Программа, выводящая график функции в декартовых координатах

На днях ребёнку в школе задали задание по графикам функций, при отсутствии под рукой готовых програм нацарапал своё приложение, причём приложение написано "двумя пальцами", т.е. без каких-либо украшательств, не очень красивым кодом и без комментариев - простая програмка, написаннная за 15 минут.

Вот исходники:

unit Main;

interface
 
uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;
 
type
  TForm1 = class(TForm)
    Panel1: TPanel;
    Button1: TButton;
    Edit1: TEdit;
    Label1: TLabel;
    Button2: TButton;
    Edit2: TEdit;
    Label2: TLabel;
    Button3: TButton;
    Edit3: TEdit;
    Label3: TLabel;
    Panel2: TPanel;
    procedure FormPaint(Sender: TObject);
    procedure Panel2MouseDown(Sender: TObject; Button: TMouseButton;
      Shift: TShiftState; X, Y: Integer);
    procedure Edit3KeyPress(Sender: TObject; var Key: Char);
    procedure Edit2KeyPress(Sender: TObject; var Key: Char);
    procedure Edit1KeyPress(Sender: TObject; var Key: Char);
    procedure Button3Click(Sender: TObject);
    procedure Button2Click(Sender: TObject);
    procedure Button1Click(Sender: TObject);
  private
    procedure DrawFunction(FormulaText:string; Cl:TColor);
    function GetValue(FormulaText:string; x: real): real;
    procedure SetupAxes;
    { Private declarations }
  public
    { Public declarations }
  end;
 
var
  Form1: TForm1;
 
implementation
 
uses math, parsing;
{$R *.dfm}
 
Function TForm1.GetValue(FormulaText:string; x:real):real;
begin
  Result:=GetFormulaValue(StringReplace(FormulaText, 'x', floattostr(x),[rfReplaceAll, rfIgnoreCase]));
end;
 
procedure TForm1.Panel2MouseDown(Sender: TObject; Button: TMouseButton;
  Shift: TShiftState; X, Y: Integer);
begin
  ReleaseCapture;
  Panel1.perform(WM_SysCommand, $F012, 0);
end;
 
procedure TForm1.SetupAxes;
  var  point:TPoint;
       i:integer;
begin
  {Draw axis X}
  Canvas.Pen.Width:=2;
  Canvas.Pen.Color:=clBlue;
  Point.X:=0;
  Point.Y:=(height div 2);
  canvas.PenPos:=Point;
  Canvas.LineTo(width, height div 2);
 
  {Draw axis Y}
  Point.X:=width div 2;
  Point.Y:=0;
  canvas.PenPos:=Point;
  Canvas.LineTo(width div 2, height);
 
  for I := 1 to (width div 40) do
    begin
      Canvas.Pen.Width:=1;
      Canvas.Pen.Style:= psDot;
      Point.X:=width div 2 +i*20;
      Point.Y:=0;
      canvas.PenPos:=Point;
      Canvas.LineTo(width div 2 +i*20, height);
    end;
  for I := -1 downto (width div 40)*(-1) do
    begin
      Canvas.Pen.Width:=1;
      Canvas.Pen.Style:= psDot;
      Point.X:=width div 2 +i*20;
      Point.Y:=0;
      canvas.PenPos:=Point;
      Canvas.LineTo(width div 2 +i*20, height);
    end;
 
  for I := 1 to (height div 40) do
    begin
      Canvas.Pen.Width:=1;
      Canvas.Pen.Style:= psDot;
      Point.Y:=height div 2 +i*20;
      Point.X:=0;
      canvas.PenPos:=Point;
      Canvas.LineTo(width, height div 2 +i*20);
    end;
 
  for I := -1 downto (height div 40)*(-1) do
    begin
      Canvas.Pen.Width:=1;
      Canvas.Pen.Style:= psDot;
      Point.Y:=height div 2 +i*20;
      Point.X:=0;
      canvas.PenPos:=Point;
      Canvas.LineTo(width, height div 2 +i*20);
    end;
end;
 
procedure TForm1.Button1Click(Sender: TObject);
begin
  Invalidate;
end;
 
procedure TForm1.Button2Click(Sender: TObject);
begin
  Invalidate;
 
end;
 
procedure TForm1.Button3Click(Sender: TObject);
begin
  Invalidate;
 
end;
 
