Fix incorrect calculation in TransformCircleToPolygon(), only noticeable

when the allowed aError is (unusually) large.

libs/kimath/include/geometry/geometry_utils.h

@@ -55,11 +55,14 @@ enum ERROR_LOC { ERROR_OUTSIDE, ERROR_INSIDE };
 int GetArcToSegmentCount( int aRadius, int aErrorMax, double aArcAngleDegree );
 
 /**
- * @return the max error when approximating a circle by segments
- * @param aRadius is the radius of the circle
+ * @return the radius diffence of the circle defined by segments inside the circle
+ * and the radius of the circle tangent to the middle of segments (defined by
+ * segments outside this circle)
+ * @param aInnerCircleRadius is the radius of the circle tangent to the middle
+ * of segments
  * @param aSegCount is the seg count to approximate the circle
  */
-int GetCircleToSegmentError( int aRadius, int aSegCount );
+int CircleToEndSegmentDeltaRadius( int aInnerCircleRadius, int aSegCount );
 
 /**
  * When creating polygons to create a clearance polygonal area, the polygon must

libs/kimath/src/convert_basic_shapes_to_polygon.cpp

@@ -56,8 +56,11 @@ void TransformCircleToPolygon( SHAPE_LINE_CHAIN& aCornerBuffer, wxPoint aCenter,
 
     if( aErrorLoc == ERROR_OUTSIDE )
     {
-        int actual_error = GetCircleToSegmentError( radius, numSegs );
-        radius += GetCircleToPolyCorrection( actual_error );
+        // The outer radius should be radius+aError
+        // Recalculate the actual approx error, as it can be smaller than aError
+        // because numSegs is clamped to a minimal value
+        int actual_delta_radius = CircleToEndSegmentDeltaRadius( radius, numSegs );
+        radius += GetCircleToPolyCorrection( actual_delta_radius );
     }
 
     for( int angle = 0; angle < 3600; angle += delta )
@@ -90,7 +93,13 @@ void TransformCircleToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aCenter, i
     int     radius = aRadius;
 
     if( aErrorLoc == ERROR_OUTSIDE )
-        radius += GetCircleToPolyCorrection( aError );
+    {
+        // The outer radius should be radius+aError
+        // Recalculate the actual approx error, as it can be smaller than aError
+        // because numSegs is clamped to a minimal value
+        int actual_delta_radius = CircleToEndSegmentDeltaRadius( radius, numSegs );
+        radius += GetCircleToPolyCorrection( actual_delta_radius );
+    }
 
     aCornerBuffer.NewOutline();
 

libs/kimath/src/geometry/geometry_utils.cpp

@@ -64,18 +64,22 @@ int GetArcToSegmentCount( int aRadius, int aErrorMax, double aArcAngleDegree )
 }
 
 
-int GetCircleToSegmentError( int aRadius, int aSegCount )
+int CircleToEndSegmentDeltaRadius( int aRadius, int aSegCount )
 {
-    // This is similar to the "inverse" of GetArcToSegmentCount()
-
-    // The minimal seg count is 2, giving error = aRadius
+    // The minimal seg count is 3, otherwise we cannot calculate the result
+    // in practice, the min count is clamped to 8 in kicad
     if( aSegCount <= 2 )
-        return aRadius;
+        aSegCount = 3;
 
+    // The angle between the center of the segment and one end of the segment
+    // when the circle is approximated by aSegCount segments
     double alpha = M_PI / aSegCount;
-    int error = KiROUND( aRadius * ( 1.0 - cos( alpha) ) );
 
-    return error;
+    // aRadius is the radius of the circle tangent to the middle of each segment
+    // and aRadius/cos(aplha) is the radius of the circle defined by seg ends
+    int delta = KiROUND( aRadius * ( 1/cos(alpha) - 1 ) );
+
+    return delta;
 }
 
 // When creating polygons to create a clearance polygonal area, the polygon must