unit mainWin;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, ExtCtrls, Math, ComCtrls;

type

  TExtendedPoint = record
    X, Y: real;
  end;

  TVector = record
    X, Y, Z: real;
  end;

  TForm1 = class(TForm)
    Button1: TButton;
    Button2: TButton;
    cnvs: TImage;
    Button3: TButton;
    Button4: TButton;
    ECPX: TEdit;
    ECPY: TEdit;
    ECPZ: TEdit;
    EFI: TTrackBar;
    ETH: TTrackBar;
    EZOOM: TTrackBar;
    Button5: TButton;
    Memo1: TMemo;
    ERO: TTrackBar;
    cnvs2: TImage;
    btndebugset: TButton;
    highres: TCheckBox;
    ProgressBar1: TProgressBar;
    ERES: TEdit;
    Label1: TLabel;
    Label2: TLabel;
    Label3: TLabel;
    Label4: TLabel;
    Label5: TLabel;
    procedure FormCreate(Sender: TObject);
    procedure CreateSet(Sender: TObject);
    procedure DrawSet(Sender: TObject);
    procedure CreateFctnGraph(Sender: TObject);
    procedure CreateFctnParamGraph(Sender: TObject);
    procedure EFIChange(Sender: TObject);
    procedure CreateBaseGrid(Sender: TObject);
    procedure cbDebugClick(Sender: TObject);
    procedure Button2Click(Sender: TObject);
    procedure ECPXKeyDown(Sender: TObject; var Key: Word;
      Shift: TShiftState);
    procedure highresClick(Sender: TObject);
    procedure ERESKeyDown(Sender: TObject; var Key: Word;
      Shift: TShiftState);
    procedure FormKeyDown(Sender: TObject; var Key: Word;
      Shift: TShiftState);
    procedure FormMouseWheel(Sender: TObject; Shift: TShiftState;
      WheelDelta: Integer; MousePos: TPoint; var Handled: Boolean);
    procedure FormShow(Sender: TObject);
    procedure ERESEnter(Sender: TObject);
    procedure ERESExit(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
    function Vctr(A, B, C: real): TVector;
    function Add(A, B: TVector): TVector;
    function Sub(A, B: TVector): TVector;
    function Mul(A: real; B: TVector): TVector;
    function Dot(A, B: TVector): real;
    function VecLength(A: TVector): real;
    function VecLengthCompare(A: TVector): real;
    procedure FindDirection;
    function FindProjection(X: TVector): TVector;
    function FindProjection2(X: TVector): TVector;    
    function VectorToString(V: TVector): string;
    function GetColorFromPos(x, y, z: real): TColor;
    function LogToScrn(Point: TExtendedPoint): TPoint;
    function ScrnToLog(Point: TPoint): TExtendedPoint;
    function LogToScrn2(Point: TExtendedPoint): TPoint;
    function Scrn2ToLog(Point: TPoint): TExtendedPoint;
    function SpaceSysToPlaneSys(X: TVector): TVector;
    function SpaceSysToPlaneSys2(X: TVector): TVector;    
    function Cross(X, Y: TVector): TVector;
  end;

var
  Form1: TForm1;
  xmax, xmin, ymax, ymin, zmin, zmax: real;
  Vector: TVector;
  CameraPos, CameraPos2: TVector;
  PlaneVec, PlaneVec2: TVector;
  Direction: TVector;
  d, d2: real;
  resfktn, reseval: real;
  Graph: array of TVector;
  CPF, CPT, CPD, CPR: real;
  CenterPos, PlaneCenterPos, Plane2CenterPos: TVector;
  T: array[1..3, 1..3] of real;
  T2: array[1..3, 1..3] of real;
  DebugGraph: array of TVector;

implementation

{$R *.dfm}

function TForm1.Vctr(A, B, C: real): TVector;
begin
  result.X := A;
  result.Y := B;
  result.Z := C;
end;

