import java.awt.*;

public class Plot3d extends java.applet.Applet
{
  //vars passed or calculated from HTML
  double XMin = -Math.PI;
  double XMax = Math.PI;
  int XCut = 30;
  double XScale;
  double YMin = -Math.PI;
  double YMax = Math.PI;
  int YCut = 30;
  double YScale;
  double ZMin = -Math.PI;
  double ZMax = Math.PI;

  double Angle = Math.PI / 6;
  double Tilt = 5 * Math.PI / 4;
  double Zoom = 2;
  double CosA;
  double CosT;
  double SinA;
  double SinT;
  double SinAT;
  double CosASinT;
  String Function = ".5*cos(x *x + y * y)";

  //misc global vars
  int TRUE = -1;
  int FALSE = 0;
  int Trace = 0;

  //eval error flag
  int BadEval = 0;
  //eval ErrorCodes
  int ParenthesisError = 1;
  int UndefinedFunction = 2;

  TextField Equation;
  Button Graph;

  public void init()
  {
    String s;
    s = getParameter("XMin");
    if(s != null) XMin = Double.valueOf(s).doubleValue();
    s = getParameter("XMax");
    if(s != null) XMax = Double.valueOf(s).doubleValue();
    s = getParameter("XCut");
    if(s != null) XCut = Integer.parseInt(s);
    s = getParameter("YMin");
    if(s != null) YMin = Double.valueOf(s).doubleValue();
    s = getParameter("YMax");
    if(s != null) YMax = Double.valueOf(s).doubleValue();
    s = getParameter("YCut");
    if(s != null) YCut = Integer.parseInt(s);
    s = getParameter("ZMin");
    if(s != null) ZMin = Double.valueOf(s).doubleValue();
    s = getParameter("ZMax");
    if(s != null) ZMax = Double.valueOf(s).doubleValue();
    s = getParameter("Angle");
    if(s != null) Angle = Double.valueOf(s).doubleValue();
    s = getParameter("Tilt");
    if(s != null) Tilt = Double.valueOf(s).doubleValue();
    s = getParameter("Zoom");
    if(s != null) Zoom = Double.valueOf(s).doubleValue();
    s = getParameter("Function");
    if(s != null) Function = s;

    // initialize trig constants
    CosA = Math.cos(Angle) / Zoom;
    CosT = Math.cos(Tilt) / Zoom;
    SinA = Math.sin(Angle) / Zoom;
    SinT = Math.sin(Tilt) / Zoom;
    SinAT = Math.sin(Angle) * SinT;
    CosASinT = Math.cos(Angle) * SinT;
    XScale = size().width / (XMax - XMin);
    YScale = size().height / (YMax - YMin);

    Equation = new TextField(Function);
    add(Equation);
    Graph = new Button("Plot");
    add(Graph);
    setBackground(new Color(0, 0, 51));
    setForeground(Color.white);
  }

  double f(double x, double y)
  {
    int a;
    if(Math.abs(x) < .000000001) x = 0;
    if(Math.abs(y) < .000000001) y = 0;
    String fn = Function.toUpperCase();
    a = fn.indexOf('X');
    while(a != -1)
    {
      fn = fn.substring(0, a) + "(" + Double.toString(x) + ")" + fn.substring(a + 1, fn.length());
      a = fn.indexOf('X');
    }
    a = fn.indexOf('Y');
    while(a != -1)
    {
      fn = fn.substring(0, a) + "(" + Double.toString(y) + ")" + fn.substring(a + 1, fn.length());
      a = fn.indexOf('Y');
    }
    double ret = eval(fn);
    if(BadEval != 0)
    {
      System.out.print("BadEval = ");
      System.out.println(BadEval);
    }
    if(Math.abs(ret - Math.cos(x*x+y*y)) > .1)
    {
      Trace=TRUE;
      ret = eval(fn);
      Trace=FALSE;
    }
    return ret;
  }

  String Clean(String expression)
  {
    String e = expression;
    e = e.toUpperCase();
    e = e.trim();
    int SpaceIndex = e.indexOf(' ');
    while(SpaceIndex != -1)
    {
      e = e.substring(0, SpaceIndex) + e.substring(SpaceIndex + 1, e.length());
      SpaceIndex = e.indexOf(' ');
    }
    return e;
  }

