Voici trois essais (à peine ébauchés) qui doivent beaucoup aux pages de Friedrich Lohmueller . Je lui ai emprunté, pour ces exemples, les macros permettant de dessiner les axes et l'astuce pour tracer les courbes en 3D. Tous les fichiers sont dans l'archive :
1- Section elliptique : ( ellipse_1.pov )
// d'après Friedrich A. Lohmueller
// date: Aug-2011
// email: Friedrich.Lohmueller_at_t-online.de
// http:// www.friedrich.lohmueller.de/
//------------------------------------------------------------------------
// Choose image_size by Wählen Sie die Bildgröße, indem
// adding to the commandline: sie in der Kommandozeile einfügen:
//
// +h700 +w700
//
//------------------------------------------------------------------------
#version 3.6; // 3.7;
global_settings{assumed_gamma 1.0}
#default{ finish{ ambient 0.1 diffuse 0.9 }}
//------------------------------------------------------------------------
#include "colors.inc"
#include "textures.inc"
#include "stones.inc"
//------------------------------------------------------------------------
#declare Camera_0 = camera { perspective
location < 50, 25,30>
look_at < 0.00, 0.00, 0.00>
angle 15
right x*image_width/image_height
}
camera{Camera_0}
//Place a light--you can have more than one!
light_source {
<10,0,10> //Change this if you want to put the light at a different point
color White*2 //Multiplying by 2 doubles the brightness
}
background { color rgb <0.5, 0.5, 1> }
//------------------------------ the Axes --------------------------------
//------------------------------------------------------------------------
#macro Axis_( AxisLen, Dark_Texture,Light_Texture)
union{
cylinder { <0,-AxisLen-3,0>,<0,AxisLen,0>,0.05
texture{checker texture{Dark_Texture }
texture{Light_Texture}
translate<0.1,0,0.1>}
}
cone{<0,AxisLen,0>,0.2,<0,AxisLen+0.7,0>,0
texture{Dark_Texture}
}
} // end of union
#end // of macro "Axis()"
//------------------------------------------------------------------------
#macro AxisXYZ( AxisLenX, AxisLenY, AxisLenZ, Tex_Dark, Tex_Light)
//--------------------- drawing of 3 Axes --------------------------------
union{
#if (AxisLenX != 0)
object { Axis_(AxisLenX, Tex_Dark, Tex_Light) rotate< 0,0,-90>}// x-Axis
text { ttf "arial.ttf", "x", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate
#end // of #if
#if (AxisLenY != 0)
object { Axis_(AxisLenY, Tex_Dark, Tex_Light) rotate< 0,0, 0>}// y-Axis
text { ttf "arial.ttf", "y", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,AxisLenY+0.20,-0.10>}
#end // of #if
#if (AxisLenZ != 0)
object { Axis_(AxisLenZ, Tex_Dark, Tex_Light) rotate<90,0, 0>}// z-Axis
text { ttf "arial.ttf", "z", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,0.1,AxisLenZ+0.10>}
#end // of #if
} // end of union
#end// of macro "AxisXYZ( ... )"
//------------------------------------------------------------------------
#declare Texture_A_Dark = texture {
pigment{color rgb<1,0.35,0>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
#declare Texture_A_Light = texture {
pigment{color rgb<1,1,1>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
object{ AxisXYZ( 6.0, 4.0, 7.0, Texture_A_Dark, Texture_A_Light)} // <<<<<<<<<<<<<<<<< adapt the axes here !!!
//-------------------------------------------------- end of coordinate axes
//--------------------------------------------------------------------------
//--------------------------- scenery objects ---------------------------
//--------------------------------------------------------------------------
// angle de la normale au plan
// n<0, cos(Omega), sin(Omega)>
#declare Omega = pi/6;
intersection{
cone { <0, 3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
plane {<0,cos(Omega),sin(Omega)>, 1 texture {Yellow_Pine}}
}
union{
#declare X = -5.5; // start X attention: x != X use capital letter X
#declare EndX = 5.5; // end X
#while ( X < EndX )
// Drawing of the "points"< X / f(X) >:
// Zeichnen der "Punkte" ( X / f(X) ):
// Color - Farbe //< X, f(X) ,0>}
sphere{ <0,0,0>,0.025 pigment{ color Red } translate< 1.414*cos(X),1.732-sin(X),-1+1.732*sin(X)>}
// next step:
#declare X = X + 0.002; // next Nr <<<-- increase this value if you have not enough RAM
// or if your computer is too slow!