function TForm1.Add(A, B: TVector): TVector;
begin
  result := Vctr(A.X + B.X, A.Y + B.Y, A.Z + B.Z);
end;

function TForm1.Sub(A, B: TVector): TVector;
begin
  result := Vctr(A.X - B.X, A.Y - B.Y, A.Z - B.Z);
end;

function TForm1.Mul(A: real; B: TVector): TVector;
begin
  result := Vctr(A*B.X, A*B.Y, A*B.Z);
end;

function TForm1.Dot(A, B: TVector): real;
begin
  Dot := A.X * B.X + A.Y * B.Y + A.Z * B.Z;
end;

function TForm1.VecLength(A: TVector): real;
begin
  VecLength := sqrt(Dot(A, A));
end;

function TForm1.VecLengthCompare(A: TVector): real;
begin
  VecLengthCompare := (Dot(A, A));
end;

procedure TForm1.FormCreate(Sender: TObject);
var
  NPlaneVec, NPlaneVec2: TVector;
  fx, fy, fx2, fy2: TVector;
  A: array[1..3, 1..3] of real;
  CPRsin, CPRcos, CZOOM: real;
begin//X_f = T^-1 X_e omm _f = _eT; i programmet är T transponatet (=inversen, ja ortogonal ty ON-basbyte!) av T i formeln

  CPF := EFI.Position * PI / 180;
  CPT := ETH.Position * PI / 180;
  CPD := 20;
  CZOOM := EZOOM.Position;
  CPR := ERO.Position * PI/180;
  CenterPos := Vctr(StrToFloat(ECPX.Text), StrToFloat(ECPY.Text), StrToFloat(ECPZ.Text));
  xmin := -CZOOM;
  xmax := CZOOM;
  ymin := -CZOOM;
  ymax := CZOOM;
  zmin := -CZOOM;
  zmax := CZOOM;
  PlaneVec := Vctr(sin(CPT) * cos(CPF), sin(CPT) * sin(CPF), cos(CPT));
  /////Test
  //if false then begin
  //setlength(Graph, length(Graph) + 1);
  //Graph[high(Graph)] := Mul(10/VecLength(PlaneVec), PlaneVec); end;
  //  memo1.Lines.Add(VectorToString(PlaneVec));
  /////Test slut
  CameraPos := Add(CenterPos, Mul(2*CPD / VecLength(PlaneVec), PlaneVec));
  d := (CPD * VecLength(PlaneVec) + Dot(PlaneVec, CenterPos)){ * Sign(d - Dot(PlaneVec, CenterPos))};               // Planekvationens högerled
  PlaneCenterPos := FindProjection(CenterPos);

  /////Test
  //Caption := floattostr(VecLength(Sub(CameraPos, CenterPos))) + ' ---- ' + floattostr(VecLength(Sub(PlaneCenterPos, CenterPos))) + ' ---- ' + floattostr(VecLength(Sub(CameraPos, PlaneCenterPos)));
  /////Test slut

  resfktn := StrToFloat(ERES.Text);

  reseval := StrToFloat(ERES.Text);

  // Rymd-Plan-omvandling

  NPlaneVec := Mul(1/VecLength(PlaneVec), PlaneVec);

  // f_z
  T[3, 1] := NPlaneVec.X;              // T är transpontatet (inversen, ty alla baser är ON => T är ortogonal) av T i f=eT.
  T[3, 2] := NPlaneVec.Y;
  T[3, 3] := NPlaneVec.Z;

  // f_x
  // Varför sätter vi inte bara t ex fx := vctr(0, -T[3, 3], T[3, 2])?
  // Det är väl klart att fx då blir ortogonal med fz?
  // Jo, det är klart, men om t ex fz = vctr(1, 0, 0), så blir ju fx nollvektorn!
  // Visst är den ortogonal med fz, men någon basvektor är det inte!