  String ParseParenthesis(String expression)
  {
    String e = expression;

    int LastFound = 0;
    double NumberValue = 0;
    int OpenParenthesis = e.indexOf('(');
    int CloseParenthesis = 0;

    while(OpenParenthesis != -1)
    {
      LastFound = OpenParenthesis;
      while (OpenParenthesis == LastFound)
      {
        CloseParenthesis = e.indexOf(')', OpenParenthesis);
        if(CloseParenthesis == -1)
        {
          BadEval = ParenthesisError;
          return expression;
        }
        LastFound = e.indexOf('(', OpenParenthesis + 1);
        if((LastFound != -1) && (LastFound < CloseParenthesis))
        {
          OpenParenthesis = LastFound;
        }
      }
      NumberValue = eval(e.substring(OpenParenthesis + 1, CloseParenthesis));
      if(BadEval != 0) return expression;
      if(NumberValue < 0)
      {
        e = e.substring(0, OpenParenthesis) + '~' + Double.toString(-NumberValue) + e.substring(CloseParenthesis + 1, e.length());
      }
      else
      {
        e = e.substring(0, OpenParenthesis) + Double.toString(NumberValue) + e.substring(CloseParenthesis + 1, e.length());
      }
      OpenParenthesis = e.indexOf('(');
    }
    if(e.indexOf(')') != -1)
    {
      BadEval = ParenthesisError;
      return expression;
    }
    else
    {
      return e.toUpperCase();
    }
  }

  int NumberStart(int NumEnd, String expression)
  {
    String e = expression;
    int NEnd = NumEnd;
    int NStart;
    for(NStart = NEnd; NStart > 0; NStart--)
    {
      if((e.substring(NStart, NStart + 1).compareTo("0") < 0) || (e.substring(NStart, NStart + 1).compareTo("9") > 0))
      {
        if(e.substring(NStart, NStart + 1).compareTo(".") != 0)
        {
          if(e.substring(NStart, NStart + 1).compareTo("E") != 0 )
          {
            if((e.substring(NStart, NStart + 1).compareTo("-") == 0) || (e.substring(NStart, NStart + 1).compareTo("+") == 0))
            {
              if (e.substring(NStart - 1, NStart).compareTo("E") != 0)
              {
                return NStart + 1;
              }
            }
            else if(e.substring(NStart, NStart + 1).compareTo("~") != 0)
            {
              return NStart + 1;
            }
          }
        }
      }
    }
    return NStart;
  }

  int NumberEnd(int NumStart, String e)
  {
    int NStart = NumStart;
    int NEnd;
    if((e.substring(NStart, NStart + 1).compareTo("-") == 0) || (e.substring(NStart, NStart + 1).compareTo("+") == 0) || (e.substring(NStart, NStart + 1).compareTo("~") == 0))
    {
      NStart++;
    }
    for(NEnd = NStart; NEnd < e.length(); NEnd++)
    {
      if((e.substring(NEnd, NEnd + 1).compareTo("0") < 0) || (e.substring(NEnd, NEnd + 1).compareTo("9") > 0))
      {
        if(e.substring(NEnd, NEnd + 1).compareTo(".") != 0)
        {
          if(e.substring(NEnd, NEnd + 1).compareTo("E") != 0 )
          {
            if((e.substring(NEnd, NEnd + 1).compareTo("-") == 0) || (e.substring(NEnd, NEnd + 1).compareTo("+") == 0))
            {
              if(e.substring(NEnd - 1, NEnd).compareTo("E") != 0)
              {
                break;
              }
            }
            else
            {
              break;
            }
          }
        }
      }
    }
    return NEnd;
  }

  int sgn(double x)
  {
    if(x < 0)
    {
      return -1;
    }
    else if (x > 0)
    {
      return 1;
    }
    else
    {
      return 0;
    }
  }

  String ParseFunctions(String expression)
  {
    String e = expression;
    int Found = TRUE;
    int FunctionStart = 0;
    int FunctionEnd = 0;
    String FunctionName = "";
    int NumEnd = 0;
    double Number = 0;

    while(Found == TRUE)
    {
      Found = FALSE;

