From 1f4577657e65d97dfd8cc121514534f0a45e0b50 Mon Sep 17 00:00:00 2001
From: KoroLion <korolion31@yandex.ru>
Date: Thu, 14 May 2020 18:17:36 +0300
Subject: [PATCH] Feature: better graphing by using gradient

---
 src/function_imaging.pas | 30 ++++++++++++++++++++++++------
 1 file changed, 24 insertions(+), 6 deletions(-)

diff --git a/src/function_imaging.pas b/src/function_imaging.pas
index 8bb1345..0f50513 100644
--- a/src/function_imaging.pas
+++ b/src/function_imaging.pas
@@ -35,7 +35,7 @@ begin
     args.width := strToInt(ParamStr(1));
     args.height := strToInt(ParamStr(2));
     args.f := ParamStr(3);
-    args.zoom := StrToFloat(ParamStr(4)) * 10;
+    args.zoom := StrToFloat(ParamStr(4));
     args.centerX := StrToFloat(ParamStr(5));
     args.centerY := StrToFloat(ParamStr(6));
     
@@ -71,11 +71,13 @@ var
   fParser: TFPExpressionParser;
   argX, argY: TFPExprIdentifierDef;
   x, y, intense: integer;
-  convX, convY, fRes: extended;
+  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];
@@ -88,7 +90,7 @@ begin
     
     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;
+        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
@@ -104,12 +106,28 @@ begin
                 pxData[x][y].set_color(255, 255, 255);
               end;
             end else begin
-              fRes := fParser.evaluate().resFloat;
+              fRes1 := fParser.evaluate().resFloat;
               
-              if (abs(fRes) > (1 / args.zoom)) then begin
+              // 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(fRes) / (1 / args.zoom));
+                intense := round(abs(fRes1) / (gradLen * pixelRadius));
                 pxData[x][y].set_color(intense, intense, intense);
               end;
             end;