  // Krav på vektorn fx är (i) (fx|fz) = 0
  //                       (ii) fx IN {z=0}
  // => (fx3 = 0) ^ (npv1 * fx1 = -npv2 * fx2)
  // Antingen är (1) npv1 = npv2 = 0
  //             (2) npv1 = 0; npv2 <> 0
  //             (3) npv1 <> 0; npv2 = 0
  //             (4) npv1 <> 0; npv2 <> 0;
  if NPlaneVec.Y = 0 then
  begin
    fx := vctr(0, 1, 0);
    // Mikebuggen
    // Bibehåll den skenbara kamerarotation som FI ger upphov till
    CPR := CPR + CPF;
  end
  else
  begin
    if CPF <= PI then
      fx := vctr(-1, NPlaneVec.X/NPlaneVec.Y, 0)
    else
      fx := vctr(1, -NPlaneVec.X/NPlaneVec.Y, 0);
    fx := Mul(1/VecLength(fx), fx);
  end;

  T[1, 1] := fx.X;
  T[1, 2] := fx.Y;
  T[1, 3] := fx.Z;

  // f_y
  fy := Cross(Vctr(T[3,1], T[3,2], T[3,3]), Vctr(T[1,1], T[1,2], T[1,3]));
  fy := Mul(1/VecLength(fy), fy);

  T[2, 1] := fy.X;
  T[2, 2] := fy.Y;
  T[2, 3] := fy.Z;

  if Dot(Cross(fx, fy), NPlaneVec) < 0 then
  begin
    fy := Mul(-1, fy); beep;
  end;

  // Rotera f_x och f_y runt f_z
  // Avbildningsmatrisen A för rotation CPR grader runt den tredje koordinataxeln

  // Bara för prestandan
  CPRsin := sin(CPR);
  CPRcos := cos(CPR);

  A[1, 1] := CPRcos;
  A[1, 2] := -CPRsin;
  A[1, 3] := 0;
  A[2, 1] := CPRsin;
  A[2, 2] := CPRcos;
  A[2, 3] := 0;
  A[3, 1] := 0;
  A[3, 2] := 0;
  A[3, 3] := 1;

  // F(fX) = fAX
  // Vi skall alltså multiplicera koordinatvektorn X uttryckt i basen f från vänster med A.
  // Koordinatmatriserna för fx och fy är (1 0 0)^t respektive (0 1 0)^t.

  fx := Vctr(A[1,1]{ * 1 + A[1,2] * 0 + A[1,3] * 0},
             A[2,1]{ * 1 + A[2,2] * 0 + A[2,3] * 0},
             A[3,1]{ * 1 + A[3,2] * 0 + A[3,3] * 0});

  fy := Vctr({A[1,1] * 0 + }A[1,2]{ * 1 + A[1,3] * 0},
             {A[2,1] * 0 + }A[2,2]{ * 1 + A[2,3] * 0},
             {A[3,1] * 0 + }A[3,2]{ * 1 + A[3,3] * 0});

  // I rätt bas också!   (fx och fy blir koordinatmatriserna i gamla f-systemet, men de skall anges i e-systemet! X_e = T X_f, där T är transponatet av matrisen T i koden.
  fx := Vctr(T[1,1] * fx.X + T[2,1] * fx.Y + T[3,1] * fx.Z,
             T[1,2] * fx.X + T[2,2] * fx.Y + T[3,2] * fx.Z,
             T[1,3] * fx.X + T[2,3] * fx.Y + T[3,3] * fx.Z);

  fy := Vctr(T[1,1] * fy.X + T[2,1] * fy.Y + T[3,1] * fy.Z,
             T[1,2] * fy.X + T[2,2] * fy.Y + T[3,2] * fy.Z,
             T[1,3] * fy.X + T[2,3] * fy.Y + T[3,3] * fy.Z);

  T[1, 1] := fx.X;
  T[1, 2] := fx.Y;
  T[1, 3] := fx.Z;

  T[2, 1] := fy.X;
  T[2, 2] := fy.Y;
  T[2, 3] := fy.Z;