#end // --------------- end of loop
} // end of union
cone { <0, -3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
//------------------------------------------------------------------------------------ end
2 - Section parabolique ( parabole_1.pov)
// d'après Friedrich A. Lohmueller
// date: Aug-2011
// email: Friedrich.Lohmueller_at_t-online.de
// http:// www.friedrich.lohmueller.de/
//------------------------------------------------------------------------
// Choose image_size by Wählen Sie die Bildgröße, indem
// adding to the commandline: sie in der Kommandozeile einfügen:
//
// +h700 +w700
//
//------------------------------------------------------------------------
#version 3.6; // 3.7;
global_settings{assumed_gamma 1.0}
#default{ finish{ ambient 0.1 diffuse 0.9 }}
//------------------------------------------------------------------------
#include "colors.inc"
#include "textures.inc"
#include "stones.inc"
//------------------------------------------------------------------------
#declare Camera_0 = camera { perspective
location < 50, 25,30>
look_at < 0.00, 0.00, 0.00>
angle 15
right x*image_width/image_height
}
camera{Camera_0}
//Place a light--you can have more than one!
light_source {
<10,0,10> //Change this if you want to put the light at a different point
color White*2 //Multiplying by 2 doubles the brightness
}
background { color rgb <0.5, 0.5, 1> }
//------------------------------ the Axes --------------------------------
//------------------------------------------------------------------------
#macro Axis_( AxisLen, Dark_Texture,Light_Texture)
union{
cylinder { <0,-AxisLen-3,0>,<0,AxisLen,0>,0.05
texture{checker texture{Dark_Texture }
texture{Light_Texture}
translate<0.1,0,0.1>}
}
cone{<0,AxisLen,0>,0.2,<0,AxisLen+0.7,0>,0
texture{Dark_Texture}
}
} // end of union
#end // of macro "Axis()"
//------------------------------------------------------------------------
#macro AxisXYZ( AxisLenX, AxisLenY, AxisLenZ, Tex_Dark, Tex_Light)
//--------------------- drawing of 3 Axes --------------------------------
union{
#if (AxisLenX != 0)
object { Axis_(AxisLenX, Tex_Dark, Tex_Light) rotate< 0,0,-90>}// x-Axis
text { ttf "arial.ttf", "x", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate
#end // of #if
#if (AxisLenY != 0)
object { Axis_(AxisLenY, Tex_Dark, Tex_Light) rotate< 0,0, 0>}// y-Axis
text { ttf "arial.ttf", "y", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,AxisLenY+0.20,-0.10>}
#end // of #if
#if (AxisLenZ != 0)
object { Axis_(AxisLenZ, Tex_Dark, Tex_Light) rotate<90,0, 0>}// z-Axis
text { ttf "arial.ttf", "z", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,0.1,AxisLenZ+0.10>}
#end // of #if
} // end of union
#end// of macro "AxisXYZ( ... )"
//------------------------------------------------------------------------
#declare Texture_A_Dark = texture {
pigment{color rgb<1,0.35,0>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
#declare Texture_A_Light = texture {
pigment{color rgb<1,1,1>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
object{ AxisXYZ( 6.0, 4.0, 7.0, Texture_A_Dark, Texture_A_Light)} // <<<<<<<<<<<<<<<<< adapt the axes here !!!
//-------------------------------------------------- end of coordinate axes
//--------------------------------------------------------------------------
//--------------------------- scenery objects ---------------------------
//--------------------------------------------------------------------------
// angle de la normale au plan
// n<0, cos(Omega), sin(Omega)>
#declare Omega = pi/4;
#declare D = 1.3;
intersection{
cone { <0, 3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
plane {<0,cos(Omega),sin(Omega)>, D texture {Yellow_Pine}}
}
union{
#declare X = -0.4; // start X attention: x != X use capital letter X
#declare EndX = 3.54; // end X
#while ( X < EndX )
// Drawing of the "points"< X / f(X) >:
// Zeichnen der "Punkte" ( X / f(X) ):
// Color - Farbe //< X, f(X) ,0>}
sphere{ <0,0,0>,0.025 pigment{ color Red } translate< 1.3*cos(X)/(0.707+0.707*sin(X)),1.3/(0.707+0.707*sin(X)),1.3*sin(X)/(0.707+0.707*sin(X))>}
// next step:
#declare X = X + 0.002; // next Nr <<<-- increase this value if you have not enough RAM
// or if your computer is too slow!
