File:Twisted cubic curve.png

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Summary

DescriptionTwisted cubic curve.png	Twisted cubic with xy and xz surfaces in the interval [-1,1]
Date	11 September 2007
Source	Own work
Author	Claudio Rocchini

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Source code (POVRAY)


#include "colors.inc"
#include "metals.inc"

global_settings {max_trace_level 5}

camera {
    perspective
    location <-2100,2400,2205>
    look_at  <0,0,0>
    right x
    up    y
  }

sky_sphere {
    pigment {
        color rgb<1,1,1>
    }
} 

light_source {<-3000,2800,2300>   color White }
light_source {< 2000,-10000,2300> color Gray45 }

#declare R1 = 5;

sphere_sweep {   
  linear_spline
  2,
  <-1000,-1000,-1000>,R1
  < 1000,-1000,-1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000, 1000,-1000>,R1
  < 1000, 1000,-1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000, 1000, 1000>,R1
  < 1000, 1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000,-1000, 1000>,R1
  < 1000,-1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
} 
sphere_sweep {   
  linear_spline
  2,
  <-1000,-1000,-1000>,R1
  <-1000, 1000,-1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  < 1000,-1000,-1000>,R1
  < 1000, 1000,-1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  < 1000,-1000, 1000>,R1
  < 1000, 1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000,-1000, 1000>,R1
  <-1000, 1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000,-1000,-1000>,R1
  <-1000,-1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  < 1000,-1000,-1000>,R1
  < 1000,-1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  < 1000, 1000,-1000>,R1
  < 1000, 1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}
sphere_sweep {   
  linear_spline
  2,
  <-1000, 1000,-1000>,R1
  <-1000, 1000, 1000>,R1 
  pigment {rgb 0}
  no_shadow
}

parametric {
            function{v*1000}              
            function{u*1000}
            function{u*u*1000}
            <-1,-1>,<1,1>
            contained_by{box{<-1000,-1000,-1000>,<1000,1000,1000>}}
            accuracy 0.00001
            precompute 20,x,y,z
            texture {  pigment { color rgbt<0.10, 0.25, 0.85, 0.76> }  }
            no_shadow
         }
         
parametric {
            function{u*u*u*1000}              
            function{u*1000}
            function{v*1000}
            <-1,-1>,<1,1>
            contained_by{box{<-1000,-1000,-1000>,<1000,1000,1000>}}
            accuracy 0.00001
            precompute 20,x,y,z
            texture {  pigment { color rgbt<0.85, 0.25, 0.10, 0.76> }  }
            no_shadow            
         }
 