  /////Test
  //Caption := floattostr(VecLength(Cross(PlaneVec, vctr(T[3,1], T[3,2], T[3,3]))));
  {                      // parvis ortogonalitet
  Caption := floattostr(dot(vctr(T[1,1], T[1,2], T[1,3]), vctr(T[2,1], T[2,2], T[2,3])));
  Caption := Caption + ' --- ' + floattostr(dot(vctr(T[1,1], T[1,2], T[1,3]), vctr(T[3,1], T[3,2], T[3,3])));
  Caption := Caption + ' --- ' + floattostr(dot(vctr(T[2,1], T[2,2], T[2,3]), vctr(T[3,1], T[3,2], T[3,3])));
  }{                     // normering
  Caption := floattostr(VecLength(vctr(T[1,1], T[1,2], T[1,3])));
  Caption := Caption + ' --- ' + floattostr(VecLength(vctr(T[2,1], T[2,2], T[2,3])));
  Caption := Caption + ' --- ' + floattostr(VecLength(vctr(T[3,1], T[3,2], T[3,3])));
  }
  /////Test slut

  //CLW
  PlaneVec2 := Vctr(sin(PI/4) * cos(PI/4), sin(PI/4) * sin(PI/4), cos(PI/4));
  CameraPos2 := Add(CenterPos, Mul(2*CPD / VecLength(PlaneVec2), PlaneVec2));
  d2 := (CPD * VecLength(PlaneVec2) + Dot(PlaneVec2, CenterPos)){ * Sign(d - Dot(PlaneVec2, CenterPos))};               // Planekvationens högerled
  Plane2CenterPos := FindProjection2(CenterPos);

  // Rymd-Plan-omvandling  CLW!

  NPlaneVec2 := Mul(1/VecLength(PlaneVec2), PlaneVec2);

  // f_z
  T2[3, 1] := NPlaneVec2.X;
  T2[3, 2] := NPlaneVec2.Y;
  T2[3, 3] := NPlaneVec2.Z;

  // f_x                               
  fx2 := vctr(-T2[3, 2], T2[3, 1], 0);
  fx2 := Mul(1/VecLength(fx2), fx2);

  T2[1, 1] := fx2.X;
  T2[1, 2] := fx2.Y;
  T2[1, 3] := fx2.Z;

  // f_y
  fy2 := Cross(Vctr(T2[3,1], T2[3,2], T2[3,3]), Vctr(T2[1,1], T2[1,2], T2[1,3]));
  fy2 := Mul(1/VecLength(fy2), fy2);

  T2[2, 1] := fy2.X;
  T2[2, 2] := fy2.Y;
  T2[2, 3] := fy2.Z;

  //CLW slut

end;

procedure TForm1.FindDirection;
begin
  Direction := Sub(CameraPos, Vector);
end;

function TForm1.FindProjection(X: TVector): TVector;
var
  t: real;
begin

  Vector := Vctr(X.X, X.Y, X.Z);
  FindDirection;
  t := (d - Dot(PlaneVec, Vector))/(Dot(PlaneVec, Direction));
  result := Add(Vector, Mul(t, Direction));

end;

function TForm1.FindProjection2(X: TVector): TVector;
var
  t: real;
  Direction2: TVector;
begin

  Vector := Vctr(X.X, X.Y, X.Z);
  Direction2 := Sub(CameraPos2, Vector);
  t := (d2 - Dot(PlaneVec2, Vector))/(Dot(PlaneVec2, Direction2));
  result := Add(Vector, Mul(t, Direction2));

end;

function TForm1.VectorToString(V: TVector): string;
begin
  result := '(' + FloatToStr(V.X) + ',  ' + FloatToStr(V.Y) + ',  ' + FloatToStr(V.Z) + ')';
end;