Procedure TForm1.DrawFunction(FormulaText:string; Cl:TColor);
  var i:integer;
      j:real;
      P:real;
      x1, x2, x0:real;
      W:integer;
      k:real;
      point:TPoint;
      error:boolean;
      prev, value:integer;
 
begin
  if FormulaText='' then exit;
 
  SetupAxes;
 
  Canvas.Pen.Color:=cl;
  Canvas.Pen.Style:= psSolid;
  Canvas.Pen.Width:=2;
 
  {setup first point}
  try
  p:=GetValue(FormulaText, width div -40);
  Point.X:=0;
  Point.Y:=round(p*20);
  canvas.PenPos:=Point;
  prev:=Point.Y;
  error:=false;
  except
  error:=true;
  end;
 
  for I := 0 to width do
    try
      if error then
        begin
          Point.X:=i;
          Point.Y:=(height div 2) - round(GetValue(FormulaText,(i-width/2)/20)*20);
          prev:=Point.Y;
          Canvas.PenPos:=Point;
        end
      else
        begin
          value:=(height div 2) - round(GetValue(FormulaText,(i-width/2)/20)*20);
          if abs(value)<height then
            Canvas.LineTo(i,value)
          else
            raise exception.Create('');  
        end;
      error:=false;
    except
      error:=true;
    end;
end;
 
 
procedure TForm1.Edit1KeyPress(Sender: TObject; var Key: Char);
begin
 
  if key=#13 then Invalidate;
 
end;
 
procedure TForm1.Edit2KeyPress(Sender: TObject; var Key: Char);
begin
  if key=#13 then Invalidate;
 
end;
 
procedure TForm1.Edit3KeyPress(Sender: TObject; var Key: Char);
begin
  if key=#13 then Invalidate;
 
end;
 
procedure TForm1.FormPaint(Sender: TObject);
begin
  DrawFunction(Edit1.Text, clRed);
  DrawFunction(Edit2.Text, clGreen);
  DrawFunction(Edit3.Text, clMaroon);
end;
 
end.

object Form1: TForm1
  Left = 357
  Top = 465
  BorderIcons = [biSystemMenu, biMinimize]
  BorderStyle = bsSingle
  Caption = 'Formula Grapher (c) Vit, 2006'
  ClientHeight = 494
  ClientWidth = 771
  Color = clBtnFace
  Font.Charset = DEFAULT_CHARSET
  Font.Color = clWindowText
  Font.Height = -11
  Font.Name = 'Tahoma'
  Font.Style = []
  OldCreateOrder = False
  Position = poScreenCenter
  OnPaint = FormPaint
  PixelsPerInch = 96
  TextHeight = 13
  object Panel1: TPanel
    Left = 48
    Top = 8
    Width = 281
    Height = 121
    TabOrder = 0
    object Label1: TLabel
      Left = 9
      Top = 27
      Width = 16
      Height = 16
      Caption = 'Y='
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clWindowText
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
    end
    object Label2: TLabel
      Left = 9
      Top = 58
      Width = 16
      Height = 16
      Caption = 'Y='
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clWindowText
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
    end
    object Label3: TLabel
      Left = 9
      Top = 89
      Width = 16
      Height = 16
      Caption = 'Y='
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clWindowText
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
    end
    object Button1: TButton
      Left = 232
      Top = 23
      Width = 41
      Height = 25
      Caption = 'Draw'
      TabOrder = 1
      OnClick = Button1Click
    end
    object Edit1: TEdit
      Left = 31
      Top = 24
      Width = 195
      Height = 24
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clRed
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
      TabOrder = 0
      OnKeyPress = Edit1KeyPress
    end
    object Button2: TButton
      Left = 232
      Top = 54
      Width = 41
      Height = 25
      Caption = 'Draw'
      TabOrder = 3
      OnClick = Button2Click
    end
    object Edit2: TEdit
      Left = 31
      Top = 55
      Width = 195
      Height = 24
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clGreen
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
      TabOrder = 2
      OnKeyPress = Edit2KeyPress
    end
    object Button3: TButton
      Left = 232
      Top = 85
      Width = 41
      Height = 25
      Caption = 'Draw'
      TabOrder = 5
      OnClick = Button3Click
    end
    object Edit3: TEdit
      Left = 31
      Top = 86
      Width = 195
      Height = 24
      Font.Charset = DEFAULT_CHARSET
      Font.Color = clMaroon
      Font.Height = -11
      Font.Name = 'Fixedsys'
      Font.Style = []
      ParentFont = False
      TabOrder = 4
      OnKeyPress = Edit3KeyPress
    end
    object Panel2: TPanel
      Left = 1
      Top = 1
      Width = 279
      Height = 16
      Align = alTop
      Color = clNavy
      TabOrder = 6
      OnMouseDown = Panel2MouseDown
    end
  end
end