      // scan for function name
      FunctionName = "";
      for(FunctionStart = 0; FunctionStart < e.length(); FunctionStart++)
      {
        if((e.substring(FunctionStart, FunctionStart+1).compareTo("A") >= 0) && (e.substring(FunctionStart, FunctionStart + 1).compareTo("Z") <= 0))
        {
          for(FunctionEnd = FunctionStart + 1; FunctionEnd < e.length(); FunctionEnd++)
          {
            if((e.substring(FunctionEnd, FunctionEnd + 1).compareTo("A") < 0) || (e.substring(FunctionEnd,FunctionEnd + 1).compareTo("Z") > 0))
            {
              FunctionName = e.substring(FunctionStart, FunctionEnd);
              Found = TRUE;
              break;
            }
          }
          if(FunctionName.compareTo("") == 0)
          {
            FunctionName = e.substring(FunctionStart,FunctionStart+1);
          }
          if(FunctionName.compareTo("E") == 0)
          {
            Found = FALSE;
          }
          else
            break;
        }
      }
      if(Found == TRUE)
      {
        NumEnd = NumberEnd(FunctionEnd, e);
        Number = eval(e.substring(FunctionEnd, NumEnd));
      }
      if(Found == TRUE)
      {
        //evaluate function
        if(FunctionName.compareTo("ABS") == 0)
          Number = Math.abs(Number);
        else if(FunctionName.compareTo("ACOS") == 0)
          Number = Math.acos(Number);
        else if(FunctionName.compareTo("ACOSH") == 0)
          Number = Math.PI / 2 - Math.atan(Number / Math.sqrt(1 - Number * Number));
        else if(FunctionName.compareTo("ACOT") == 0)
          Number = Math.atan(Number) + Math.PI / 2;
        else if(FunctionName.compareTo("ACOTH") == 0)
          Number = Math.log((Number + 1) / (Number - 1)) / 2;
        else if(FunctionName.compareTo("ACSC") == 0)
          Number = Math.atan(Number / Math.sqrt(Number * Number - 1)) + (sgn(Number) - 1) * Math.PI / 2;
        else if(FunctionName.compareTo("ACSCH") == 0)
          Number = Math.log((sgn(Number) * Math.sqrt(1 + Number * Number) + 1) / Number);
        else if(FunctionName.compareTo("ASIN") == 0)
          Number = Math.atan(Number / Math.sqrt(1 - Number * Number));
        else if(FunctionName.compareTo("ASINH") == 0)
          Number = Math.log(Number + Math.sqrt(Number * Number + 1));
        else if(FunctionName.compareTo("ASEC") == 0)
          Number = Math.atan(Number / Math.sqrt(Number * Number + 1)) + (sgn(Number) - 1) * Math.PI / 2;
        else if(FunctionName.compareTo("ASECH") == 0)
          Number = Math.log((Math.sqrt(1 - Number * Number) + 1) / Number);
        else if(FunctionName.compareTo("ATAN") == 0)
          Number = Math.atan(Number);
        else if (FunctionName.compareTo("ATANH") == 0)
          Number = Math.log((1 + Number) / (1 - Number)) / 2;
        else if(FunctionName.compareTo("COS") == 0)
          Number = Math.cos(Number);
        else if(FunctionName.compareTo("COSH") == 0)
          Number = (Math.exp(Number) + Math.exp(-Number)) / 2;
        else if(FunctionName.compareTo("COT") == 0)
          Number = 1 / Math.tan(Number);
        else if(FunctionName.compareTo("COTH") == 0)
          Number = (Math.exp(Number) + Math.exp(-Number)) / (Math.exp(Number) - Math.exp(-Number));
        else if(FunctionName.compareTo("CSC") == 0)
          Number = 1 / Math.sin(Number);
        else if(FunctionName.compareTo("CSCH") == 0)
          Number = 2 / (Math.exp(Number) - Math.exp(-Number));
        else if(FunctionName.compareTo("EXP") == 0)
          Number = Math.exp(Number);
        else if(FunctionName.compareTo("LOG") == 0)
          Number = Math.log(Number);
        else if(FunctionName.compareTo("RAND") == 0)
          Number = Math.random() * Number;
        else if(FunctionName.compareTo("ROUND") == 0)
          Number = Math.round(Number);
        else if(FunctionName.compareTo("SEC") == 0)
          Number = 1 / Math.cos(Number);
        else if(FunctionName.compareTo("SECH") == 0)
          Number = 2 / (Math.exp(Number) + Math.exp(-Number));
        else if(FunctionName.compareTo("SIGN") == 0)
          Number = sgn(Number);
        else if(FunctionName.compareTo("SIN") == 0)
          Number = Math.sin(Number);
        else if(FunctionName.compareTo("SINH") == 0)
          Number = (Math.exp(Number) - Math.exp(-Number)) / 2;
        else if(FunctionName.compareTo("SQRT") == 0)
          Number = Math.sqrt(Number);
        else if(FunctionName.compareTo("TAN") == 0)
          Number = Math.tan(Number);
        else if(FunctionName.compareTo("TANH") == 0)
          Number = (Math.exp(Number) - Math.exp(-Number)) / (Math.exp(Number) + Math.exp(-Number));
        else
        {
          BadEval = UndefinedFunction;
          return expression;
        }
        if(Number < 0)
        {
          e = e.substring(0, FunctionStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
        }
        else
        {
          e = e.substring(0, FunctionStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
        }
      }
    }
    return e.toUpperCase();
  }

