File:Gnomonic.png

Summary[edit]

DescriptionGnomonic.png	English: Gnomonic projection (projection from the center of the sphere) Latviešu: Gnomoniskā projekcija (projekcija no sfēras centra)
Date	8 May 2009
Source	Own work (Original text: Own work by uploader, created with Mathematica 7.0.1)
Author	Marozols
Other versions	This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file “Gnomonic.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Source Code[edit]

 

This diagram was created with Mathematica.

 (*Origin*) o = {0, 0, 0}; (*Coordinate axis*) {ex, ey, ez} = IdentityMatrix[3]; (*With of the plane*) w = 2; (*Overhang coefficient*) \[Delta] = 1.2; (*Axis*) axis = {Black, Arrow3D[{o, w*ex}], Arrow3D[{o, w*ey}], Arrow3D[{o, w*ez}]}; (*Sphere*) sph = {Orange, Opacity[0.7], Sphere[o]}; (*Plane1*) pln1 = {LightGray, Polygon[{{-w, w, -1}, {w, w, -1}, {w, -w, -1}, {-w, -w, -1}}]}; (*Plane2*) pz = Normalize@{0.7, 0.3, 1.1}; px = Normalize@{-pz[[2]], pz[[1]], 0}; py = Last@Orthogonalize[{pz, px, ey}]; t = Abs[1/py[[3]]]; \[CurlyEpsilon] = 1.01; pln2 = {LightGray, Opacity[0.3], Polygon[(*(#-(\[CurlyEpsilon]-1)pz)&/@*){\[Delta]*px + \[Delta]*t* py, \[Delta]*px - \[Delta]*py, -\[Delta]*px - \[Delta]* py, -\[Delta]*px + \[Delta]*t*py}]}; (*Circle*) \[Gamma] = \[Pi]/4; MediumThick = Thickness[0.004]; crc = {Black, MediumThick, Line@Table[\[CurlyEpsilon] (px*Cos[\[Alpha]] + py*Sin[\[Alpha]]), {\[Alpha], (\[Pi] + \[Gamma])/2, 2 \[Pi] + (\[Pi] - \[Gamma])/2, 0.05}]}; (*Projection*) r = Table[ px*Cos[\[Alpha]] + py*Sin[\[Alpha]], {\[Alpha], (\[Pi] - \[Gamma])/ 2, (\[Pi] + \[Gamma])/2, \[Gamma]/6}]; r1 = (#/Abs[#[[3]]]) & /@ r; proj = {Black, PointSize[0.01], Point[o], Point /@ (\[CurlyEpsilon]*r), Point /@ r1, Line[{o, #}] & /@ r1, Red, MediumThick, Line[\[CurlyEpsilon]*r], Line[r1]}; (*Graphics*) DefaultThick = Thickness[0.0015]; g = Graphics3D[{DefaultThick, EdgeForm[DefaultThick], sph, pln1, pln2, crc, proj}, Boxed -> False, Lighting -> "Neutral", ViewPoint -> 2 {0.7, -0.3, 0.1}, ImageSize -> 600, Method -> {"ShrinkWrap" -> True}]; g = Append[g, PlotRegion -> {{-0.02, 1.02}, {-0.03, 1.03}}] 

Licensing[edit]

Marozols, the copyright holder of this work, hereby publishes it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Attribution: Marozols

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

You may select the license of your choice.

 

This diagram was created with Mathematica.