Для разбора математических выражений использовался модуль Parsing из RxLib:

{*******************************************************}
{                                                       }
{         Delphi VCL Extensions (RX)                    }
{                                                       }
{         Copyright (c) 1995, 1996 AO ROSNO             }
{         Copyright (c) 1997, 1998 Master-Bank          }
{                                                       }
{*******************************************************}
 
unit Parsing;
 
interface
 
{ $I RX.INC}
 
uses SysUtils, Classes;
 
type
  TParserFunc = (pfArcTan, pfCos, pfSin, pfTan, pfAbs, pfExp, pfLn, pfLog,
    pfSqrt, pfSqr, pfInt, pfFrac, pfTrunc, pfRound, pfArcSin, pfArcCos,
    pfSign, pfNot);
  ERxParserError = class(Exception);
{$IFDEF WIN32}
  TUserFunction = function(Value: Extended): Extended;
{$ELSE}
  TUserFunction = Pointer;
{$ENDIF}
 
  TRxMathParser = class(TObject)
  private
    FCurPos: Cardinal;
    FParseText: string;
    function GetChar: Char;
    procedure NextChar;
    function GetNumber(var AValue: Extended): Boolean;
    function GetConst(var AValue: Extended): Boolean;
    function GetFunction(var AValue: TParserFunc): Boolean;
    function GetUserFunction(var Index: Integer): Boolean;
    function Term: Extended;
    function SubTerm: Extended;
    function Calculate: Extended;
  public
    function Exec(const AFormula: string): Extended;
    class procedure RegisterUserFunction(const Name: string; Proc: TUserFunction);
    class procedure UnregisterUserFunction(const Name: string);
  end;
 
function GetFormulaValue(const Formula: string): Extended;
 
{$IFNDEF WIN32}
function Power(Base, Exponent: Extended): Extended;
{$ENDIF}
 
implementation
 
//uses RxTConst;
uses dialogs;
 
const
  SpecialChars = [#0..' ', '+', '-', '/', '*', ')', '^'];
 
  FuncNames: array[TParserFunc] of PChar =
    ('ARCTAN', 'COS', 'SIN', 'TAN', 'ABS', 'EXP', 'LN', 'LOG',
    'SQRT', 'SQR', 'INT', 'FRAC', 'TRUNC', 'ROUND', 'ARCSIN', 'ARCCOS',
    'SIGN', 'NOT');
 
{ Parser errors }
 
procedure InvalidCondition(Str: String);
begin
  raise Exception.Create(Str);
end;
 
{ IntPower and Power functions are copied from Borland's MATH.PAS unit }
 
function IntPower(Base: Extended; Exponent: Integer): Extended;
{$IFDEF WIN32}
asm
        mov     ecx, eax
        cdq
        fld1                      { Result := 1 }
        xor     eax, edx
        sub     eax, edx          { eax := Abs(Exponent) }
        jz      @@3
        fld     Base
        jmp     @@2
@@1:    fmul    ST, ST            { X := Base * Base }
@@2:    shr     eax,1
        jnc     @@1
        fmul    ST(1),ST          { Result := Result * X }
        jnz     @@1
        fstp    st                { pop X from FPU stack }
        cmp     ecx, 0
        jge     @@3
        fld1
        fdivrp                    { Result := 1 / Result }
@@3:
        fwait
end;
{$ELSE}
var
  Y: Longint;
begin
  Y := Abs(Exponent);
  Result := 1.0;
  while Y > 0 do begin
    while not Odd(Y) do begin
      Y := Y shr 1;
      Base := Base * Base;
    end;
    Dec(Y);
    Result := Result * Base;
  end;
  if Exponent < 0 then Result := 1.0 / Result;
end;
{$ENDIF WIN32}
 
