File talk:Parabola & cubic curve in projective space.png
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// POV-Ray 3.7 Scene File
// By Rupert Millard
// http://www.rupertmillard.net
//
//
// DERIVED from "a_geo_sph1.pov"
// Author: Friedrich A. Lohmueller, 2005/2009
// email: Friedrich.Lohmueller_at_t-online.de
// homepage: http://wwww.f-lohmueller.de
//
//------------------------------------------------------------------------
#if ( version < 3.7 ) global_settings{ assumed_gamma 1.0 } #end
//------------------------------------------------------------------------
#include "colors.inc"
#include "textures.inc"
#include "glass.inc"
#include "metals.inc"
#include "golds.inc"
#include "stones.inc"
#include "woods.inc"
#include "shapes.inc"
#include "shapes2.inc"
#include "functions.inc"
#include "math.inc"
#include "transforms.inc"
//------------------------------------------------------------------------
#declare Camera_0 = camera { // xy-view
angle 20
location <0.0 , 0.0 ,-10.0>
right x*image_width/image_height
look_at <0.0, 0.0 , 0.0>
}
#declare Camera_1 = camera { // diagonal view
location <0,0,-3>
right x*image_width/image_height
look_at <0 , 0 ,0>
rotate <35,-15,0>
translate <0,1,0>
}
#declare Camera_2 = camera { // yz-view
angle 20
location <31.0 , 7.0 ,1.0>
right x*image_width/image_height
look_at <1.5 , 1.4 , 1.0>
}
#declare Camera_3 = camera {
angle 20
location < 0.0 , 37.5 ,-0.0001>
right x*image_width/image_height
look_at <0 , 0 , 2.0>
}
camera{Camera_1}
//------------------------------------------------------------------------
// sun -------------------------------------------------------------------
light_source{<3000,5500,-1000> color White rotate 20*y}
// sky -------------------------------------------------------------------
sky_sphere{ pigment{ gradient <0,1,0>
color_map{ [0 color rgb<1,1,1> ]//White
[0.4 color rgb<1,1,1>]//~Navy
[0.6 color rgb<1,1,1>]//<0.14,0.14,0.56>]//~Navy
[1.0 color rgb<1,1,1> ]//White
}
scale 2 }
} // end of sky_sphere
//------------------------------------------------------------------------
//------------------------------ 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 <AxisLenX+0.05,0.4,-0.10>}
#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<1,0.45,0>}
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( 0, 0, 0, Texture_A_Dark, Texture_A_Light)} // <<<<<<<<<<<<<<<<< adapt the axes here !!!
//-------------------------------------------------- end of coordinate axes
// ground -----------------------------------------------------------------
//---------------------------------<<< settings of squered plane dimensions
#declare RasterScale = 1.0/2;
#declare RasterHalfLine = 0.035/2;
#declare RasterHalfLineZ = 0.035/2;
//-------------------------------------------------------------------------
#macro Raster(RScale, HLine)
pigment{ gradient x scale RScale
color_map{[0.000 color rgbt<1,1,1,1>*0.2]
[0+HLine color rgbt<1,1,1,1>*0.2]
[0+HLine color rgbt<1,1,1,1>]
[1-HLine color rgbt<1,1,1,1>]
[1-HLine color rgbt<1,1,1,1>*0.2]
[1.000 color rgbt<1,1,1,1>*0.2]} }
finish { ambient 0.15 diffuse 0.85}
#end// of Raster(RScale, HLine)-macro
//-------------------------------------------------------------------------
plane { <0,1,0>, 0 // plane with layered textures
texture { pigment{color rgbt<1,1,1,0.7>*1.1}
finish {ambient 0.45 diffuse 0.85}}
texture { Raster(RasterScale,RasterHalfLine ) rotate<0,0,0> }
texture { Raster(RasterScale,RasterHalfLineZ) rotate<0,90,0>}
rotate<0,0,0>
no_shadow
}
//------------------------------------------------ end of squered plane XZ
//--------------------------------------------------------------------------
//---------------------------- objects in scene ----------------------------
//--------------------------------------------------------------------------
#default{ finish {ambient 0.15 diffuse 0.85} } //
/* Some Sample rgb colors - Einige Beispiele f�r rgb Farben
- Qualche esempio per colori rgb
//===========================================================================
pigment { color Green }
Black rgb<0,0,0> ; Gray rgb<1,1,1>*0.5 ; White rgb<1,1,1> ;
Red rgb<1,0,0> ; Green rgb<0,1,0> ; Blue rgb<0,0,1> ; Yellow rgb<1,1,0> ;
Orange rgb<1,0.5,0>; Cyan rgb<0,1,1> ; Magenta<1,0,1,> ;
orange yellow rgba<1,0.65,0> ; YellowGreen rgb<0.5,1,0> ;
Dark Red rgb<0.5,0,0> ; dark green rgb<0,0.5,0> ; dark blue rgb<0,0,0.5>
transparent colors - halbtransparente Farben - colori semi trasparenti:
Red semi transparent:
pigment{ color Red transmit 0.5 } = pigment { color rgbt<1,0,0,0.5>}
*/
//-----------------------------------------------------------------------------------
#declare Rl = 0.055; // radius of lines - Radius der Strecken
