From 7b9621f2346a3fcaa63696367e5521c9f21668d4 Mon Sep 17 00:00:00 2001
From: wp_xyz <wp_xxyyzzz@gmx.net>
Date: Fri, 11 Jul 2025 00:42:00 +0200
Subject: [PATCH] LCL/Graphics: Fix win32 widgetset Arc method overload with
 angle arguments to behave like in all other widgetsets. Issue #41748.

---
 components/lazutils/graphmath.pp     | 38 ++++++++++++++++++++++++++++
 lcl/interfaces/win32/win32winapi.inc |  6 ++++-
 2 files changed, 43 insertions(+), 1 deletion(-)

diff --git a/components/lazutils/graphmath.pp b/components/lazutils/graphmath.pp
index bf7ff79c2a..bb20facf8d 100644
--- a/components/lazutils/graphmath.pp
+++ b/components/lazutils/graphmath.pp
@@ -72,6 +72,9 @@ function Distance(const Pt, SP, EP : TFloatPoint) : Extended; overload;
 
 function EccentricAngle(const PT : TPoint; const Rect : TRect) : Extended;
 
+procedure EllipseParams2Coords(X, Y, Width, Height: Integer;
+  Angle1, Angle2: Integer; var SX, SY, EX, EY: Integer);
+
 function EllipseRadialLength(const Rect : TRect; EccentricAngle : Extended) : Longint;
 function EllipsePolygon(const aRect: TRect): TPointArray;
 
@@ -340,6 +343,41 @@ begin
   EY := EP.Y;
 end;
 
+{-------------------------------------------------------------------------------
+  Method:   EllipseParams2Coords
+  Params:   x, y, width, height, angle1, angle2, sx, sy, ex, ey
+  Returns:  Nothing
+
+  In parametric form, the ellipse equation for every point (x, y) along the
+  perimeter is
+    x = a * cos (t),  y = b * sin(t)
+  where a and b are the major and minor half-axes of the ellipse, and t is
+  an "angle" parameter ranging between 0 and 2*pi.
+
+  This procedure used by the Windows Arc method calculates the start and end
+  points, (SX, SY) and (EX, EY), respectively, of an arc beginning at
+  parameter t = angle1 and ending at parameter t = angle1 + angle2.
+  But note that angle1 and angle2 are expressed as multiples of 1/16 degree.
+  Positive values of the angles are in counter-clockwise, negative values in
+  clockwise direction.
+  Zero degrees is at 3'o clock position.
+-------------------------------------------------------------------------------}
+procedure EllipseParams2Coords(X, Y, Width, Height: Integer;
+  Angle1, Angle2: Integer; var SX, SY, EX, EY: Integer);
+var
+  sinAngle1, cosAngle1, sinAngle2, cosAngle2: Extended;
+  a, b: Integer;
+begin
+  SinCos(DegToRad(Angle1/16), sinAngle1, cosAngle1);
+  SinCos(DegToRad((Angle1 + Angle2)/16), sinAngle2, cosAngle2);
+  a := Width div 2;
+  b := Height div 2;
+  SX := X + a + round(cosAngle1 * a);
+  SY := Y + b - round(sinAngle1 * b);
+  EX := X + a + round(cosAngle2 * a);
+  EY := Y + b - round(sinAngle2 * b);
+end;
+
 {------------------------------------------------------------------------------
   Method:   Arc2Bezier
   Params:   X, Y, Width, Height, Angle1, Angle2, Rotation, Points, Count
diff --git a/lcl/interfaces/win32/win32winapi.inc b/lcl/interfaces/win32/win32winapi.inc
index da900a0c9e..a7ef01846f 100644
--- a/lcl/interfaces/win32/win32winapi.inc
+++ b/lcl/interfaces/win32/win32winapi.inc
@@ -46,6 +46,10 @@
   circle equals 5760 (16*360). Positive values of Angle and AngleLength mean
   counter-clockwise while negative values mean clockwise direction.
   Zero degrees is at the 3'o clock position.
+
+  But note that due to the elliptic eccetricity these angles are not the
+  same as "real" polar angles, but only correspond to the parameter t in the
+  ellipse equations:  x = a * cos(t);  y = b * sin(t)
  ------------------------------------------------------------------------------}
 function TWin32WidgetSet.Arc(DC: HDC; Left, Top, Right, Bottom, Angle16Deg, Angle16DegLength: Integer): Boolean;
 var
@@ -58,7 +62,7 @@ begin
   if Angle16DegLength < 0 then OldArcDirection := Windows.SetArcDirection(DC, AD_CLOCKWISE)
   else OldArcDirection := Windows.SetArcDirection(DC, AD_COUNTERCLOCKWISE);
 
-  Angles2Coords(Left, Top, Right - Left, Bottom - Top, Angle16Deg, Angle16DegLength, SX, SY, EX, EY);
+  EllipseParam2Coords(Left, Top, Right - Left, Bottom - Top, Angle16Deg, Angle16DegLength, SX, SY, EX, EY);
   Result := Boolean(Windows.Arc(DC, Left, Top, Right, Bottom, SX, SY, EX, EY));
   // Revert the arc direction to the previous value
   Windows.SetArcDirection(DC, OldArcDirection);