Math 3D-Plotter

​

​

​

​

// function-Plotter 3D: 

//-------------------------------- 

// use n,p and F1

// use o, i for export to POV-Ray

// h,r camera 

// s - save as image

// 

​

// version 2 

​

final String PathToPOVRayExe = "C:\\Programme\\POV-Ray for Windows v3.62\\bin\\pvengine-sse2.exe"; 

​

// imports ---------------------------

​

//import eu.fluidforms.utils.*;

//import eu.fluidforms.processing.*;

//import eu.fluidforms.geom.*;

//import eu.fluidforms.primitives.*;

//import eu.fluidforms.io.*;

//import eu.fluidforms.parser.*;

//

//

//

//// use strg-e

​

​

​

// use camera from peasyCam 

import peasy.org.apache.commons.math.*;

import peasy.*;

import peasy.org.apache.commons.math.geometry.*;

​

// use opengl

import processing.opengl.*;

​

// consts --------------------------

​

final int MaxFunctions = 10;

​

// vars -----------------------------

​

// cam

PeasyCam cam;

​

// Vectors: 

// Lookup

PVector[][] MyResults = new PVector [400][400]; 

​

// Max value for MyResults

int MaxindexI=0;

int MaxindexJ=0;

​

// number of Formula

int GraphNumber = 0; 

​

// z = result

float result = 1.0;

​

// Text for left corner

String DefineShowText=""; 

​

// when has special text been shown

int ShowSpecialMessageStartTime = 0; 

String SpecialText = ""; 

​

// some boolean Flags

boolean boolShowCoor = false; // -x,-y,-z, x,y,z

boolean boolShowMovie = false; 

boolean boolHelpModus = false; 

boolean boolShowSpecialMessage = false; 

​

// Main functions ---------------------------- 

​

​

void setup() {

​

  // Init

​

  // size ( 900, 650, OPENGL ); 

  size ( 850, 650, P3D ); 

  cam = new PeasyCam(this, 100);

  background(117);

​

  // move

  cam.pan(100,50);

  cam.setDistance(830);

  cam.setResetOnDoubleClick (true);   

​

  noStroke();

  fill(color(254,0,0));

  fill (254,0,0);

​

  PFont font;

  font = createFont("FFScala-32.vlw",12); 

  textFont(font); 

​

  // FluidForms.setup(this);

​

} // setup 

​

void draw() {

​

  background(117);

  if (boolShowCoor) {

    ShowCoor(); 

  }

  if (boolShowMovie){

    cam.rotateY(radians(-1));

  }

  if (boolShowSpecialMessage){

    float mNow = millis();

    if  (ShowSpecialMessageStartTime + 5000 <= mNow) { 

      boolShowSpecialMessage=false;  

    }

  }  

​

  CallUpMathFunction () ; 

​

} // function 

​

void keyPressed(){

​

  if (boolHelpModus) {

    loop();

    boolHelpModus=false; 

  }

​

  else 

  {

​

    if (key == CODED) {

​

      switch (keyCode) { 

      case KeyEvent.VK_F1: 

        // F1 

        background(117); 

        ShowText(HelpText() +  "\nPress any key...");

        boolHelpModus=true ; 

        noLoop(); 

        break; 

      case UP:

        cam.rotateX(radians(-1));

        break; 

      case DOWN:

        cam.rotateX(radians(1));

        break;       

      case LEFT:

        cam.rotateY(radians(1));

        break; 

      case RIGHT:

        cam.rotateY(radians(-1));

        break;       

      default: 

        // 

        break; 

      } // switch

    } // if 

​

    else {

​

      // not key == CODED   

      switch(key){

      case 'r':

        cam.reset(); 

        break;

      case 'h':

        // horizontal

        setCamHorizontal();

        break;       

      case 'q':

        boolShowCoor = ! boolShowCoor; 

        break; 

      case 'c':

        background (117);

        break;

      case 'm':

        boolShowMovie = ! boolShowMovie; 

        break; 

      case 'p':

        // cam.reset(444);

        GraphNumber = GraphNumber - 1;    

        if (GraphNumber<0) { 

          GraphNumber = 0; 

        }

        break; 

      case 'n':

        // cam.reset(444);

        GraphNumber = GraphNumber + 1;

        if (GraphNumber>MaxFunctions) { 

          GraphNumber = MaxFunctions; 

        }    

        break; 

      case 's':        