  String ParseExponent(String expression)
  {
    String e = expression;
    int ExponentIndex = 0;
    int NumStart = 0;
    int NumEnd = 0;
    double Number = 0;

    while(e.indexOf("^") != -1)
    {
      ExponentIndex = e.indexOf("^");
      NumStart = NumberStart(ExponentIndex - 1, e);
      NumEnd = NumberEnd(ExponentIndex + 1, e);
      Number = Math.pow(eval(e.substring(NumStart, ExponentIndex)), eval(e.substring(ExponentIndex + 1, NumEnd)));
      if(Number < 0)
      {
        e = e.substring(0,NumStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
      }
      else
      {
        e = e.substring(0,NumStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
      }
    }
    return e.toUpperCase();
  }

  String ParseMultiplication(String expression)
  {
    String e = expression;
    int MultiplicationIndex = 0;
    int NumStart = 0;
    int NumEnd = 0;
    double Number = 0;

    while(e.indexOf("*") != -1)
    {
      MultiplicationIndex = e.indexOf("*");
      NumStart = NumberStart(MultiplicationIndex - 1, e);
      NumEnd = NumberEnd(MultiplicationIndex + 1, e);
      Number = eval(e.substring(NumStart, MultiplicationIndex)) * eval(e.substring(MultiplicationIndex + 1, NumEnd));
      if(Number < 0)
      {
        e = e.substring(0,NumStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
      }
      else
      {
        e = e.substring(0,NumStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
      }
    }
    return e.toUpperCase();
  }

  String ParseDivision(String expression)
  {
    String e = expression;
    int DivisionIndex = 0;
    int NumStart = 0;
    int NumEnd = 0;
    double Number = 0;

    while(e.indexOf("/") != -1)
    {
      DivisionIndex = e.indexOf("/");
      NumStart = NumberStart(DivisionIndex - 1, e);
      NumEnd = NumberEnd(DivisionIndex + 1, e);
      Number = eval(e.substring(NumStart, DivisionIndex)) / eval(e.substring(DivisionIndex + 1, NumEnd));
      if (Number < 0)
      {
        e = e.substring(0,NumStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
      }
      else
      {
        e = e.substring(0,NumStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
      }
    }
    return e.toUpperCase();
  }

  String ParseAddition(String expression)
  {
    String e = expression;
    int AdditionIndex = 0;
    int NumStart = 0;
    int NumEnd = 0;
    double Number = 0;

    while(e.indexOf("+") != -1)
    {
      AdditionIndex = e.indexOf("+");
      NumStart = NumberStart(AdditionIndex - 1, e);
      NumEnd = NumberEnd(AdditionIndex + 1, e);
      Number = eval(e.substring(NumStart, AdditionIndex)) + eval(e.substring(AdditionIndex + 1, NumEnd));
      if(Number < 0)
      {
        e = e.substring(0,NumStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
      }
      else
      {
        e = e.substring(0,NumStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
      }
    }
    return e.toUpperCase();
  }

  String ParseSubtraction(String expression)
  {
    String e = expression;
    int SubtractionIndex = 0;
    int NumStart = 0;
    int NumEnd = 0;
    double Number = 0;

    while(e.indexOf("-") != -1)
    {
      SubtractionIndex = e.indexOf("-");
      NumStart = NumberStart(SubtractionIndex - 1, e);
      NumEnd = NumberEnd(SubtractionIndex + 1, e);
      Number = eval(e.substring(NumStart, SubtractionIndex)) - eval(e.substring(SubtractionIndex + 1, NumEnd));
      if(Number < 0)
      {
        e = e.substring(0,NumStart) + "~" + Double.toString(-Number) + e.substring(NumEnd, e.length());
      }
      else
      {
        e = e.substring(0,NumStart) + Double.toString(Number) + e.substring(NumEnd, e.length());
      }
    }
    return e.toUpperCase();
  }

  double eval(String expression)
  {
    BadEval = 0;
    String e = expression;
    int flag=0;

    e = Clean(e);

