// POV-Ray 3.7 Scene File "Regulare_Tetrahedron_Vectors_1.pov" // author: Friedrich A. Lohmueller, Dec-2009/Jan-2011 // homepage: www.f-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 "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_Number = 1 ; //--------------------------------------------------------------------------------------------------------<<<< #switch ( Camera_Number ) #case (0) #declare Camera_Position = < 0.00, 0.00, -2.80> ; // front view #declare Camera_Look_At = < 0.00, 0.00, 0.00> ; #declare Camera_Angle = 40 ; #break #case (1) #declare Camera_Position = < 3.20, 2.00, -2.70> ; // diagonal view #declare Camera_Look_At = < 0.00, 0.10, 0.00> ; #declare Camera_Angle = 20 ; #break #case (2) #declare Camera_Position = < 0.00, 0.00, -2.50> ; // right side view #declare Camera_Look_At = < 0.00, 0.00, 0.00> ; #declare Camera_Angle = 45 ; #break #case (3) #declare Camera_Position = < 0.00, 3.00, -0.01> ; // top view #declare Camera_Look_At = < 0.00, 0.00, 0.00> ; #declare Camera_Angle = 45 ; #break #else #declare Camera_Position = < 3.20, 2.00, -2.70> ; // diagonal view #declare Camera_Look_At = < 0.00, 0.10, 0.00> ; #declare Camera_Angle = 20 ; #break #end // of "#switch ( Camera_Number )" ----------------------------- //------------------------------------------------------------------ //-------------------------------------------------------------------------------------------------------<<<< camera{ location Camera_Position right x*image_width/image_height angle Camera_Angle look_at Camera_Look_At } //------------------------------------------------------------------------------------------------------<<<<< //------------------------------------------------------------------------ //------------------------------------------------------------------------ // sun ------------------------------------------------------------------- light_source{<-500,1500,-1500> color White*0.9} // sun light light_source{ Camera_Position color rgb<0.9,0.9,1>*0.1} // flash light // sky ------------------------------------------------------------------- sky_sphere{ pigment{ gradient <0,1,0> color_map{ [0 color rgb<1,1,1> ]//White [0.5 color rgb<0.14,0.14,0.56>*0.7]//~Navy [0.5 color rgb<0.14,0.14,0.56>*0.7]//~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,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 -------------------------------- #declare Text_Rotate = < 20,-45,0>; // rotate Text_Rotate 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} rotate Text_Rotate 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} rotate Text_Rotate scale 0.5 translate <-0.75,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} rotate Text_Rotate scale 0.75 translate <-0.75,0.2,AxisLenZ+0.10>} #end // of #if } // end of union #end// of macro "AxisXYZ( ... )" //------------------------------------------------------------------------ #declare Texture_A_Dark = texture { pigment{ color rgb<1,0.4,0>} finish { phong 1} } #declare Texture_A_Light = texture { pigment{ color rgb<1,1,1>} finish { phong 1} } // axes ------------------------------------------------------------------- object{ AxisXYZ( 6.2, 5.2, 7.2, Texture_A_Dark, Texture_A_Light) scale 0.15 no_shadow } //-------------------------------------------------- end of coordinate axes /* // ground ----------------------------------------------------------------- //---------------------------------<<< settings of squared plane dimensions #declare RasterScale = 0.1; #declare RasterHalfLine = 0.035; #declare RasterHalfLineZ = 0.035; //------------------------------------------------------------------------- #macro Raster(RScale, HLine) pigment{ gradient x scale RScale color_map{[0.000 color rgbt<1,1,1,0>*0.7] [0+HLine color rgbt<1,1,1,0>*0.7] [0+HLine color rgbt<1,1,1,1>] [1-HLine color rgbt<1,1,1,1>] [1-HLine color rgbt<1,1,1,0>*0.7] [1.000 color rgbt<1,1,1,0>*0.7]} } #end// of Raster(RScale, HLine)-macro //------------------------------------------------------------------------- plane { <0,1,0>, 0 // plane with layered textures texture { pigment{color White*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> translate<0,0,0> } //------------------------------------------------ end of squared plane XZ */ //-------------------------------------------------------------------------- //---------------------------- objects in scene ---------------------------- //-------------------------------------------------------------------------- // sizes of lines and points ----------------------------------------------- #declare Rl = 0.010; // lines radius #declare Rp = 0.020; // points radius // textures ---------------------------------------------------------------- #declare Edge_Texture = texture { pigment{ color rgb< 0.75, 1.0, 0.0> } finish { phong 1 reflection 0.00} } // end of texture #declare Corners_Texture = texture { pigment{ color rgb<0.4,1,0>*0.35 } finish { phong 1 reflection 0.00} } // end of texture #declare Surface_Texture = texture { pigment{ color rgbt< 0.75, 1.0, 0.0, 0.75> } finish { phong 1 reflection 0.00} } // end of texture //------------------------------------------------------------------------------------------------------- //------------------------------------------------------------------------------------------------------- //--------------------------------------------------------------------- macro "Vector(Start,End,Radius)"! #macro Vector(P_start,P_end, R_Vector) union{ cylinder{ P_start, P_end - ( vnormalize(P_end - P_start)*9.5*R_Vector), R_Vector } cone { P_end - ( vnormalize(P_end - P_start)*10*R_Vector), 3*R_Vector, P_end, 0 } }// end of union #end //------------------------------------------------------------------------------------- end of macro // alternatively: #include "analytical_g.inc" //-------------------------------------------------------------------------------------------------------- // ------------------------------------------------------------------------------------------------------- #declare Side_a = 1; // length of a side of a regular tetrahedron // ---- equilateral triangle ----------------------------------------------------------------------------- //#declare Th = 1/2*sqrt(3)*Side_a; // the height of an equilateral triangle //#declare Sh = 1/6*sqrt(3)*Side_a; // the height of the incenter of an equilateral triangle //#declare Rc = 1/3*sqrt(3)*Side_a; // radius of circumcircle of an equilateral triangle // ---- regular tetrahedron ------------------------------------------------------------------------------ //#declare Tetra_H = sqrt (2/3) * Side_a; // the height of a regular tetrahedron #declare R_circum = sqrt( 3/8 ) * Side_a; // radius of the circumsphere of a regular tetrahedron //#declare R_in = 1/3 * Rc ; // or = 1/sqrt(24) * A = Tetra_H-R_circum ; radius insphere //#declare Face_Corner_Center_Angle = degrees ( atan ( R_in / Rf ) ); //#declare Face_to_Face_Angle = degrees( atan(2*sqrt(2))) ; // degrees ( atan ( Tetra_H/ Sh ) ); ~ 71 //#declare Edge_to_Face_Angle = degrees( atan(sqrt(2))) ; // ~ 55 #declare Vertex_Center_Vertex_Angle = degrees( acos( -1/3 )) ; // ~ 109.471 // ------------------------------------------------------------------------------------------------------- // caculation of the vectors ------------------------------------------ #declare V1 = <0,R_circum,0>; #declare V2 = vrotate ( V1, < Vertex_Center_Vertex_Angle, 0, 0> ); #declare V3 = vrotate ( V2, < 0, 120, 0> ); #declare V4 = vrotate ( V2, < 0,-120, 0> ); // vectors ------------------------------------------------------------ object{ Vector( o,V1, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow} object{ Vector( o,V2, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow} object{ Vector( o,V3, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow} object{ Vector( o,V4, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow} // corners ------------------------------------------------------------ sphere{ V1, Rp texture{ Corners_Texture } no_shadow } sphere{ V2, Rp texture{ Corners_Texture } no_shadow } sphere{ V3, Rp texture{ Corners_Texture } no_shadow } sphere{ V4, Rp texture{ Corners_Texture } no_shadow } // lettering ---------------------------------------------------------- text{ ttf "arial.ttf", "A", 0.02, 0.0 rotate<20,-40,0> texture{ Corners_Texture } scale<1,1,1>*0.10 translate V1 + <-0.10,0,-0.10> no_shadow } // end of text object ------------------------------------------- text{ ttf "arial.ttf", "B", 0.02, 0.0 rotate<20,-40,0> texture{ Corners_Texture } scale<1,1,1>*0.12 translate V2 + < 0.00,-0.05, 0.15> no_shadow } // end of text object ------------------------------------------- text{ ttf "arial.ttf", "C", 0.02, 0.0 rotate<20,-40,0> texture{ Corners_Texture } scale<1,1,1>*0.09 translate V3 + < 0.00,-0.12,-0.05> no_shadow } // end of text object ------------------------------------------- text{ ttf "arial.ttf", "D", 0.02, 0.0 rotate<20,-40,0> texture{ Corners_Texture } scale<1,1,1>*0.10 translate V4 + <-0.15,-0.05,-0.10> no_shadow } // end of text object ------------------------------------------- //--------------------------------------------------------------------- #declare Point_A = V1; #declare Point_B = V2; #declare Point_C = V3; #declare Point_D = V4; // edges --------------------------------------------------------- cylinder{ Point_A, Point_B, Rl texture{ Edge_Texture } } cylinder{ Point_B, Point_C, Rl texture{ Edge_Texture } } cylinder{ Point_C, Point_A, Rl texture{ Edge_Texture } } cylinder{ Point_A, Point_D, Rl texture{ Edge_Texture } } cylinder{ Point_B, Point_D, Rl texture{ Edge_Texture } } cylinder{ Point_C, Point_D, Rl texture{ Edge_Texture } } // surfaces------------------------------------------------------- triangle{ Point_A, Point_B, Point_C texture{ Surface_Texture } } triangle{ Point_A, Point_B, Point_D texture{ Surface_Texture } } triangle{ Point_B, Point_C, Point_D texture{ Surface_Texture } } triangle{ Point_C, Point_A, Point_D texture{ Surface_Texture } } //---------------------------------------------------------------- // The corners of a regular tetraeder based on x-axis: //#declare Point_A = <-Side_a/2, 0, 0>; //#declare Point_B = < Side_a/2, 0, 0>; //#declare Point_C = < 0, 0,Th>; //#declare Point_D = < 0,Tetra_H,Sh>; // "top" //----------------------------------------------------------------