        // Opens file chooser 

        String savePath = selectOutput("Save as picture...");  

        if (savePath != null) 

        { 

          delay(10);

          saveFrame(savePath);

        } 

        break; 

      case 'i':

        ShowLookupWithPovRaySpheres(); 

        break;   

      case 'o':

        ShowLookupWithPovRayPoly(); 

        break;           

      default:

        break; 

      } // switch 

    } // if 

  } // if 

​

  // for functions that rely on Lookup: init Lookup

  switch (GraphNumber) {

    // only when number is odd (and >=5)

  case 5:

    DefineShowText="Formula " + GraphNumber + ": \nz=x*x*y \nuse Previous and Next, F1 Help\ncan export to POV-Ray";

    InitGraph_ItimesItimesJ();

    break; 

  case 7:

    DefineShowText="Formula " + GraphNumber + ": \nSphere (distorted, looks good in OPENGL) \nuse Previous and Next, F1 Help\ncan export to POV-Ray";  

    InitGraph_Sphere(); 

    break; 

  case 9:

    DefineShowText="Formula " + GraphNumber + ": \nCrescent \nuse Previous and Next, F1 Help\ncan export to POV-Ray";

    InitGraph_Cresent(); 

    break; 

  case 6:

  case 8:

  case 10:

    break; 

  default: 

    MaxindexI=0;

    MaxindexJ=0;        

    break; 

  }  // switch 

​

} // keyPressed 

​

// functions related to draw etc. -------------------------------------------

​

void CallUpMathFunction () {

​

  switch(GraphNumber) {

  case 0:

    ShowText("Formula " + GraphNumber + ": \nz=1 \nuse Previous and Next, F1 Help");

    ShowGraph0();

    break; 

  case 1:

    ShowText("Formula " + GraphNumber + ": \nz=sin(x) \nuse Previous and Next, F1 Help");

    ShowGraph1();

    break;     

  case 2:

    ShowText("Formula " + GraphNumber + ": \ny=cos(x); z=sin(x) \nuse Previous and Next, F1 Help");    

    ShowGraph2();

    break;         

  case 3:

    ShowText("Formula " + GraphNumber + ": \nx=r*cos(i)*cos(j); y=r*sin(i)*sin(j); z=r*sin(i) \nuse Previous and Next, F1 Help");        

    ShowGraph3();

    break;  

  case 4:

    ShowText("Formula " + GraphNumber + ": \nz=sin(x) \nuse Previous and Next, F1 Help");

    ShowGraph4();

    break;      

  case 5:  // odd numbers 

  case 7:   

  case 9:   

    ShowText(DefineShowText);

    ShowLookupAsBoxes();  

    break; 

  case 6:    // even numbers 

  case 8: 

  case 10: 

    ShowText(DefineShowText);

    ShowLookupAsGrid();

    break; 

  default:

    // ShowGraph1();

    break; 

  } // switch 

​

}

​

// --------------------------------------------------------------------------

// direct functions without lookUp - evil...

​

void ShowGraph0() {

​

  for (int i = -80; i < 80; i = i+5) {

    int posX = i*4; 

    for (int j = -80; j < 80; j = j+5) {

      int posY = j*4; 

      result = 1.0; 

      BoxParameters ( posX,(100-result)-100 ,-posY-20,

      3,3,3, 

      0,0,0, color(200,result,0) ); 

    }

  }

}

​

void ShowGraph1() {

​

  for (int i = 0; i < 360; i = i+5) {

    int posX = i; 

    for (int j = -80; j < 80; j = j+5) {

      int posY = j*4; 

      result = 100* sin(radians(posX)); 

      BoxParameters ( posX,(100-result)-100 ,-posY-20,

      3,3,3, 

      0,0,0, color(200,result,0) ); 

    }

  }

}

​

void ShowGraph2() {

​

  for (int i = 0; i < 360; i = i+5) {

    int posX = i; 

    for (int j = -80; j < 80; j = j+5) {

      float posY = 100* cos(radians(posX));

      result = 100* sin(radians(posX)); 

      BoxParameters ( posX,(100-result)-100 ,-posY-20,

      3,3,3, 

      0,0,0, color(200,result,0) ); 

    }

  }

}

​

void ShowGraph3() {

​

  // see http://local.wasp.uwa.edu.au/~pbourke/geometry/sphere/

​

  float r1 = 100 ; 

