User:Jacobolus/Stereo


 * Materials for a future stereographic projection article

Stereographic projections through the "south" pole (mapping the "north" pole to the origin):
 * https://archive.org/details/encyklomentmatik02weberich/page/n359/
 * doi: 10.1112/plms/s1-17.1.379
 * Fundamentals of Spacecraft Attitude Determination and Control, 10.1007/978-1-4939-0802-8_2
 * https://arxiv.org/pdf/1703.01244.pdf
 * Wierenga 1938 https://krex.k-state.edu/bitstream/handle/2097/24186/LD2668T41938W51.pdf?sequence=1
 * https://archive.org/details/bwb_P8-ABB-831/page/7/
 * Wolten, G. (1970). Plotting stereographic projections as an orienter-setting subroutine. Metallography, 3(4), 391–397.
 * E.J.W. Whittaker (1984) https://www.iucr.org/education/pamphlets/11

Cesàro

 * Oughtred, William (1651) The Solution of All Sphærical Triangles, Both Right and Oblique, by the Planisphære. Oxford: Leonard Lichfield


 * (also see, )
 * (also see, )
 * (also see, )


 * Hilton, Harold (1904). "On Spherical Curves". Proceedings of the London Mathematical Society 2, no. 1: 267-282.
 * Hilton, H. (1905). "On Speherical Curves. Part II." Proceedings of the London Mathematical Society, 2(1), 150-160.

Graphical methods (stereonet, etc.)

 * Freeman, Alexander (1872). "Graphic Conversion of Stellar Condinates." Monthly Notices of the Royal Astronomical Society, Vol. 33, p. 18 33: 18.
 * Hutchinson, A. (1908). "On a protractor for use in constructing stereographic and gnomonic projections of the sphere". Mineralogical Magazine, 15(69), 93–112. doi:10.1180/minmag.1908.015.69.01
 * Dilloway, A. J. (1942). The Cartographic Solution of Great Circle Problems. Journal of the Royal Aeronautical Society, 46(373), 4–31. doi:10.1017/s0368393100100057
 * E.J.W. Whittaker (1984) The Stereographic Projection. University College Cardiff Press. https://www.iucr.org/education/pamphlets/11
 * https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=8841&context=masters_theses
 * https://www.geokniga.org/bookfiles/geokniga-structural-analysis-and-synthesis-laboratory-course-structural-geology.pdf
 * Symmetry of Crystals and Molecules, By Marcus Frederick & Charles Ladd 2014, OUP
 * Symmetry of Crystals and Molecules, By Marcus Frederick & Charles Ladd 2014, OUP

Computing

 * Packer (1977) "Computer-Generated Standard Stereographic Projections"

History



 * https://doi.org/10.1029/TR017i001p00100
 * Euler:
 * https://scholarlycommons.pacific.edu/euler-works/490/
 * https://scholarlycommons.pacific.edu/euler-works/491/

Geometry
Two essential properties:


 * Circles to circles property
 * Conformal (angle preserving)

Antipodal points
Every point on the sphere is opposite to another point lying on the same axis through the center (a diameter). The two points are said to be antipodes to each-other; each is the other's antipodal point.

Great circles
The analog of straight lines (geodesics) in spherical geometry are called great circles. A great circle is the intersection between a sphere embedded in Euclidean space and a plane through the sphere's center. The axis perpendicular to that plane intersects the sphere in two places called the poles of the great circle.

The stereographic projection picks out one great circle, the primitive circle, whose pole is the center of projection. (When the stereographic projection of the Earth is centered on one of the geographic poles, the primitive circle is the equator.)

Every great circle on the sphere is projected to a straight line or circle in the plane which is perpendicular to the primitive circle.

Conformal rotation vector
The conformal rotation vector, whose coordinates are also known as modified Rodrigues parameters or Wiener–Milenkovic parameters, is a three-dimensional vector representing a three-dimensional rotation or orientation. It is the stereographic projection of a versor (unit quaternion) onto the pure-imaginary hyperplane. It was first described by Thomas Wiener (1962), called the conformal rotation vector by Veljko Milenkovic (1982), and named the modified Rodrigues vector by Malcolm Shuster (1993). It is related to the Rodrigues vector first described by Olinde Rodrigues (1840) and called by Josiah Gibbs (1884) the vector semitangent of version.

"modified Rodrigues parameters", "conformal rotation vector", "stereographic ..."


 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.
 * Shoham, M., & Jen, F.-H. (1993). On rotations and translations with application to robot manipulators. Advanced Robotics, 8(2), 203–229.