    // scan for simple numeric expression
    int ScanIndex = 0;
    if((e.substring(0, 1).compareTo("-") == 0) || (e.substring(0, 1).compareTo("+") == 0) || (e.substring(0, 1).compareTo("~") == 0))
    {
      ScanIndex++;
    }
    for(ScanIndex = ScanIndex; ScanIndex < e.length(); ScanIndex++)
    {
      if((e.substring(ScanIndex, ScanIndex + 1).compareTo("0") < 0) || (e.substring(ScanIndex, ScanIndex + 1).compareTo("9") > 0))
      {
        if(e.substring(ScanIndex, ScanIndex + 1).compareTo(".") != 0)
        {
          if((e.substring(ScanIndex, ScanIndex + 1).compareTo("-") == 0) || (e.substring(ScanIndex, ScanIndex + 1).compareTo("+") == 0))
          {
            if(e.substring(ScanIndex - 1, ScanIndex).compareTo("E") != 0)
            {
              break;
            }
          }
          else if(e.substring(ScanIndex, ScanIndex + 1).compareTo("E") != 0)
          {
            break;
          }
          else
            flag=1;
        }
      }
    }
    if(ScanIndex == e.length())
    {
      if(e.substring(0, 1).compareTo("~") == 0)
      {
        e = "-" + e.substring(1, e.length());
      }
      return Double.valueOf(e).doubleValue();
    }

    e = ParseParenthesis(e);
    if (BadEval != 0) return 0;
    e = ParseFunctions(e);
    if (BadEval != 0) return 0;
    e = ParseExponent(e);
    if (BadEval != 0) return 0;
    e = ParseMultiplication(e);
    if (BadEval != 0) return 0;
    e = ParseDivision(e);
    if (BadEval != 0) return 0;
    e = ParseAddition(e);
    if (BadEval != 0) return 0;
    e = ParseSubtraction(e);
    if (BadEval != 0) return 0;

    return eval(e);
  }

  int GetX(double x, double y, double z)
  {
    return (int) ((x * CosA - y * SinA - XMin) * XScale);
  }

  int GetY(double x, double y, double z)
  {
    return (int) ((x * SinAT + y * CosASinT + z * CosT - YMin) * YScale);
  }

  public void paint(Graphics g)
  {        
    // draw border
    g.setColor(new Color(0, 0, 51));
    g.fillRect(0, 0, size().width, size().height);

    // display function
    g.setColor(Color.white);
    g.drawString(Function, 5, size().height - 10);

    // draw axis
    g.setColor(Color.yellow);
    g.drawLine(GetX(0, 0, ZMin),GetY(0, 0, ZMin),GetX(0, 0, ZMax),GetY(0, 0, ZMax));
    g.drawLine(GetX(0, YMin, 0),GetY(0, YMin, 0),GetX(0, YMax, 0),GetY(0, YMax, 0));
    g.drawLine(GetX(XMin, 0, 0),GetY(XMin, 0, 0),GetX(XMax, 0, 0),GetY(XMax, 0, 0));

    // Plot Function
    double IncX = (XMax - XMin) / XCut;
    double IncY = (YMax - YMin) / YCut;
    double x;
    double y;
    double z;
    double nz;
    g.setColor(Color.blue);
    for(x = XMin; x <= XMax; x += IncX)
    {
      nz = f(x, YMin);
      for(y = YMin + IncY; y <= YMax; y += IncY)
      {
        z = nz;
        nz = f(x, y);
        g.drawLine(GetX(x, y - IncY, z), GetY(x, y - IncY, z), GetX(x, y, nz), GetY(x, y, nz));
      }
    }
    for (y = YMin; y <= YMax; y += IncY)
    {
      nz = f(XMin, y);
      for(x = XMin + IncX; x <= XMax; x += IncX)
      {
        z = nz;
        nz = f(x, y);
        g.drawLine(GetX(x - IncX, y, z), GetY(x - IncX, y, z), GetX(x, y, nz), GetY(x, y, nz));
      }
    }
  }
  
  public boolean action(Event evt, Object o)
  {
    if(evt.target instanceof Button)
    {
      Function = Equation.getText();
      Graphics g = getGraphics();
      paint(g);
    }
    return true;
  }
  
}