​

  for (int i = 0; i < 360; i = i+10) {

​

    for (int j = -180; j < 180; j = j+10) {

​

      float x1 = 10 + r1* cos(i) *cos(j);

      float y1 = 10 + r1* sin(i) *sin(j);

      float z1 = 10 + r1* sin(i) ;

      BoxParameters ( x1,z1,y1,

      3,3,3, 

      0,0,0, color(200,result,0) ); 

    }

  }

}

​

void ShowGraph4() {

​

  for (int i = -180; i < 180; i = i+5) {

    int posX = i*4; 

    for (int j = -80; j < 80; j = j+5) {

      int posY = j*4; 

      result =100* sin(radians(i)); 

      BoxParameters ( posX,(100-result)-100 ,-posY-20,

      3,3,3, 

      0,0,0, color(200,result,0) ); 

    }

  }

}

​

// ----------------------------------------------------------

// Show LookUps - different ways

​

void ShowLookupAsBoxes() {

  // not so nice

  colorMode(RGB,400);

  noStroke();

​

  if ((MaxindexI <= 0) && (MaxindexJ <= 0)) { 

    ShowSpecialMessage("LookUp-Table not defined."); 

  } 

  else {

    for (int i = 0; i < MaxindexI; i = i+3) {

      for (int j = 0; j < MaxindexJ; j = j+3) {

​

        BoxParameters (MyResults[i][j].x,MyResults[i][j].y,MyResults[i][j].z,

        3,3,3, 

        0,0,0, 

        color(2+abs(MyResults[i][j].x),2+abs(MyResults[i][j].y),2+abs(MyResults[i][j].z)) ); 

      } // j 

    } //i

  } // else 

} // ShowGraph1

​

void ShowLookupAsGrid() {

  // nice

  colorMode(RGB,400);

  noStroke();

  if ((MaxindexI <= 0) && (MaxindexJ <= 0)) { 

    ShowSpecialMessage("LookUp-Table not defined."); 

  } 

  else {

    for (int i = 0; i < MaxindexI; i = i+1) {

      for (int j = 0; j < MaxindexJ; j = j+1) {

        fill (2+abs(MyResults[i][j].x),2+abs(MyResults[i][j].y),2+abs(MyResults[i][j].z));

        beginShape(QUAD); 

        vertex(MyResults[i][j].x,MyResults[i][j].y,MyResults[i][j].z);      

        vertex(MyResults[i+1][j].x,MyResults[i+1][j].y,MyResults[i+1][j].z);      

        vertex(MyResults[i+1][j+1].x,MyResults[i+1][j+1].y,MyResults[i+1][j+1].z);  

        vertex(MyResults[i][j+1].x,MyResults[i][j+1].y,MyResults[i][j+1].z);      

        endShape(CLOSE); 

      } // j 

    } //i

  } // else 

} // ShowGraph2

​

void ShowLookupWithPovRaySpheres() {

  // With spheres in POV-Ray

  //colorMode(RGB,400);

  //noStroke();

  if (DoesPOVRayExist()) {

    if ((MaxindexI <= 0) && (MaxindexJ <= 0)) { 

      ShowSpecialMessage("LookUp-Table not defined."); 

    } 

    else {    

      ShowSpecialMessage("Can take a while..."); 

      String Buffer = ""; 

      String MyText = ""; 

      println ("Start preparing Povray Spheres");

      for (int i = 0; i < MaxindexI; i = i+3) {

        for (int j = 0; j < MaxindexJ; j = j+3) {

          // fill (2+abs(MyResults[i][j].x),2+abs(MyResults[i][j].y),2+abs(MyResults[i][j].z));

​

          Buffer = Buffer + 

            "MySphere (" + 

            ((MyResults[i][j].x) * .1 ) + ", " + 

            ((8 - MyResults[i][j].z) * .1 ) + ", " + 

            ( (8 - MyResults[i][j].y) * .1 + 1.2) +  

            ")" + "\n";

​

        } // j 

      } //i

​

      println ("Now the files...");

​

      MyText = GetText("","") + "\n // Commands here " + Buffer; 

      WriteToFile ( MyText ); 

​

      println ("Finished preparing Povray");

    } // else

  } // if DoesPOVRayExist

​

} // function 

​

void ShowLookupWithPovRayPoly() {

  // with polygons in PovRay

  // colorMode(RGB,400);

