Refinements in Arc to Polygon transform: slightly better shapes of arc ends.

Note also the transform is still not good: the same parameters are applied
to convert inner arc, outer arc and middle arc of a thick arc to segments.
But these parameters depend on arc radius (or circle radius) value.

libs/kimath/include/geometry/shape_arc.h

@@ -2,7 +2,7 @@
  * This program source code file is part of KiCad, a free EDA CAD application.
  *
  * Copyright (C) 2018 CERN
- * Copyright (C) 2019-2020 KiCad Developers, see AUTHORS.txt for contributors.
+ * Copyright (C) 2019-2021 KiCad Developers, see AUTHORS.txt for contributors.
  * @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
  *
  * This program is free software; you can redistribute it and/or
@@ -61,7 +61,7 @@ public:
      */
     SHAPE_ARC( const VECTOR2I& aArcStart, const VECTOR2I& aArcMid, const VECTOR2I& aArcEnd,
                int aWidth );
-   
+
     /**
      * SHAPE_ARC ctor.
      * Builds a SHAPE_ARC which is tangent to two segments and a given radius
@@ -144,8 +144,19 @@ public:
         return SEG( m_start, m_end );
     }
 
+    /**
+     * @return the central angle of the arc shape in degrees, normalized between 0.0, 360.0 deg
+     */
     double  GetCentralAngle() const;
+
+    /**
+     * @return the start angle of the arc shape in degrees, normalized between 0.0, 360.0 deg
+     */
     double  GetStartAngle() const;
+
+    /**
+     * @return the end angle of the arc shape in degrees, normalized between 0.0, 360.0 deg
+     */
     double  GetEndAngle() const;
 
     /**

libs/kimath/src/convert_basic_shapes_to_polygon.cpp

@@ -43,6 +43,14 @@ void TransformCircleToPolygon( SHAPE_LINE_CHAIN& aCornerBuffer, wxPoint aCenter,
 {
     wxPoint corner_position;
     int     numSegs = GetArcToSegmentCount( aRadius, aError, 360.0 );
+
+    // The shape will be built with a even number of segs. Reason: the horizontal
+    // diameter begins and ends to points on the actual circle, or circle
+    // expanded by aError if aErrorLoc == ERROR_OUTSIDE.
+    // This is used by Arc to Polygon shape convert.
+    if( numSegs & 1 )
+        numSegs++;
+
     int     delta = 3600 / numSegs;           // rotate angle in 0.1 degree
     int     radius = aRadius;
 
@@ -67,6 +75,14 @@ void TransformCircleToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aCenter, i
 {
     wxPoint corner_position;
     int     numSegs = GetArcToSegmentCount( aRadius, aError, 360.0 );
+
+    // The shape will be built with a even number of segs. Reason: the horizontal
+    // diameter begins and ends to points on the actual circle, or circle
+    // expanded by aError if aErrorLoc == ERROR_OUTSIDE.
+    // This is used by Arc to Polygon shape convert.
+    if( numSegs & 1 )
+        numSegs++;
+
     int     delta = 3600 / numSegs;           // rotate angle in 0.1 degree
     int     radius = aRadius;
 
@@ -367,6 +383,21 @@ void TransformArcToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aStart, wxPoi
             wxPoint( arcSpine.GetPoint( -1 ).x, arcSpine.GetPoint( -1 ).y ), radial_offset, aError,
             aErrorLoc );
 
+    // The circle polygon is built with a even number of segments, so the
+    // horizontal diameter has 2 corners on the biggest diameter
+    // Rotate these 2 corners to match the start and ens points of inner and outer
+    // end points of the arc appoximation outlines, build below.
+    // The final shape is much better.
+    double arc_angle_end_deg = arc.GetStartAngle();
+
+    if( arc_angle_end_deg != 0 & arc_angle_end_deg != 180.0 )
+        polyshape.Outline(0).Rotate( arc_angle_end_deg * M_PI/180.0, arcSpine.GetPoint( 0 ) );
+
+    arc_angle_end_deg = arc.GetEndAngle();
+
+    if( arc_angle_end_deg != 0 & arc_angle_end_deg != 180.0 )
+        polyshape.Outline(1).Rotate( arc_angle_end_deg * M_PI/180.0, arcSpine.GetPoint( -1 ) );
+
     if( aErrorLoc == ERROR_OUTSIDE )
         radial_offset += aError;
     else