FunctionImagingInPascal/src/function_imaging.pas

{$MODE OBJFPC}

uses fpexprpars, sysutils, 
     BMPImage, utils;

type
  TArgs = record
    width: longint;
    height: longint;
    f: string;
    zoom: extended;
    centerX: extended;
    centerY: extended;
    outPath: string;
  end;
  
procedure setDefaultArgs(var args: TArgs);
begin
  with args do begin
    width := 512;
    height := 512;
    f := 'sin(x) - y';
    zoom := 10;
    centerX := 0;
    centerY := 0;
    outPath := './function_images';
  end;
end;

procedure getArgs(var args: TArgs);
var
  param: string;
begin
  try
    args.width := strToInt(ParamStr(1));
    args.height := strToInt(ParamStr(2));
    args.f := ParamStr(3);
    args.zoom := StrToFloat(ParamStr(4));
    args.centerX := StrToFloat(ParamStr(5));
    args.centerY := StrToFloat(ParamStr(6));
    
    param := ParamStr(7);
    if (length(param) > 0) then begin
      args.outPath := param;
    end;
  except
  end;
end;

function getFilename(args: TArgs): string;
var
  fname: string;
  fn: string;
begin
  fname := '{f}_(z={z},cx={cx},cy={cy},WxH={w}x{h}).bmp';
  
  fn := stringReplace(args.f, ' ', '', [rfReplaceAll]);
  fname := StringReplace(fname, '{f}', fn, []);
  fname := StringReplace(fname, '{z}', floatToStr(args.zoom), []);
  fname := StringReplace(fname, '{cx}', floatToStr(args.centerX), []);
  fname := StringReplace(fname, '{cy}', floatToStr(args.centerY), []);
  fname := StringReplace(fname, '{w}', intToStr(args.width), []);
  fname := StringReplace(fname, '{h}', intToStr(args.height), []);
  
  getFilename := fname;
end;

function getPxData(args: TArgs): TPxData;
var
  pxData: TPxData;
  fParser: TFPExpressionParser;
  argX, argY: TFPExprIdentifierDef;
  x, y, intense: integer;
  convX, convY, fRes1, fRes2, pixelRadius: extended;
  dfDx, dfDy, delta, gradLen: extended;
  ineq: boolean;
begin
  setLength(pxData, args.width, args.height);
  fParser := TFPExpressionParser.create(nil);
  pixelRadius := 1 / args.zoom;
  
  try
    fParser.builtIns := [bcMath];
    argX := fParser.identifiers.addFloatVariable('x', 0.0);
    argY := fParser.identifiers.addFloatVariable('y', 0.0);
    //fParser.expression := 'sin(x*x*x * y*y) - cos(x*x * y*y*y)';
    fParser.expression := args.f;
    
    ineq := (pos('>', fParser.expression) <> 0) or (pos('>=', fParser.expression) <> 0) or (pos('<', fParser.expression) <> 0) or (pos('<=', fParser.expression) <> 0); 
    
    for y := 0 to args.height - 1 do begin
      for x := 0 to args.width - 1 do begin
        convX := (x - args.width / 2) / args.zoom + args.centerX;
        convY := -(y - args.height / 2) / args.zoom + args.centerY;
        
        if (abs(convX) < (1 / args.zoom)) or (abs(convY) < (1 / args.zoom)) then begin
          pxData[x][y].set_color(0, 255, 0);
        end else begin
          try
            argX.asFloat := convX;
            argY.asFloat := convY;
            if (ineq) then begin
              if (fParser.evaluate().resBoolean) then begin
                pxData[x][y].set_color(0, 0, 0);
              end else begin
                pxData[x][y].set_color(255, 255, 255);
              end;
            end else begin
              fParser.expression := stringReplace(fParser.expression, '=', '-', []);
              fRes1 := fParser.evaluate().resFloat;
              
              // finding derivative of a function at this point (numeric)
              delta := 0.00001;
              
              argX.asFloat := convX + delta;
              argY.asFloat := convY;
              fRes2 := fParser.evaluate().resFloat;
              dfDx := (fRes2 - fRes1) / delta;
              
              argX.asFloat := convX;
              argY.asFloat := convY + delta;
              fRes2 := fParser.evaluate().resFloat;
              dfDy := (fRes2 - fRes1) / delta;
              
              // calculating length of a gradient at this point
              gradLen := sqrt(sqr(dfDx) + sqr(dfDy));
              
              if (abs(fRes1) > (gradLen * pixelRadius)) then begin
                pxData[x][y].set_color(255, 255, 255);
              end else begin
                intense := round(abs(fRes1) / (gradLen * pixelRadius));
                pxData[x][y].set_color(intense, intense, intense);
              end;
            end;
          except
            pxData[x][y].set_color(255, 255, 255);
          end;
        end;
      end;
    end;
  finally
    fParser.free();
  end;
  
  getPxData := pxData;
end;

var
  args: TArgs;
  outPath: string;
  filename: string;
  
  img: TBMPImage;
  color: TColor;
  pxData: TPxData;
begin
  setDefaultArgs(args);
  getArgs(args);
  
  pxData := getPxData(args);
  
  color.set_color(255, 255, 255);
  img.init(args.width, args.height, color);
  img.set_pixel_data(pxData);
  
  filename := getFilename(args);
  outPath := args.outPath + '/' + filename;
  img.save(outPath);
  
  writeln('Image generated and saved at ' + outPath);
end.