  // noStroke();

​

  if (DoesPOVRayExist()) {

    if ((MaxindexI <= 0) && (MaxindexJ <= 0)) { 

      ShowSpecialMessage("LookUp-Table not defined."); 

    } 

    else {

      ShowSpecialMessage("Can take a while (5 minutes or more)..."); 

      String Buffer = ""; 

      String MyText = ""; 

      println ("Start preparing Povray Polygons");

      for (int i = 0; i < MaxindexI; i = i+1) {

        for (int j = 0; j < MaxindexJ; j = j+1) {

          // fill (2+abs(MyResults[i][j].x),2+abs(MyResults[i][j].y),2+abs(MyResults[i][j].z));

​

          Buffer = Buffer + 

            "MyPoly (" + 

            MyResults[i][j].x*.1 + ", " + MyResults[i][j].y *.1+ ", " + MyResults[i][j].z*.1  + ", " + 

            MyResults[i+1][j].x*.1 + ", " + MyResults[i+1][j].y *.1+ ", " + MyResults[i+1][j].z*.1 + ", " + 

            MyResults[i+1][j+1].x*.1 + ", " + MyResults[i+1][j+1].y*.1 + ", " + MyResults[i+1][j+1].z*.1 + ", " + 

            MyResults[i][j+1].x *.1+ ", " + MyResults[i][j+1].y*.1 + ", " + MyResults[i][j+1].z *.1 + 

            ")" + "\n";

​

        } // j 

      } //i

​

      println ("Now the files...");

​

      MyText = GetText("","") + "\n // Commands here \n " + Buffer; 

      WriteToFile ( MyText ); 

​

      println ("Finished preparing Povray");

    } // else

  } //   if DoesPOVRayExist

​

} // function 

​

// -----------------------------------------------------------------

// Inits of LookUps (MyResults) - that's the way to do it

​

void InitGraph_Sphere() { 

​

  // see http://local.wasp.uwa.edu.au/~pbourke/geometry/sphere/

​

  int indexI=0;

  int indexJ=0;

  float r1 = 100 ; 

​

  for (int i = 0; i < 360; i = i+10) {

    indexJ=0;

    for (int j = -180; j < 180; j = j+10) {

​

      float x1 = 10 + r1* cos(i) *cos(j);

      float y1 = 10 + r1* cos(i) *sin(j);

      float z1 = 10 + r1* sin(i) ;

      MyResults[indexI][indexJ] = new PVector(x1,y1,z1);

      indexJ = indexJ + 1;

​

    }

    indexI=indexI+1; 

  }

  MaxindexJ = indexJ-1; 

  MaxindexI = indexI-1; 

} // function

​

void InitGraph_ItimesItimesJ() {

​

  int indexI=0;

  int indexJ=0;

​

  for (int i = -80; i < 80; i = i+1) {

    float posX = i*4.0; 

    indexJ=0; 

    for (int j = -80; j < 80; j = j+1) {

      float posY = j*4.0; 

      result = .001*i*i*j;            

      MyResults[indexI][indexJ] = new PVector(posX,(100-result)-100 ,-posY-20);

      indexJ = indexJ + 1;

    } // j 

    indexI=indexI+1; 

  } //i

  MaxindexJ = indexJ-1; 

  MaxindexI = indexI-1; 

} // function

​

void InitGraph_Cresent() {

​

  // see http://local.wasp.uwa.edu.au/~pbourke/geometry/cresent/

​

  //x = (2 + sin(2 pi u) sin(2 pi v)) sin(3 pi v) 

  //y = (2 + sin(2 pi u) sin(2 pi v)) cos(3 pi v) 

  //

  //z = cos(2 pi u) sin(2 pi v) + 4 v - 2 

  //

  //with 0 <= u <= 1, 0 <= v <= 1 

​

  float r1 = 100 ; 

  float u= 0;

  float x1,y1,z1;

  int indexI=0; 

  int indexJ = 0;

​

  for (int i = 0; i < 101; i = i+1) {

    float v=0;

    indexJ = 0; 

    for (int j = 0; j < 101; j = j+1) {

​

      x1 = (2 + sin(2 *PI *u) * sin(2 *PI *v)) *sin(3 *PI *v) ;

      y1 = (2 + sin(2 *PI *u) * sin(2 *PI *v)) *cos(3 *PI *v); 

      z1 = cos(2 *PI *u) *sin(2 *PI *v) + 4 *v - 2 ;

