论文信息 - A new formula for winding number

A new formula for winding number

We give a new formula for the winding number of smooth planar curves and show how this can be generalized to curves on closed orientable surfaces. This gives a geometric interpretation of the notion of winding number due to B. Reinhart and D.R.J. Chillingworth.

Grant Cairns | G. Cairns | Margaret Mcintyre | Margaret Mcintyre

[1] M. Spivak. A comprehensive introduction to differential geometry , 1979 .

[2] G. C. Shephard,et al. Rotation and winding numbers for planar polygons and curves , 1990 .

[3] D. R. J. Chillingworth,et al. Winding numbers on surfaces, I , 1972 .

[4] Stephen P. Humphries,et al. A Generalization of Winding Number Functions on Surfaces , 1989 .

[5] M. Berger,et al. Differential Geometry: Manifolds, Curves, and Surfaces , 1987 .

[6] H. Whitney. On regular closed curves in the plane , 1937 .

[7] G. Cairns,et al. A Six-Vertex Theorem for Bounding Normal Planar Curves , 1993 .

[8] Bruce L. Reinhart. Algorithms for Jordan Curves on Compact Surfaces , 1962 .

[9] B. Reinhart. The winding number on two manifolds , 1960 .

[10] Winding number and isotopies for closed curves on S2 , 1984 .

[11] Stephen Smale,et al. Regular curves on Riemannian manifolds , 1958 .