procedure TForm1.CreateSet(Sender: TObject);
var
  i: integer;
begin

//  for x := low(Graph) to high(Graph) do


//        MySet[x, y, z] := x + z - y = 100;
//        MySet[x, y, z] := (x < 50) or (x > 150) or (y < 50) or (y > 150) or (sqrt((x-100)*(x-100) + 2*(y-100)*(y-100) + 3*(z-100)*(z-100) + (x-100)*(y-100) - (z-100)*(x-100)) <= 80);
//        MySet[x, y, z] := (x < 50) or (x > 150) or (y < 50) or (y > 150);
//        MySet[x, y, z] := sqrt((x-100)*(x-100) + 2*(y-100)*(y-100) + 3*(z-100)*(z-100) + (x-100)*(y-100) - (z-100)*(x-100)) <= 80;
//        MySet[x, y, z] := (sqrt((x-50)*(x-50) + (y-50)*(y-50) + (z-40)*(z-40)) <= 40) Or (sqrt((x-150)*(x-150) + (y-150)*(y-150) + (z-worldsize+40)*(z-worldsize+40)) <= 40)

end;

procedure TForm1.DrawSet(Sender: TObject);
var
  i: integer;
  prj: TVector;
  extp: TExtendedPoint;
  scrn: TPoint;
  Buffer, Buffer2: TBitmap;
  crdist: integer;
  crdistin, crdistout, pbpos: integer;
  MinDist: TBitmap; //hellre en array[1..screenwidth] of arraw[1..screenheight] of real, men ger stack overflow...

  //Test
  //st:TStringList;
  //Test slut

  // Camera Localisation Window
  CamLocGraph: array of TVector;
  prj2: TVector;
  extp2: TExtendedPoint;
  scrn2: TPoint;
  // End CLW
begin

  Buffer := TBitmap.Create;
  Buffer.Width := cnvs.Width;
  Buffer.Height := cnvs.Height;
  Buffer.Canvas.Brush.Color := clWhite;
  Buffer.Canvas.FillRect(Rect(0, 0, Buffer.Width, Buffer.Height));

//CLW
  Buffer2 := TBitmap.Create;
  Buffer2.Width := cnvs2.Width;
  Buffer2.Height := cnvs2.Height;
  Buffer2.Canvas.Brush.Color := clWhite;
  Buffer2.Canvas.FillRect(Rect(0, 0, Buffer2.Width, Buffer2.Height));
//CLW slut

  MinDist := TBitmap.Create;        // MED BLOCKET NEDAN!
  MinDist.Width := Buffer.Width;
  MinDist.Height := Buffer.Height;

  MinDist.Canvas.Draw(0, 0, Buffer); //MED BLOCKET NEDAN!

/////TEST
//      st := TStringList.Create;
/////Test slut

  ProgressBar1.Min := 0;
  ProgressBar1.Max := 100;
  ProgressBar1.Position := ProgressBar1.Min;

  for i := low(Graph) to high(Graph) do
  begin
    prj := SpaceSysToPlaneSys(FindProjection(Graph[i]));
    /////Test
    //st.Add(VectorToString(prj));
    /////Test slut
    extp.X := prj.X;
    extp.Y := prj.Y;
    scrn := LogToScrn(extp);                                 
    crdist := round(VecLengthCompare(Sub(CameraPos, Graph[i])));                    //  Utan blocket: 10 s; Med blocket: 60+ sekunder. Varför??????? Troligtvis tar det tid att läsa från/skriva till TBitmap.Canvas. Kanske löses problemet med arrayen ovan?
    crdistin := MinDist.Canvas.Pixels[scrn.X, scrn.Y];
    if crdistin = 0 then
      crdistout := crdist
    else
      crdistout := min(crdistin, crdist);

    MinDist.Canvas.Pixels[scrn.X, scrn.Y] := crdistout;

    if MinDist.Canvas.Pixels[scrn.X, scrn.Y] = crdist then                          {}
      Buffer.Canvas.Pixels[scrn.X, scrn.Y] := GetColorFromPos(Graph[i].X, Graph[i].Y, Graph[i].Z);