function Power(Base, Exponent: Extended): Extended;
begin
  if Exponent = 0.0 then Result := 1.0
  else if (Base = 0.0) and (Exponent > 0.0) then Result := 0.0
  else if (Frac(Exponent) = 0.0) and (Abs(Exponent) <= MaxInt) then
    Result := IntPower(Base, Trunc(Exponent))
  else Result := Exp(Exponent * Ln(Base))
end;
 
{ User defined functions }
 
type
{$IFDEF WIN32}
  TFarUserFunction = TUserFunction;
{$ELSE}
  TFarUserFunction = function(Value: Extended): Extended;
{$ENDIF}
 
var
  UserFuncList: TStrings;
 
function GetUserFuncList: TStrings;
begin
  if not Assigned(UserFuncList) then begin
    UserFuncList := TStringList.Create;
    with TStringList(UserFuncList) do begin
      Sorted := True;
      Duplicates := dupIgnore;
    end;
  end;
  Result := UserFuncList;
end;
 
procedure FreeUserFunc; far;
begin
  UserFuncList.Free;
  UserFuncList := nil;
end;
 
{ Parsing routines }
 
function GetFormulaValue(const Formula: string): Extended;
begin
  with TRxMathParser.Create do
  try
    Result := Exec(Formula);
  finally
    Free;
  end;
end;
 
{ TRxMathParser }
 
function TRxMathParser.GetChar: Char;
begin
  Result := FParseText[FCurPos];
end;
 
procedure TRxMathParser.NextChar;
begin
  Inc(FCurPos);
end;
 
function TRxMathParser.GetNumber(var AValue: Extended): Boolean;
var
  C: Char;
  SavePos: Cardinal;
  Code: Integer;
  IsHex: Boolean;
  TmpStr: string;
begin
  Result := False;
  C := GetChar;
  SavePos := FCurPos;
  TmpStr := '';
  IsHex := False;
  if C = '$' then begin
    TmpStr := C;
    NextChar;
    C := GetChar;
    while C in ['0'..'9', 'A'..'F', 'a'..'f'] do begin
      TmpStr := TmpStr + C;
      NextChar;
      C := GetChar;
    end;
    IsHex := True;
    Result := (Length(TmpStr) > 1) and (Length(TmpStr) <= 9);
  end
  else if C in ['+', '-', '0'..'9', '.', DecimalSeparator] then begin
    if (C in ['.', DecimalSeparator]) then TmpStr := '0' + '.'
    else TmpStr := C;
    NextChar;
    C := GetChar;
    if (Length(TmpStr) = 1) and (TmpStr[1] in ['+', '-']) and
      (C in ['.', DecimalSeparator]) then TmpStr := TmpStr + '0';
    while C in ['0'..'9', '.', 'E', 'e', DecimalSeparator] do begin
      if C = DecimalSeparator then TmpStr := TmpStr + '.'
      else TmpStr := TmpStr + C;
      if (C = 'E') then begin
        if (Length(TmpStr) > 1) and (TmpStr[Length(TmpStr) - 1] = '.') then
          Insert('0', TmpStr, Length(TmpStr));
        NextChar;
        C := GetChar;
        if (C in ['+', '-']) then begin
          TmpStr := TmpStr + C;
          NextChar;
        end;
      end
      else NextChar;
      C := GetChar;
    end;
    if (TmpStr[Length(TmpStr)] = '.') and (Pos('E', TmpStr) = 0) then
      TmpStr := TmpStr + '0';
    Val(TmpStr, AValue, Code);
    Result := (Code = 0);
  end;
  Result := Result and (FParseText[FCurPos] in SpecialChars);
  if Result then begin
    if IsHex then AValue := StrToInt(TmpStr)
    { else AValue := StrToFloat(TmpStr) };
  end
  else begin
    AValue := 0;
    FCurPos := SavePos;
  end;
end;
 