​

      MyResults[indexI][indexJ] = new PVector(100*x1,100*y1,100*z1);

​

      v = v + 0.03; // .01

      indexJ=indexJ+1; 

    }

    u = u + 0.03; // .01 

    indexI=indexI+1; 

  }

  MaxindexJ = indexJ - 1; 

  MaxindexI = indexI - 1; 

}

​

// Other functions ---------------------------- 

​

void ShowCoor() { 

​

  stroke(222,222,222);

​

  // all smaller 0 ----------------------------

  line ( -100, 0, 0, 0, 0, 0 );

  text("-x", -100, 0,0); 

​

  line ( 0, 100, 0, 0, 0, 0 );

  text("-z", 0,100,0); 

​

  line ( 0, 0, 100, 0, 0, 0 );

  text("-y", 0,0,100); 

​

  // all greater 0 ------------------------------

  line ( 0, 0, 0, 100,   0,   0 );

  text("x", 100, 0,0); 

​

  line ( 0, 0, 0, 0,   -100,   0 );

  text("z", 0,-100,0); 

​

  line ( 0, 0, 0, 0,     0, -100 );    

  text("y", 0,0,-100); 

​

} // function 

​

void ShowText (String MyText) {

  cam.beginHUD();

  fill(254, 254, 254);

  textMode(SCREEN);

  if (boolShowSpecialMessage) {   

    text(SpecialText, 40,45);   

  } 

  else {

    text(MyText, 40,45); 

  }

  textMode(MODEL);

  cam.endHUD();

} // function 

​

void BoxParameters ( float x,float y,float z, 

float w, float h, float d,  

float RotateX, float RotateY, float RotateZ,

color color1) {

  // Position and size and rotation of a box 

  stroke(0); 

  fill (color1);

  pushMatrix();

  translate ( x,y,z );

  rotateX ( radians(RotateX) );

  rotateY ( radians(RotateY) );

  rotateZ ( radians(RotateZ) );  

  box ( w,h,d );

  popMatrix();

​

} // function 

​

void setCamHorizontal() {

​

  // Brings Gamefield/cam in horizontal position 

  // without distorting the rotation around the x-axis.

  // Connected with letter 'h'.

  // Sometimes it does distort the rotation around the x-axis.

​

  float[] rotations = cam.getRotations(); // x, y, and z rotations required to face camera in model space  

  // camera.setRotations(double pitch, double yaw, double roll); // rotations are applied in that order

  // println( rotations[0] + " " +  rotations[1] + " " +  rotations[2] );

  // cam.rotateX(1);

  // Wert 1 nach hinten drehend, 2 nach links (Drehachse senkrecht), 3 Drehachse in den Schirm hinein ragend

  cam.setRotations( 0,  rotations[1], 0 ); // rotations are applied in that order

​

} // function 

​

// ---------------------------------------------------------------

​

String HelpText () {

​

  String Buffer = ""; 

​

  //   Buffer

​

  Buffer = "=== HELP === " +  "\n " +  "\n"; 

  Buffer = Buffer + "3D-Function plotter. " +  ""; 

  Buffer = Buffer + "You reach this help via F1. " ;  

  Buffer = Buffer + "\nSome functions are calculated directly, others via lookup-table.  " ;    

  Buffer = Buffer + "\nThe latter are shown first via small boxes, then as a grid (not working properly with \nthe sphere, but looks cool with OPENGL if you zoom in the sphere).  \n\n\n" ;   

  Buffer = Buffer + " ------ Issues: ---------\n\n";

  Buffer = Buffer + "The shown formulas are not always correct, there are some adjustments of the scales and so on.\n" ;  

  Buffer = Buffer + "Also the coordinates are not always perfect.\n" ;  

  Buffer = Buffer + "There are issues with P3D (when camera is to close to the graph) \nand OPENGL (in some browsers). " ;  

  Buffer = Buffer + "\n\n"  ; 

  Buffer = Buffer + "\n"  ;   

  Buffer = Buffer + " ------ Navigating the functions: ---------";

  Buffer = Buffer + "\n\nUse P for Previous function and N for next function. " ;  

  // Buffer = Buffer + "\nCamera resets with p and n. " ;  

  Buffer = Buffer + "\nIf first or last function is reached, nothing happens. " ;        