#declare Rp = 0.105; // radius of points - Radius der Punkte
//
//------------------------------------------------------------------------------------
#include "analytical_g.inc"
//------------------------------------------------------------------------------------
// -----------------------------------------------------------------------------------
// -----------------------------------------------------------------------------------
// --------------------- Punti e Vettori - Punkte und Vektoren - Points and Vectors
//------------------------------------------------------------------------------------
#declare M1 = < 0.0, 1.0, 0.0>;
#declare R1 = 1.0;
#declare M2 = < 2.0,3.0, 1.0>;
#declare Rx = 3.00;
#declare Ry = 1.00;
#declare Rz = 2.00;
/*object{ Show_Yxz( M1, Rl/2) pigment{ color Yellow }}
object{ Show_Yxz( M2, Rl/2) pigment{ color Yellow }}*/
//------------------------------------------------------------------------------------
// --------------------------------------------------------------- Zeichnen ----------
// ---------------------------------------------------------------- Drawing ----------
sphere{ M1, R1 pigment{ color Yellow transmit 0.6 } finish {phong 1}}
/*object{ Vector( M1, M1+<0,R1,0>, Rl/2) pigment{ color Red } }
object{ Vector( M1, M1+<0,0,-R1>, Rl/2) pigment{ color Red } }*//*
torus{ R1, Rl/2 translate M1 pigment{ color Orange } }
torus{ R1, Rl/2 rotate< 90,0,0> translate M1 pigment{ color Orange } }
torus{ R1, Rl/2 rotate< 0,0,90> translate M1 pigment{ color Orange } }*/
#declare Points = 50;
#declare StartX = -10; // start X attention: x != X use capital letter X
#declare EndX = 10; // end X
#declare lw = 0.01;
sphere_sweep {
cubic_spline, Points,
#declare X = StartX;
#while ( X <= EndX )
<X, 0, X*X>, lw
#declare X = X + (EndX-StartX)/(Points-1);
#end // --------------- end of loop
pigment{ color Red }
no_shadow
}
#declare StartX = -2; // start X attention: x != X use capital letter X
#declare EndX = 10; // end X
sphere_sweep {
cubic_spline, Points,
#declare X = StartX;
#while ( X <= EndX )
<X, 0, pow(X,3)>, lw
#declare X = X + (EndX-StartX)/(Points-1);
#end // --------------- end of loop
pigment{ color Blue }
no_shadow
}
#declare Points = 25;
#declare StartX = 0; // start X attention: x != X use capital letter X
#declare EndX = 1; // end X (never gets here)
#declare Projection1 = array[Points];
#declare Projection2 = array[Points];
#declare X = StartX;
#declare i = 0;
#while ( i < Points )
#declare X = StartX + i/Points*(EndX-StartX);
#declare U = (X/((1-X)*(1+X)));
#declare q = sqrt(pow(U,2)+pow(U,4)+1);
#declare Projection1[i]=<U/q, -1/q, pow(U,2)/q>;
#declare q = sqrt(pow(U,2)+pow(U,6)+1);
#declare Projection2[i]=<U/q, -1/q, pow(U,3)/q>;
// #debug concat(str(q,5,5), "<", str(U/q,5,5), ",", str(-1/q,5,5), ",", str(pow(U,2)/q,5,5),">\n")
#declare i=i+1;
#end
sphere_sweep {
cubic_spline, Points*2+2,
<0,0,1>, lw
#declare i = Points-1;
#while ( i >1)
Projection1[i], lw
#declare i=i-1;
#end
#declare i = 0;
#while ( i < Points)
Projection1[i]*<-1,1,1>, lw
// #debug concat("<", str(Projection1[i].x,5,5), ",", str(Projection1[i].y,5,5), ",", str(Projection1[i].z,5,5),">\n")
#declare i=i+1;
#end
<0,0,1>, lw
Projection1[Points-1], lw
Projection1[Points-2], lw
pigment{ color Red }
translate <0,1,0>
no_shadow
}
sphere_sweep {
cubic_spline, Points*2+2,
<0,0,-1>, lw
#declare i = Points-1;
#while ( i >1)
<-1,-1,-1>*Projection1[i], lw
#declare i=i-1;
#end
#declare i = 0;
#while ( i < Points)
Projection1[i]*<1,-1,-1>, lw
#declare i=i+1;
#end
<0,0,-1>, lw
<-1,-1,-1>*Projection1[Points-1], lw
<-1,-1,-1>*Projection1[Points-2], lw
pigment{ color Red }
translate <0,1,0>
no_shadow
}
#declare epsilon=1e-9;
#declare lw=lw-epsilon;
sphere_sweep {
cubic_spline, Points*2+2
<-epsilon,0,1>, lw
<0,0,1>, lw
#declare i = Points-1;
#while ( i >1)
Projection2[i], lw
#declare i=i-1;
#end
#declare i = 0;
#while ( i < Points)
Projection2[i]*<-1,1,-1>, lw
#declare i=i+1;
#end
<0,0,-1>, lw
<epsilon,0,-1>, lw
pigment{ color Blue }
translate <0,1,0>
no_shadow
}
sphere_sweep {
cubic_spline, Points*2+2
<epsilon,0,-1>, lw
<0,0,-1>, lw
#declare i = Points-1;
#while ( i >1)
Projection2[i]*<-1,-1,-1>, lw
#declare i=i-1;
#end
#declare i = 0;
#while ( i < Points)
Projection2[i]*<1,-1,1>, lw
#debug concat("<", str(Projection1[i].x,5,5), ",", str(Projection1[i].y,5,5), ",", str(Projection1[i].z,5,5),">\n")
#declare i=i+1;
#end
<0,0,1>, lw
<-epsilon,0,1>, lw
pigment{ color Blue }
translate <0,1,0>
no_shadow
}
//------------------------------------------------------------------------------------
//-------------------------------------------------------------------------------- end