function TRxMathParser.GetConst(var AValue: Extended): Boolean;
begin
  Result := False;
  case FParseText[FCurPos] of
    'E':
      if FParseText[FCurPos + 1] in SpecialChars then
      begin
        AValue := Exp(1);
        Inc(FCurPos);
        Result := True;
      end;
    'P':
      if (FParseText[FCurPos + 1] = 'I') and
        (FParseText[FCurPos + 2] in SpecialChars) then
      begin
        AValue := Pi;
        Inc(FCurPos, 2);
        Result := True;
      end;
  end
end;
 
function TRxMathParser.GetUserFunction(var Index: Integer): Boolean;
var
  TmpStr: string;
  I: Integer;
begin
  Result := False;
  if (FParseText[FCurPos] in ['A'..'Z', 'a'..'z', '_']) and
    Assigned(UserFuncList) then
  begin
    with UserFuncList do
      for I := 0 to Count - 1 do begin
        TmpStr := Copy(FParseText, FCurPos, Length(Strings[I]));
        if (CompareText(TmpStr, Strings[I]) = 0) and
          (Objects[I] <> nil) then
        begin
          if FParseText[FCurPos + Cardinal(Length(TmpStr))] = '(' then
          begin
            Result := True;
            Inc(FCurPos, Length(TmpStr));
            Index := I;
            Exit;
          end;
        end;
      end;
  end;
  Index := -1;
end;
 
function TRxMathParser.GetFunction(var AValue: TParserFunc): Boolean;
var
  I: TParserFunc;
  TmpStr: string;
begin
  Result := False;
  AValue := Low(TParserFunc);
  if FParseText[FCurPos] in ['A'..'Z', 'a'..'z', '_'] then begin
    for I := Low(TParserFunc) to High(TParserFunc) do begin
      TmpStr := Copy(FParseText, FCurPos, StrLen(FuncNames[I]));
      if CompareText(TmpStr, StrPas(FuncNames[I])) = 0 then begin
        AValue := I;
        if FParseText[FCurPos + Cardinal(Length(TmpStr))] = '(' then begin
          Result := True;
          Inc(FCurPos, Length(TmpStr));
          Break;
        end;
      end;
    end;
  end;
end;
 
function TRxMathParser.Term: Extended;
var
  Value: Extended;
  NoFunc: TParserFunc;
  UserFunc: Integer;
  Func: Pointer;
begin
  if FParseText[FCurPos] = '(' then begin
    Inc(FCurPos);
    Value := Calculate;
    if FParseText[FCurPos] <> ')' then InvalidCondition('SParseNotCramp');
    Inc(FCurPos);
  end
  else begin
    if not GetNumber(Value) then
      if not GetConst(Value) then
        if GetUserFunction(UserFunc) then begin
          Inc(FCurPos);
          Func := UserFuncList.Objects[UserFunc];
          Value := TFarUserFunction(Func)(Calculate);
          if FParseText[FCurPos] <> ')' then InvalidCondition('SParseNotCramp');
          Inc(FCurPos);
        end
        else if GetFunction(NoFunc) then begin
          Inc(FCurPos);
          Value := Calculate;
          try
            case NoFunc of
              pfArcTan: Value := ArcTan(Value);
              pfCos: Value := Cos(Value);
              pfSin: Value := Sin(Value);
              pfTan:
                if Cos(Value) = 0 then InvalidCondition('SParseDivideByZero')
                else Value := Sin(Value) / Cos(Value);
              pfAbs: Value := Abs(Value);
              pfExp: Value := Exp(Value);
              pfLn:
                if Value <= 0 then InvalidCondition('SParseLogError')
                else Value := Ln(Value);
              pfLog:
                if Value <= 0 then InvalidCondition('SParseLogError')
                else Value := Ln(Value) / Ln(10);
              pfSqrt:
                if Value < 0 then InvalidCondition('SParseSqrError')
                else Value := Sqrt(Value);
              pfSqr: Value := Sqr(Value);
              pfInt: Value := Round(Value);
              pfFrac: Value := Frac(Value);
              pfTrunc: Value := Trunc(Value);
              pfRound: Value := Round(Value);
              pfArcSin:
                if Value = 1 then Value := Pi / 2
                else Value := ArcTan(Value / Sqrt(1 - Sqr(Value)));
              pfArcCos:
                if Value = 1 then Value := 0
                else Value := Pi / 2 - ArcTan(Value / Sqrt(1 - Sqr(Value)));
              pfSign:
                if Value > 0 then Value := 1
                else if Value < 0 then Value := -1;
              pfNot: Value := not Trunc(Value);
            end;
          except
            on E: ERxParserError do raise
            else InvalidCondition('SParseInvalidFloatOperation');
          end;
          if FParseText[FCurPos] <> ')' then InvalidCondition('SParseNotCramp');
          Inc(FCurPos);
        end
        else InvalidCondition('SParseSyntaxError');
  end;
  Result := Value;
end;
 
