Abstract: The necessary and sufficient conditions for representing circular arc by rational parameter form are explained. On the base, the rational parameter equation of the bicircular arc determined by three points is established. The interpolation of rational bicircular arcs is provided, that contains the establishing equation of continuity, calculating the angles between chords and cutting lines, and constructing the spline curves. Besides a class of surfaces with line segments are constructed and it's cross setions are bicircular arc splines.

Key words: computational geometry, circulararcs, plines, interpolation　equations