    //CLW
    prj2 := SpaceSysToPlaneSys2(FindProjection2(Graph[i]));
    extp2.X := prj2.X;
    extp2.Y := prj2.Y;
    scrn2 := LogToScrn2(extp2);
    Buffer2.Canvas.Pixels[scrn2.X, scrn2.Y] := clBlack;
    //CLW slut

    // Progress
    if i mod 2000 = 0 then
    begin                           
      pbpos := round(100*(i / high(Graph)));
      if ProgressBar1.Position <> pbpos then
      begin
        ProgressBar1.Position := pbpos;
        ProgressBar1.Repaint;
      end;
    end;
  end;

  cnvs.Canvas.Draw(0, 0, Buffer);
  ProgressBar1.Position := 100;

  Buffer.Free;
  MinDist.Free;

/////Test
//    memo1.Lines.AddStrings(st);
//    st.Free;
/////Test slut

//CLW
  prj2 := SpaceSysToPlaneSys2(FindProjection2(Mul(0.5, PlaneCenterPos)));
  extp2.X := prj2.X;
  extp2.Y := prj2.Y;
  scrn2 := LogToScrn2(extp2);
  Buffer2.Canvas.Brush.Color := clRed;
  Buffer2.Canvas.FillRect(Rect(scrn2.X-2, scrn2.Y-2, scrn2.X+2, scrn2.Y+2));
  cnvs2.Canvas.Draw(0, 0, Buffer2);
  Buffer2.Free;
//CLW slut

memo1.clear;

memo1.lines.add('Medelpunkt: ' + VectorToString(vctr(strtofloat(ECPX.Text), strtofloat(ECPY.Text), strtofloat(ECPZ.Text))));

memo1.lines.add('THETA: ' + IntToStr(ETH.Position) + ' grader');
memo1.lines.add('FI: ' + IntToStr(EFI.Position) + ' grader');
memo1.lines.add('Kamerarotation: ' + IntToStr(ERO.Position) + ' grader');
memo1.lines.add('Zoomnivå: -' + IntToStr(EZOOM.Position));

memo1.lines.add('Upplösning: ' + FloatToStr(resfktn));
memo1.lines.add('Antal punkter uppritade: ' + IntToStr(length(Graph)));

end;

function TForm1.GetColorFromPos(x, y, z: real): TColor;
begin
//  result := RGB(255, round(255*((zmax-2*z)/(zmax-zmin))), round(255*((zmax-2*z)/(zmax-zmin)))); //RED
  result := RGB(round(255*((zmax-2*z)/(zmax-zmin))), round(255*((zmax-2*z)/(zmax-zmin))), 255); //BLUE
end;

function TForm1.LogToScrn(Point: TExtendedPoint): TPoint;
begin
  result.X := Round((cnvs.Width / (xmax-xmin))*(Point.X - xmin));
  result.Y := cnvs.Height - Round((cnvs.Height / (ymax-ymin))*(Point.Y - ymin));
end;

function TForm1.ScrnToLog(Point: TPoint): TExtendedPoint;
begin
  result.X := ((xmax-xmin)/cnvs.Width) * Point.X + xmin;
  result.Y := ((ymax-ymin)/cnvs.Height) * (cnvs.Height - Point.Y) + ymin;
end;

function TForm1.LogToScrn2(Point: TExtendedPoint): TPoint;
begin
  result.X := Round((cnvs2.Width / (xmax-xmin))*(Point.X - xmin));
  result.Y := cnvs2.Height - Round((cnvs2.Height / (ymax-ymin))*(Point.Y - ymin));
end;

function TForm1.Scrn2ToLog(Point: TPoint): TExtendedPoint;
begin
  result.X := ((xmax-xmin)/cnvs2.Width) * Point.X + xmin;
  result.Y := ((ymax-ymin)/cnvs2.Height) * (cnvs2.Height - Point.Y) + ymin;
end;