function TRxMathParser.SubTerm: Extended;
var
  Value: Extended;
begin
  Value := Term;
  while FParseText[FCurPos] in ['*', '^', '/'] do begin
    Inc(FCurPos);
    if FParseText[FCurPos - 1] = '*' then
      Value := Value * Term
    else if FParseText[FCurPos - 1] = '^' then
      Value := Power(Value, Term)
    else if FParseText[FCurPos - 1] = '/' then
      try
        Value := Value / Term;
      except
        InvalidCondition('SParseDivideByZero');
      end;
  end;
  Result := Value;
end;
 
function TRxMathParser.Calculate: Extended;
var
  Value: Extended;
begin
  Value := SubTerm;
  while FParseText[FCurPos] in ['+', '-'] do begin
    Inc(FCurPos);
    if FParseText[FCurPos - 1] = '+' then Value := Value + SubTerm
    else Value := Value - SubTerm;
  end;
  if not (FParseText[FCurPos] in [#0, ')', '>', '<', '=', ',']) then
    InvalidCondition('SParseSyntaxError');
  Result := Value;
end;
 
function TRxMathParser.Exec(const AFormula: string): Extended;
var
  I, J: Integer;
begin
  J := 0;
  Result := 0;
  FParseText := '';
  for I := 1 to Length(AFormula) do begin
    case AFormula[I] of
      '(': Inc(J);
      ')': Dec(J);
    end;
    if AFormula[I] > ' ' then FParseText := FParseText + UpCase(AFormula[I]);
  end;
  if J = 0 then begin
    FCurPos := 1;
    FParseText := FParseText + #0;
    if (FParseText[1] in ['-', '+']) then FParseText := '0' + FParseText;
    Result := Calculate;
  end
  else InvalidCondition('SParseNotCramp');
end;
 
class procedure TRxMathParser.RegisterUserFunction(const Name: string;
  Proc: TUserFunction);
var
  I: Integer;
begin
  if (Length(Name) > 0) and (Name[1] in ['A'..'Z', 'a'..'z', '_']) then
  begin
    if not Assigned(Proc) then UnregisterUserFunction(Name)
    else begin
      with GetUserFuncList do begin
        I := IndexOf(Name);
        if I < 0 then I := Add(Name);
{$IFDEF WIN32}
        Objects[I] := @Proc;
{$ELSE}
        Objects[I] := Proc;
{$ENDIF}
      end;
    end;
  end
  else InvalidCondition('SParseSyntaxError');
end;
 
class procedure TRxMathParser.UnregisterUserFunction(const Name: string);
var
  I: Integer;
begin
  if Assigned(UserFuncList) then
    with UserFuncList do begin
      I := IndexOf(Name);
      if I >= 0 then Delete(I);
      if Count = 0 then FreeUserFunc;
    end;
end;
 
initialization
  UserFuncList := nil;
{$IFDEF WIN32}
finalization
  FreeUserFunc;  
{$ELSE}
  AddExitProc(FreeUserFunc);
{$ENDIF}
end.

Автор: Vit