  Buffer = Buffer + "\n " ;  

  Buffer = Buffer + "\n " ;  

  Buffer = Buffer + "\n " ;    

  Buffer = Buffer + " ------ Moving the view of the Graph: ---------";

  Buffer = Buffer + "\n " ;

  Buffer = Buffer + "\n" ;

  Buffer = Buffer + "Left-drag to rotate; \nmouse wheel, or right-drag up and down to zoom; \nmiddle-drag (cmd-left-drag on mac) to pan.  \n " ;  

  Buffer = Buffer + "Use Mouse-Double-Click or 'r' to reset view. " ;  

  Buffer = Buffer + "\n " ;

  Buffer = Buffer + "\n "  ; 

  Buffer = Buffer + "\n "  ; 

  Buffer = Buffer + " ------ Keys to use (not mentioned above): --------"  ; 

  Buffer = Buffer + "\n\n"  ; 

  Buffer = Buffer + "m - toggle camera animation (slow rotation)\n"  ; 

  Buffer = Buffer + "q - toggle coordinates \n"  ;   

  Buffer = Buffer + "Up and Down Cursor-Key - rotate\n"  ; 

  Buffer = Buffer + "Left and Right Cursor-Key - rotate \n"  ; 

  Buffer = Buffer + "h - turns the Graph horizontal; sometimes also rotating around the x-axis\n"; 

  Buffer = Buffer + "s - save as simple tiff-image-file\n"; 

  Buffer = Buffer + "i - save as POV-Ray with spheres\n";   

  Buffer = Buffer + "o - save as POV-Ray with surface\n";     

  Buffer = Buffer + "ESC - quit .\n"  ;   

  Buffer = Buffer + "\n "  ;

  Buffer = Buffer + ""  ; 

  Buffer = Buffer + "Thanks goes to Paul Bourke for his page: http://local.wasp.uwa.edu.au/~pbourke/geometry. \nUsed sphere and crescent from there. "  ;

  Buffer = Buffer + "Thanks goes to PeasyCam. "  ;

​

  return (Buffer);

​

} // function help 

​

// PovRay-Export ----------------------------------------------------------------------------------------- 

​

String GetText( String strPfadKommentar, String strNameKommentar) {

​

  //    Dim i

  //    Dim j

  //    Dim a(205]

  //    Dim strT

​

  int i = 0; 

​

  String [] a = new String[350]; 

​

​

  a[i] = "// Persistence of Vision Ray Tracer Scene Description File"; 

  i = i + 1;

  a[i] = "// File: " + strPfadKommentar + " " + strNameKommentar; 

  i = i + 1;

  a[i] = "// Vers: 3.6"; 

  i = i + 1;

  a[i] = "// Desc: Basic Scene Example"; 

  i = i + 1;

  a[i] = "// Date: " + TodaysDate(); 

  i = i + 1;

  a[i] = "// Auth: ?"; 

  i = i + 1;

  a[i] = "//"; 

  i = i + 1;

​

  a[i] = "// This file was generated by math3D, using code by processing - see www.processing.org."; 

  i = i + 1;  

  a[i] = "// You probably need to adjust the code here in POV-Ray;"; 

  i = i + 1;  

  a[i] = "// e.g. adjust the camera (choose between two); adjust the plane (maybe your work is under it...), adjust the scale of your model, the lights..."; 

  i = i + 1;  

​

  a[i] = ""; 

  i = i + 1;

  a[i] = "#version 3.6;"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "// \"colors\""; 

  i = i + 1;

  a[i] = "#include \"colors.inc\""; 

  i = i + 1;

  a[i] = "// a lot of stone textures"; 

  i = i + 1;

  a[i] = "// T_Stone1 - T_Stone44"; 

  i = i + 1;

  a[i] = "#include \"stones.inc\""; 

  i = i + 1;

  a[i] = "// various [mostly layered] wood textures"; 

  i = i + 1;

  a[i] = "// T_Wood1 - T_Wood35"; 

  i = i + 1;

  a[i] = "#include \"woods.inc\""; 

  i = i + 1;

  a[i] = "// several different gold colors, finishes and textures"; 

  i = i + 1;

  a[i] = "#include \"golds.inc\""; 

  i = i + 1;

  a[i] = "// various metal colors, finishes and textures"; 

  i = i + 1;

  a[i] = "// brass, copper, chrome, silver"; 