procedure TForm1.CreateFctnGraph(Sender: TObject);

  function fktn(x, y: real): real;
  begin
    result := 1.5*sin(sqrt(x*x + y*y));
  end;

var
  x, y: real;
begin

//  SetLength(Graph, 0);
  y := ymin;
  repeat
    x := xmin;
    repeat
      SetLength(Graph, length(Graph) + 1);
      Graph[high(Graph)] := Vctr(x, y, fktn(x, y));
      x := x + resfktn;
      if length(Graph) > 100000000 then begin abort; application.Terminate; end;
    until
      x > xmax;
    y := y + resfktn;
  until
    y > ymax;

end;

procedure TForm1.CreateFctnParamGraph(Sender: TObject);
  function fktn(s, t: real): TVector;
  begin
    result := vctr(sin(s) * cos(t), sin(s) * sin(t), cos(s));
  end;

var
  s, t: real;
begin

  t := 0;
  repeat
    s := 0;
    repeat
      if length(Graph) > 100000000 then begin abort; application.Terminate; end;
      SetLength(Graph, Length(Graph) + 3);
      Graph[high(Graph)-2] := add(fktn(t,s), vctr(-3, -2, -1));      
      Graph[high(Graph)-1] := add(fktn(t,s), vctr(2, 2, 2));
      Graph[high(Graph)] := add(fktn(t,s), vctr(3, 4, 0));
      s := s + resfktn;
    until
      s > 2*Pi;
    t := t + resfktn;
  until
    t > PI;

end;

function TForm1.SpaceSysToPlaneSys(X: TVector): TVector;
begin

  X := Sub(X, PlaneCenterPos);

  result := Vctr(T[1,1] * X.X + T[1,2] * X.Y + T[1,3] * X.Z,
                 T[2,1] * X.X + T[2,2] * X.Y + T[2,3] * X.Z,
                 T[3,1] * X.X + T[3,2] * X.Y + T[3,3] * X.Z);

end;

function TForm1.SpaceSysToPlaneSys2(X: TVector): TVector;
begin

  X := Sub(X, Plane2CenterPos);

  result := Vctr(T2[1,1] * X.X + T2[1,2] * X.Y + T2[1,3] * X.Z,
                 T2[2,1] * X.X + T2[2,2] * X.Y + T2[2,3] * X.Z,
                 T2[3,1] * X.X + T2[3,2] * X.Y + T2[3,3] * X.Z);

end;


function TForm1.Cross(X, Y: TVector): TVector;
begin

  result := Vctr(X.Y * Y.Z - X.Z * Y.Y,
                 X.Z * Y.X - X.X * Y.Z,
                 X.X * Y.Y - X.Y * Y.X);

end;

procedure TForm1.EFIChange(Sender: TObject);
begin
  FormCreate(sender);
  DrawSet(sender);
end;

procedure TForm1.CreateBaseGrid(Sender: TObject);
const
  bvlength = 20;
  arlength = 2;
  dotres = 0.1;
var
  t: real;
  x,y,z : real;
begin

  t := 0;
  repeat
    SetLength(Graph, length(Graph) + 1);
    Graph[high(Graph)] := Vctr(t, 0, 0);
    t := t + 0.04;
  until
    t > bvlength;

  t := 0;
  repeat
    SetLength(Graph, length(Graph) + 1);
    Graph[high(Graph)] := Vctr(0, t, 0);
    t := t + 0.04;
  until
    t > bvlength;

  t := 0;
  repeat
    SetLength(Graph, length(Graph) + 1);
    Graph[high(Graph)] := Vctr(0, 0, t);
    t := t + 0.04;
  until
    t > bvlength;
end;

procedure TForm1.cbDebugClick(Sender: TObject);
begin
  FormCreate(sender);
end;

procedure TForm1.Button2Click(Sender: TObject);
begin
  FormCreate(sender); DrawSet(sender);
end;

