Biangular coordinates

In mathematics, biangular coordinates are a coordinate system for the plane where $C_{1}$ and $C_{2}$ are two fixed points, and the position of a point P not on the line ${\overline {C_{1}C_{2}}}$ is determined by the angles $\angle PC_{1}C_{2}$ and $\angle PC_{2}C_{1}.$ ^[1]

The sine rule can be used to convert from biangular coordinates to two-center bipolar coordinates.

Applications

Biangular coordinates can be used in geometric modelling and CAD.^[2]^[3]

References

^ Naylor, Michael; Winkel, Brian (2010), "Biangular Coordinates Redux: Discovering a New Kind of Geometry", The College Mathematics Journal, 41 (1): 29–41
^ Ziatdinov, R.; Kim, T. W.; Nabiyev, R. I. (2015), "Two-point G1 Hermite interpolation in biangular coordinates", Journal of Computational and Applied Mathematics, 287: 1–11
^ Ziatdinov, R.; Yoshida, N.; Kim, T. W. (2017), "Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin", Computer Aided Geometric Design, 56: 35–47

External links

G. B. M. Zerr Biangular Coordinates, American Mathematical Monthly 17 (2), February 1910
J. C. L. Fish, Coordinates Of Elementary Surveying
George Shoobridge Carr, A synopsis of elementary results in pure mathematics (see page 742)

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[1] Naylor, Michael; Winkel, Brian (2010), "Biangular Coordinates Redux: Discovering a New Kind of Geometry", The College Mathematics Journal, 41 (1): 29–41

[2] Ziatdinov, R.; Kim, T. W.; Nabiyev, R. I. (2015), "Two-point G1 Hermite interpolation in biangular coordinates", Journal of Computational and Applied Mathematics, 287: 1–11

[3] Ziatdinov, R.; Yoshida, N.; Kim, T. W. (2017), "Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin", Computer Aided Geometric Design, 56: 35–47

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Applications

See also

References

External links