#end // --------------- end of loop
} // end of union
cone { <0, -3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
//------------------------------------------------------------------------------------ end
3 - Section hyperbolique (hyperbole_1.pov)
// d'après Friedrich A. Lohmueller
// date: Aug-2011
// email: Friedrich.Lohmueller_at_t-online.de
// http:// www.friedrich.lohmueller.de/
#version 3.6; // 3.7;
global_settings{assumed_gamma 1.0}
#default{ finish{ ambient 0.1 diffuse 0.9 }}
//------------------------------------------------------------------------
#include "colors.inc"
#include "textures.inc"
#include "stones.inc"
//------------------------------------------------------------------------
#declare Camera_0 = camera { perspective
location < 50, 25,30>
look_at < 0.00, 0.00, 0.00>
angle 15
right x*image_width/image_height
}
camera{Camera_0}
//Place a light--you can have more than one!
light_source {
<10,0,10> //Change this if you want to put the light at a different point
color White*2 //Multiplying by 2 doubles the brightness
}
background { color rgb <0.5, 0.5, 1> }
//------------------------------ the Axes --------------------------------
//------------------------------------------------------------------------
#macro Axis_( AxisLen, Dark_Texture,Light_Texture)
union{
cylinder { <0,-AxisLen-3,0>,<0,AxisLen,0>,0.05
texture{checker texture{Dark_Texture }
texture{Light_Texture}
translate<0.1,0,0.1>}
}
cone{<0,AxisLen,0>,0.2,<0,AxisLen+0.7,0>,0
texture{Dark_Texture}
}
} // end of union
#end // of macro "Axis()"
//------------------------------------------------------------------------
#macro AxisXYZ( AxisLenX, AxisLenY, AxisLenZ, Tex_Dark, Tex_Light)
//--------------------- drawing of 3 Axes --------------------------------
union{
#if (AxisLenX != 0)
object { Axis_(AxisLenX, Tex_Dark, Tex_Light) rotate< 0,0,-90>}// x-Axis
text { ttf "arial.ttf", "x", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate
#end // of #if
#if (AxisLenY != 0)
object { Axis_(AxisLenY, Tex_Dark, Tex_Light) rotate< 0,0, 0>}// y-Axis
text { ttf "arial.ttf", "y", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,AxisLenY+0.20,-0.10>}
#end // of #if
#if (AxisLenZ != 0)
object { Axis_(AxisLenZ, Tex_Dark, Tex_Light) rotate<90,0, 0>}// z-Axis
text { ttf "arial.ttf", "z", 0.15, 0 texture{Tex_Dark}
scale 0.5 translate <-0.55,0.1,AxisLenZ+0.10>}
#end // of #if
} // end of union
#end// of macro "AxisXYZ( ... )"
//------------------------------------------------------------------------
#declare Texture_A_Dark = texture {
pigment{color rgb<1,0.35,0>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
#declare Texture_A_Light = texture {
pigment{color rgb<1,1,1>}
finish {ambient 0.15 diffuse 0.85 phong 1}
}
object{ AxisXYZ( 6.0, 4.0, 7.0, Texture_A_Dark, Texture_A_Light)} // <<<<<<<<<<<<<<<<< adapt the axes here !!!
//-------------------------------------------------- end of coordinate axes
//--------------------------------------------------------------------------
//--------------------------- scenery objects ---------------------------
//--------------------------------------------------------------------------
// angle de la normale au plan
// n<0, cos(Omega), sin(Omega)>
#declare Omega = pi/2;
#declare D = 1;
#declare bicone = union {
cone { <0, 3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
cone { <0, -3, 0>, 3, <0, 0, 0>, 0 texture {Yellow_Pine}}
}
intersection{
object {bicone}
plane {<0,cos(Omega),sin(Omega)>, D texture {Yellow_Pine}}
}
union{
#declare X = -1.7627; // start X attention: x != X use capital letter X
#declare EndX = 1.76275; // end X
#while ( X < EndX )
// Drawing of the "points"< X / f(X) >:
// Zeichnen der "Punkte" ( X / f(X) ):
sphere{ <0,0,0>,0.025 pigment{ color Red } translate< sinh(X),cosh(X),1>}
sphere{ <0,0,0>,0.025 pigment{ color Red } translate< sinh(X),-cosh(X),1>}
// next step:
#declare X = X + 0.002; // next Nr <<<-- increase this value if you have not enough RAM
// or if your computer is too slow!
#end // --------------- end of loop
} // end of union
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