Geometric design of smooth composite ruled surface strips using dual spherical geometry

This paper deals with geometric construction of smooth composite ruled surface strips. Oriented lines that constitute the rulings of the ruled surfaces are represented by unit vectors with three components over the ring of dual numbers. The problem of designing a smooth ruled surface is studied as that of designing a one-real-parametric curve on the unit dual sphere. Geometric conditions for piecing two ruled surfaces smoothly are developed using differential geometry of curves on the dual sphere. A coordinate frame invariant method for line segmentation is also presented. Finally, a geometric algorithm is presented for constructing composite Bezier ruled surface strips with second-order geometric continuity. The resulting surface strips are coordinate-frame invariant and their rulings are more uniformly parameterized than those obtained with other methods.