  i = i + 1;

  a[i] = "#include \"metals.inc\""; 

  i = i + 1;

  a[i] = "// various metal colors, finishes and textures"; 

  i = i + 1;

  a[i] = "// brass, copper, chrome, silver"; 

  i = i + 1;

  a[i] = "#include \"metals.inc\""; 

  i = i + 1;

  a[i] = "// various glass finishes, colors and interiors"; 

  i = i + 1;

  a[i] = "#include \"glass.inc\""; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "/*"; 

  i = i + 1;

  a[i] = "global_settings {"; 

  i = i + 1;

  a[i] = "  assumed_gamma 1.0"; 

  i = i + 1;

  a[i] = "}   */"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "// ----------------------------------------"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "camera {"; 

  i = i + 1;

  a[i] = "  location  <15.0, 30.5, 15  >"; 

  i = i + 1;

  a[i] = "  look_at   <15.0, 0.0,  15.0>"; 

  i = i + 1;

  a[i] = "}"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "camera {"; 

  i = i + 1;

  a[i] = "  location  <90.0, 0.0, -80.0>"; 

  i = i + 1;

  a[i] = "  // direction 1.5*z"; 

  //  i = i + 1;

  a[i] = "  // right     x*image_width/image_height"; 

  // i = i + 1;

  a[i] = "  look_at   < 10.0, 0.0, 0.0>"; 

  i = i + 1;

  a[i] = "}"; 

  i = i + 1;

  a[i] = "  "; 

  i = i + 1;

  a[i] = "  "; 

  i = i + 1;

  a[i] = "sky_sphere {"; 

  i = i + 1;

  a[i] = "  pigment {"; 

  i = i + 1;

  a[i] = "    gradient y"; 

  i = i + 1;

  a[i] = "    color_map {"; 

  i = i + 1;

  a[i] = "      [0.0 rgb <0.6,0.7,1.0>]"; 

  i = i + 1;

  a[i] = "      [0.7 rgb <0.0,0.1,0.8>]"; 

  i = i + 1;

  a[i] = "    }"; 

  i = i + 1;

  a[i] = "  }"; 

  i = i + 1;

  a[i] = "}"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "light_source {"; 

  i = i + 1;

  a[i] = "  <0, 0, 0>            // light's position (translated below]"; 

  i = i + 1;

  a[i] = "  color rgb <1, 1, 1>  // light's color"; 

  i = i + 1;

  a[i] = "  translate <-30, 30, -300>"; 

  i = i + 1;

  a[i] = "}"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "// ----------------------------------------"; 

  i = i + 1;

  a[i] = ""; 

  i = i + 1;

  a[i] = "#macro MySphere (x1,y1,z1)  // ---------------------------------------------------------------------------"; 

  i = i + 1;

  a[i] = "    "; 

  i = i + 1;

  a[i] = "    sphere {"; 

  i = i + 1;

  a[i] = "        <x1,z1,y1>, 1"; 

  i = i + 1;

  a[i] = "        // texture { T_Stone2 }"; 

  i = i + 1;

  a[i] = "        texture { F_Glass5 } // texture { T_Glass1 }"; 

  i = i + 1;

  a[i] = "        "; 

  i = i + 1;

  a[i] = "        /*"; 

  i = i + 1;

  a[i] = "        // material {} is a wrapper for interior and texture"; 

  i = i + 1;

  a[i] = "        // you can declare it like texture and interior too"; 

  i = i + 1;

  a[i] = "        // Note that it has nothing to do with material_map  */ "; 

  i = i + 1;

  a[i] = "        material {"; 

  i = i + 1;

  a[i] = "          texture {"; 

  i = i + 1;

  a[i] = "            pigment { color rgbt <x1, y1, z1, 0.5> }"; 

  i = i + 1;

  a[i] = "            finish { diffuse 0.2 specular 0.6 }"; 

  i = i + 1;

  a[i] = "          }"; 

  i = i + 1;

  a[i] = "          interior {"; 

  i = i + 1;

  a[i] = "          // ior 1.5"; 

  i = i + 1;

  a[i] = "          }"; 

  i = i + 1;

  a[i] = "        }   "; 

  i = i + 1;

  a[i] = "     "; 

  i = i + 1;

  a[i] = "    }"; 

  i = i + 1;

  a[i] = "#end // macro  "; 

  i = i + 1;

  a[i] = "";