biangular coordinates

Image:BiangularCoordinateSystem.JPG

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_1C_2} is determined by the angles \angle PC_1C_2 and \angle PC_2C_1.{{Citation

| last1 = Naylor

| first1 = Michael

| last2 = Winkel

| first2 = Brian

| title = Biangular Coordinates Redux: Discovering a New Kind of Geometry

| journal = The College Mathematics Journal

| volume = 41

| issue = 1

| pages = 29–41

| year = 2010

| doi = 10.4169/074683410X475092

| language = English}}

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.{{Citation

| last1 = Ziatdinov

| first1 = R.

| last2 = Kim

| first2 = T. W.

| last3 = Nabiyev

| first3 = R. I.

| title = Two-point G1 Hermite interpolation in biangular coordinates

| journal = Journal of Computational and Applied Mathematics

| volume = 287

| pages = 1–11

| year = 2015

| doi = 10.1016/j.cam.2015.02.040

| url = https://www.sciencedirect.com/science/article/pii/S0377042715001107

| language = English

}}{{Citation

| last1 = Ziatdinov

| first1 = R.

| last2 = Yoshida

| first2 = N.

| last3 = Kim

| first3 = T. W.

| title = Visualization and analysis of regions of monotonic curvature for interpolating segments of extended sectrices of Maclaurin

| journal = Computer Aided Geometric Design

| volume = 56

| pages = 35–47

| year = 2017

| doi = 10.1016/j.cagd.2017.06.003

| url = https://www.sciencedirect.com/science/article/pii/S0167839617301206

| language = English

| url-access = subscription

}}

See also

References

{{reflist}}