Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces

@inproceedings{Onder2010SomeRA,
  title={Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces},
  author={Mehmet Onder and H. Huseyin Uugurlu},
  year={2010}
}
abstract: In this study, we give dual characterizations for Mannheim offsets of ruled surfaces in terms of their integral invariants and obtain a new characterization for the Mannheim offsets of a developable surface, i.e., we show that the striction lines of developable Mannheim offset surfaces are Mannheim partner curves. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of ruled surfaces and their integral invariants. 

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References

SHOWING 1-10 OF 13 REFERENCES
Rational Ruled Surfaces and Their Offsets
TLDR
It is shown that both offset types of rational ruled surfaces are rational, and simple tool paths which are rational quartics are described.
On the integral invariants of a closed ruled surface
SummaryIn this paper, it is shown that the dual integral invariant of a closed ruled surface, the dual angle of pitch, corresponds to the dual spherical surface area described by the dual spherical
On the computational geometry of ruled surfaces
Bertrand offsets of ruled and developable surfaces
On the invariants of trajectory surfaces
Some results on closed ruled surfaces and closed space curves
The approximation of non-degenerate offset surfaces
Mannheim partner curves in 3-space
Abstract.In this paper, we study Mannheim partner curves in three dimensional space. We obtain the necessary and sufficient conditions for the Mannheim partner curves in Euclidean space
...
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