File:Coordinate system rotation svg.svg
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Size of this PNG preview of this SVG file: 754 × 599 pixels. Other resolutions: 302 × 240 pixels | 604 × 480 pixels | 966 × 768 pixels | 1,280 × 1,017 pixels | 2,560 × 2,035 pixels | 780 × 620 pixels.
Original file (SVG file, nominally 780 × 620 pixels, file size: 55 KB)
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Summary[edit]
| Description |
English: This image gives a geometric proof of the formulas for rotating a two-dimensional cartesian coordinate system by an angle of α. If a point P has the coordinates (x,y) in the original coordinate system (blue), then P has the coordinates (x’,y’) in the rotated coordinate system (red), where x’ = x·cos α + y·sin α and y’ = -x·sin α + y·cos α. The latter equations can be seen from the picture. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| SVG development | |
| Source code | LaTex\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=220\unitlength,paperheight=175\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{220\unitlength}
\setlength{\textheight}{175\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
\definecolor{cS} {rgb}{0.00,0.00,0.50} % source coordinates
\definecolor{aS} {rgb}{0.00,0.00,0.99} % source auxiliary
\definecolor{cT} {rgb}{0.50,0.00,0.00} % target coordinates
\definecolor{aT} {rgb}{0.99,0.00,0.00} % target auxiliary
\definecolor{lT} {rgb}{0.99,0.60,0.60} % target lengths
\begin{document}
\begin{picture}(215,170)(-65,-10)
% source coordinate system
\thicklines%
\textcolor{cS}{\put(0,-10){\vector(0,1){170}}}%
\textcolor{cS}{\put(-10,0){\vector(1,0){160}}}%
\thinlines%
\textcolor{cS}{\put(90,-2){\line(0,1){4}}}%
\textcolor{cS}{\put(-2,140){\line(1,0){4}}}%
\textcolor{aS}{\put(90,2){\line(0,1){138}}}%
\textcolor{aS}{\put(2,140){\line(1,0){88}}}%
\textcolor{cS}{\put(90,-3){\makebox(0,0)[t]{$x$}}}%
\textcolor{cS}{\put(-3,140){\makebox(0,0)[r]{$y$}}}%
% target coordinate system
\thicklines%
\textcolor{cT}{\put(-8,-4){\vector(2,1){150}}}%
\textcolor{cT}{\put(4,-8){\vector(-1,2){70}}}%
\thinlines%
\textcolor{cT}{\put(-40,75){\line(2,1){4}}}%
\textcolor{aT}{\put(-36,77){\line(2,1){126}}}%
\textcolor{cT}{\put(129,62){\line(-1,2){2}}}%
\textcolor{aT}{\put(127,66){\line(-1,2){40}}}%
\textcolor{cT}{\put(129,62){\makebox(0,0)[t]{$x'$}}}%
\textcolor{cT}{\put(-40,75){\makebox(0,0)[r]{$y'$}}}%
% sin, cos partitioning for x'
\textcolor{aT}{\put(90,0){\line(-1,2){59}}}%
%
\textcolor{lT}{\put(30,20){\vector(-2,-1){32}}}%
\textcolor{lT}{\put(38,24){\vector(2,1){32}}}%
\textcolor{lT}{\put(41,21){\makebox(0,0)[br]{$x \cdot \cos\alpha$}}}%
%
\textcolor{lT}{\put(61,130.500){\vector(2,1){27}}}%
\textcolor{lT}{\put(53,126.500){\vector(-2,-1){21}}}%
\textcolor{lT}{\put(65,127){\makebox(0,0)[br]{$y \cdot \sin\alpha$}}}%
% sin, cos partitioning for y'
\textcolor{aT}{\put(0,140){\line(-2,-1){56}}}%
\textcolor{aT}{\put(0,140){\line(1,-2){18}}}%
\textcolor{lT}{\put(-23,56){\vector(1,-2){27}}}%
\textcolor{lT}{\put(-25,60){\vector(-1,2){27}}}%
\textcolor{lT}{\put(-27,56){\makebox(0,0)[bl]{$y \cdot \cos\alpha$}}}%
%
\textcolor{lT}{\put(4,122){\vector(-1,2){8}}}%
\textcolor{lT}{\put(6,118){\vector(1,-2){8}}}%
\textcolor{lT}{\put(9,122){\makebox(0,0)[tr]{$x \cdot \sin\alpha$}}}%
% point to be rotated
\textcolor{black}{\put(90,140){\circle*{1}}}%
\textcolor{black}{\put(91,141){\makebox(0,0)[bl]{$P$}}}%
% rotation angles
\textcolor{black}{\put(8,2){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(88,10){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(-2,10){\makebox(0,0){$\alpha$}}}%
\textcolor{black}{\put(82,138){\makebox(0,0){$\alpha$}}}%
\end{picture}
\end{document}
|
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- 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.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:46, 28 July 2018 | | 780 × 620 (55 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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