procedure TForm1.ECPXKeyDown(Sender: TObject; var Key: Word;
  Shift: TShiftState);
begin
  if (Key = VK_UP) and (Sender is TEdit) then with Sender as TEdit do Text := IntToStr(StrToInt(Text) + 1);
  if (Key = VK_DOWN) and (Sender is TEdit) then with Sender as TEdit do Text := IntToStr(StrToInt(Text) - 1);
  FormCreate(sender); DrawSet(sender);
end;

procedure TForm1.highresClick(Sender: TObject);
begin
  SetLength(Graph, 0);
  FormCreate(sender);
  DrawSet(sender);
end;

procedure TForm1.ERESKeyDown(Sender: TObject; var Key: Word;
  Shift: TShiftState);
begin
  if key = vk_return then begin FormCreate(Sender); SetLength(Graph, 0); {20080329: del 2008-06-01 undel} CreateBaseGrid(Sender); {20080329:del *Param*} CreateFctnGraph(Sender); DrawSet(Sender); KeyPreview := true; Memo1.SetFocus; end;
end;

procedure TForm1.FormKeyDown(Sender: TObject; var Key: Word;
  Shift: TShiftState);
var
  intstep: integer;
begin

  if ssCtrl in Shift then
  begin

    intstep := IfThen(ssShift in Shift, 1, 15);

    if ssAlt in Shift then
    begin
      if Key = VK_LEFT then ERO.Position := (360 + ERO.Position + intstep) mod 360;
      if Key = VK_RIGHT then ERO.Position := (360 + ERO.Position - intstep) mod 360;
    end
    else
    begin

      if Key = VK_LEFT then EFI.Position := (360 + EFI.Position - intstep) mod 360;
      if Key = VK_RIGHT then EFI.Position := (360 + EFI.Position + intstep) mod 360;
      if Key = VK_UP then ETH.Position := ETH.Position - intstep;
      if Key = VK_DOWN then ETH.Position := ETH.Position + intstep;
    end;

  end
  else
  begin

    intstep := IfThen(ssShift in Shift, 1, 5);

    if ssAlt in Shift then
    begin
      if Key = VK_UP then ECPZ.Text := IntToStr(StrToInt(ECPZ.Text) + intstep);
      if Key = VK_DOWN then ECPZ.Text := IntToStr(StrToInt(ECPZ.Text) - intstep);
    end
    else
    begin

      if Key = VK_LEFT then ECPY.Text := IntToStr(StrToInt(ECPY.Text) - intstep);
      if Key = VK_RIGHT then ECPY.Text := IntToStr(StrToInt(ECPY.Text) + intstep);
      if Key = VK_UP then ECPX.Text := IntToStr(StrToInt(ECPX.Text) - intstep);
      if Key = VK_DOWN then ECPX.Text := IntToStr(StrToInt(ECPX.Text) + intstep);
    end;
  end;

  if (Key = VK_LEFT) or (Key = VK_RIGHT) or (Key = VK_UP) or (Key = VK_DOWN) then
  begin
    FormCreate(Sender);
    DrawSet(Sender);
  end;

end;

procedure TForm1.FormMouseWheel(Sender: TObject; Shift: TShiftState;
  WheelDelta: Integer; MousePos: TPoint; var Handled: Boolean);
begin
  EZOOM.Position := EZOOM.Position - sign(WheelDelta);
  FormCreate(Sender);
  DrawSet(Sender);  
end;

procedure TForm1.FormShow(Sender: TObject);
begin
{  20080329: del  20080601 undel } CreateBaseGrid(Sender);
//  20080329: del CreateFctnParamGraph(Sender); ins following row:
  CreateFctnGraph(Sender);
  DrawSet(Sender);
end;

procedure TForm1.ERESEnter(Sender: TObject);
begin
  KeyPreview := false;
end;

procedure TForm1.ERESExit(Sender: TObject);
begin
  KeyPreview := true;
end;

end.