sphere_sweep{
linear_spline
32,
<-1000,-1000,-1000>,5,
<-818.67,-935.484,-1000>,5,
<-660.703,-870.968,-1000>,5,
<-524.487,-806.452,-1000>,5,
<-408.412,-741.935,-1000>,5,
<-310.866,-677.419,-1000>,5,
<-230.237,-612.903,-1000>,5,
<-164.916,-548.387,-1000>,5,
<-113.289,-483.871,-1000>,5,
<-73.7471,-419.355,-1000>,5,
<-44.6779,-354.839,-1000>,5,
<-24.4705,-290.323,-1000>,5,
<-11.5135,-225.806,-1000>,5,
<-4.1959,-161.29,-1000>,5,
<-0.906314,-96.7742,-1000>,5,
<-0.0335672,-32.2581,-1000>,5,
<0.0335672,32.2581,-1000>,5,
<0.906314,96.7742,-1000>,5,
<4.1959,161.29,-1000>,5,
<11.5135,225.806,-1000>,5,
<24.4705,290.323,-1000>,5,
<44.6779,354.839,-1000>,5,
<73.7471,419.355,-1000>,5,
<113.289,483.871,-1000>,5,
<164.916,548.387,-1000>,5,
<230.237,612.903,-1000>,5,
<310.866,677.419,-1000>,5,
<408.412,741.935,-1000>,5,
<524.487,806.452,-1000>,5,
<660.703,870.968,-1000>,5,
<818.67,935.484,-1000>,5,
<1000,1000,-1000>,5 
pigment {rgb <0.4,0.4,0.4>}
no_shadow
}
sphere_sweep{
linear_spline
32,
<-1000,-1000,1000>,5,
<-818.67,-935.484,1000>,5,
<-660.703,-870.968,1000>,5,
<-524.487,-806.452,1000>,5,
<-408.412,-741.935,1000>,5,
<-310.866,-677.419,1000>,5,
<-230.237,-612.903,1000>,5,
<-164.916,-548.387,1000>,5,
<-113.289,-483.871,1000>,5,
<-73.7471,-419.355,1000>,5,
<-44.6779,-354.839,1000>,5,
<-24.4705,-290.323,1000>,5,
<-11.5135,-225.806,1000>,5,
<-4.1959,-161.29,1000>,5,
<-0.906314,-96.7742,1000>,5,
<-0.0335672,-32.2581,1000>,5,
<0.0335672,32.2581,1000>,5,
<0.906314,96.7742,1000>,5,
<4.1959,161.29,1000>,5,
<11.5135,225.806,1000>,5,
<24.4705,290.323,1000>,5,
<44.6779,354.839,1000>,5,
<73.7471,419.355,1000>,5,
<113.289,483.871,1000>,5,
<164.916,548.387,1000>,5,
<230.237,612.903,1000>,5,
<310.866,677.419,1000>,5,
<408.412,741.935,1000>,5,
<524.487,806.452,1000>,5,
<660.703,870.968,1000>,5,
<818.67,935.484,1000>,5,
<1000,1000,1000>,5 
pigment {rgb <0.4,0.4,0.4>}
no_shadow
}
sphere_sweep{
linear_spline
32,
<-1000,-1000,1000>,5,
<-1000,-935.484,875.13>,5,
<-1000,-870.968,758.585>,5,
<-1000,-806.452,650.364>,5,
<-1000,-741.935,550.468>,5,
<-1000,-677.419,458.897>,5,
<-1000,-612.903,375.65>,5,
<-1000,-548.387,300.728>,5,
<-1000,-483.871,234.131>,5,
<-1000,-419.355,175.858>,5,
<-1000,-354.839,125.911>,5,
<-1000,-290.323,84.2872>,5,
<-1000,-225.806,50.9886>,5,
<-1000,-161.29,26.0146>,5,
<-1000,-96.7742,9.36524>,5,
<-1000,-32.2581,1.04058>,5,
<-1000,32.2581,1.04058>,5,
<-1000,96.7742,9.36524>,5,
<-1000,161.29,26.0146>,5,
<-1000,225.806,50.9886>,5,
<-1000,290.323,84.2872>,5,
<-1000,354.839,125.911>,5,
<-1000,419.355,175.858>,5,
<-1000,483.871,234.131>,5,
<-1000,548.387,300.728>,5,
<-1000,612.903,375.65>,5,
<-1000,677.419,458.897>,5,
<-1000,741.935,550.468>,5,
<-1000,806.452,650.364>,5,
<-1000,870.968,758.585>,5,
<-1000,935.484,875.13>,5,
<-1000,1000,1000>,5 
pigment {rgb <0.4,0.4,0.4>}
no_shadow
}
sphere_sweep{
linear_spline
32,
<1000,-1000,1000>,5,
<1000,-935.484,875.13>,5,
<1000,-870.968,758.585>,5,
<1000,-806.452,650.364>,5,
<1000,-741.935,550.468>,5,
<1000,-677.419,458.897>,5,
<1000,-612.903,375.65>,5,
<1000,-548.387,300.728>,5,
<1000,-483.871,234.131>,5,
<1000,-419.355,175.858>,5,
<1000,-354.839,125.911>,5,
<1000,-290.323,84.2872>,5,
<1000,-225.806,50.9886>,5,
<1000,-161.29,26.0146>,5,
<1000,-96.7742,9.36524>,5,
<1000,-32.2581,1.04058>,5,
<1000,32.2581,1.04058>,5,
<1000,96.7742,9.36524>,5,
<1000,161.29,26.0146>,5,
<1000,225.806,50.9886>,5,
<1000,290.323,84.2872>,5,
<1000,354.839,125.911>,5,
<1000,419.355,175.858>,5,
<1000,483.871,234.131>,5,
<1000,548.387,300.728>,5,
<1000,612.903,375.65>,5,
<1000,677.419,458.897>,5,
<1000,741.935,550.468>,5,
<1000,806.452,650.364>,5,
<1000,870.968,758.585>,5,
<1000,935.484,875.13>,5,
<1000,1000,1000>,5 
pigment {rgb <0.4,0.4,0.4>}
no_shadow
}
sphere_sweep{
linear_spline
32,
<-1000,-1000,1000>,20,
<-818.67,-935.484,875.13>,20,
<-660.703,-870.968,758.585>,20,
<-524.487,-806.452,650.364>,20,
<-408.412,-741.935,550.468>,20,
<-310.866,-677.419,458.897>,20,
<-230.237,-612.903,375.65>,20,
<-164.916,-548.387,300.728>,20,
<-113.289,-483.871,234.131>,20,
<-73.7471,-419.355,175.858>,20,
<-44.6779,-354.839,125.911>,20,
<-24.4705,-290.323,84.2872>,20,
<-11.5135,-225.806,50.9886>,20,
<-4.1959,-161.29,26.0146>,20,
<-0.906314,-96.7742,9.36524>,20,
<-0.0335672,-32.2581,1.04058>,20,
<0.0335672,32.2581,1.04058>,20,
<0.906314,96.7742,9.36524>,20,
<4.1959,161.29,26.0146>,20,
<11.5135,225.806,50.9886>,20,
<24.4705,290.323,84.2872>,20,
<44.6779,354.839,125.911>,20,
<73.7471,419.355,175.858>,20,
<113.289,483.871,234.131>,20,
<164.916,548.387,300.728>,20,
<230.237,612.903,375.65>,20,
<310.866,677.419,458.897>,20,
<408.412,741.935,550.468>,20,
<524.487,806.452,650.364>,20,
<660.703,870.968,758.585>,20,
<818.67,935.484,875.13>,20,
<1000,1000,1000>,20 
pigment {rgb <0.2,1,0.2>}
no_shadow
}

