Quaternionic and Dual Quaternionic Darboux Ruled Surfaces

Abstract

In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

Keywords

• Darboux vector
• distribution parameter
• dual spherical curve
• dual angle of pitch
• quaternion
• spatial quaternion
• ruled surface.

References

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