a certain
pattern. Through a systematic analysis to the shape of its intersection lines, it is for the first time to
put forward the existence of the parabola-type intersection line in the One-Sheet Hyperbolid.
Simplification of the drawing of projection point ranges provides theoretical support to further
application of CAD software to automatically produce the Hyperbolid.

Key words: projection point ranges, one-sheet hyperbolid, intersection line, paraboloid