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

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.

This file is licensed under the Creative Commons Attribution 3.0 Unported 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.

You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	09:50, 10 September 2014		541 × 536 (145 KB)	RokerHRO	optipng -o7 → 27.30% decrease
	14:13, 10 September 2007		541 × 536 (199 KB)	Rocchini	{{Information \|Description=Twisted cubic with xy and xz surfaces in the interval [-1,1] \|Source=self-made \|Date=2007-09-11 \|Author= Claudio Rocchini }}

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Usage on ar.wikipedia.org
- تنوع جبري
Usage on ast.wikipedia.org
- Variedá alxebraica
Usage on ba.wikipedia.org
- Алгебраик күп төрлөлөк
Usage on ca.wikipedia.org
- Varietat algebraica
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Usage on de.wikiversity.org
- Algebraische Raumkurven/Gedrehte Kubik/Projektionen auf Ebenen/Beispiel
- Kurs:Algebraische Kurven (Osnabrück 2008)/Vorlesung 19
- Kurs:Algebraische Kurven (Osnabrück 2012)/Vorlesung 19
- Monomiale Kurve/Affin/Restklassenbeschreibung/Textabschnitt
- Kurs:Algebraische Kurven (Osnabrück 2017-2018)/Vorlesung 19
- Kurs:Algebraische Kurven (Osnabrück 2017-2018)/Vorlesung 19/kontrolle
Usage on el.wikipedia.org
- Μάικλ Ατίγια
Usage on en.wikibooks.org
- Commutative Algebra/Irreducibility, algebraic sets and varieties
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Usage on es.wikibooks.org
- Curso de alemán para principiantes con audio/Lección 106b
Usage on fa.wikipedia.org
- واریته جبری
Usage on fr.wikipedia.org
- Michael Atiyah
Usage on gl.wikipedia.org
- Variedade alxébrica
- Michael Atiyah
Usage on he.wikipedia.org
- פורטל:מתמטיקה/מאמר נבחר/אוסף
- עקום המומנטים
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- 베로네세 매장
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- Алгебраическое многообразие
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Usage on www.wikidata.org
- Q7858555
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- 代數簇

File:Twisted cubic curve.png

Summary

Source code (POVRAY)

Licensing

Captions

Items portrayed in this file

depicts

creator

some value

copyright status

copyrighted

copyright license

Creative Commons Attribution 3.0 Unported

GNU Free Documentation License, version 1.2 or later

inception

11 September 2007

source of file

original creation by uploader

File history

File usage

Global file usage