File:Parabola in projective space.svg
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Original file (SVG file, nominally 600 × 600 pixels, file size: 243 KB)
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Summary
| Description |
English: y=x2 & y=x3 projected on RP2 mapped onto a sphere. |
| Date | |
| Source | Own work |
| Author | RupertMillard |
Intended to replace en:File:Parabola_in_projective_space.png, which is in a raster format.
Made in gnuplot. The code:
#!/usr/bin/gnuplot -persist
set parametric
set urange [-0.9999:0.9999]
set vrange [-1:1]
set isosamples 25, 25
set xrange [-2:2]
set yrange [-2:2]
set zrange [-1:1]
set style line 1 lt rgb "#dddddd" lw 1
set style line 2 lt rgb "#9999ff" lw 1
set style line 3 lt rgb "#0000ff" lw 1
set style line 4 lt rgb "#ff9999" lw 1
set style line 5 lt rgb "#ff0000" lw 1
set border 15 ls 1
unset key
set noxtics
set noytics
set noztics
set view 55, 25
set terminal svg
# For scaling [-1:1] to [-∞:∞]
scale(x) = (x/((1-x)*(1+x)))
splot cos(u*pi)*cos(v*pi), sin(u*pi)*cos(v*pi), sin(v*pi) ls 1, \
(u*2),(u*2)**2,-1 ls 2, \
scale(u)/sqrt(scale(u)**2+scale(u)**4+1), scale(u)**2/sqrt(scale(u)**2+scale(u)**4+1), -1/sqrt(scale(u)**2+scale(u)**4+1) ls 3, \
-scale(u)/sqrt(scale(u)**2+scale(u)**4+1), -scale(u)**2/sqrt(scale(u)**2+scale(u)**4+1), 1/sqrt(scale(u)**2+scale(u)**4+1) ls 3, \
(u*2),(u*2)**3,-1 ls 4, \
scale(u)/sqrt(scale(u)**2+scale(u)**6+1), scale(u)**3/sqrt(scale(u)**2+scale(u)**6+1), -1/sqrt(scale(u)**2+scale(u)**6+1) ls 5, \
-scale(u)/sqrt(scale(u)**2+scale(u)**6+1), -scale(u)**3/sqrt(scale(u)**2+scale(u)**6+1), 1/sqrt(scale(u)**2+scale(u)**6+1) ls 5
Then the svg was cropped by changing the output to contain this line:
<svg width="600" height="600" viewBox="145 130 310 280"
Licensing
|
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:09, 15 September 2009 | | 600 × 600 (243 KB) | RupertMillard | This is now a correct, 1 to 2 projection. |
| 21:54, 14 September 2009 |  | 600 × 600 (177 KB) | RupertMillard | {{Information |Description={{en|1=y=x^2 & y=x^3 projected onto R^2.}} |Source=Own work by uploader |Author=RupertMillard |Date=2009-09-14 |Permission= |other_versions= }} Category:Algebraic geometry |
File usage
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