From a04d6401c1f60ddb9d23736fa42ac2958118af2c Mon Sep 17 00:00:00 2001
From: Seth Hillbrand <seth@kipro-pcb.com>
Date: Fri, 11 Jun 2021 12:34:57 -0700
Subject: [PATCH] Transform arcs more accurately

Segment approximation for arcs leaves small "indents" where the rounded
edges of two segments don't quite meet.

This gives closer approximation by calculating the inner and outer joint
points based on the radius, eliminating the indents.
---
 .../src/convert_basic_shapes_to_polygon.cpp   | 41 +++++++++++++++----
 1 file changed, 33 insertions(+), 8 deletions(-)

diff --git a/libs/kimath/src/convert_basic_shapes_to_polygon.cpp b/libs/kimath/src/convert_basic_shapes_to_polygon.cpp
index e1cd9378b0..431d565bb1 100644
--- a/libs/kimath/src/convert_basic_shapes_to_polygon.cpp
+++ b/libs/kimath/src/convert_basic_shapes_to_polygon.cpp
@@ -354,21 +354,46 @@ void TransformArcToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aStart, wxPoi
 {
     SHAPE_ARC        arc( aStart, aMid, aEnd, aWidth );
     SHAPE_LINE_CHAIN arcSpine = arc.ConvertToPolyline( aError );
+    int              radial_offset = ( aWidth + 1 ) / 2;
+
+    /// We start by making rounded ends on the arc
+    TransformCircleToPolygon( aCornerBuffer,
+            wxPoint( arcSpine.GetPoint( 0 ).x, arcSpine.GetPoint( 0 ).y ), radial_offset, aError,
+            aErrorLoc );
+
+    TransformCircleToPolygon( aCornerBuffer,
+            wxPoint( arcSpine.GetPoint( -1 ).x, arcSpine.GetPoint( -1 ).y ), radial_offset, aError,
+            aErrorLoc );
 
     if( aErrorLoc == ERROR_OUTSIDE )
-        aWidth += 2 * aError;
+        radial_offset += aError;
     else
-        aWidth -= 2 * aError;
+        radial_offset -= aError;
 
-    for( int ii = 0; ii < arcSpine.GetSegmentCount(); ++ii )
+    if( radial_offset < 0 )
+        radial_offset = 0;
+
+    std::vector<VECTOR2I> outside_pts;
+    SHAPE_POLY_SET        polyshape;
+
+    polyshape.NewOutline();
+
+    VECTOR2I center = arc.GetCenter();
+    int      radius = ( arc.GetP0() - center ).EuclideanNorm();
+
+    for( std::size_t ii = 0; ii < arcSpine.GetPointCount(); ++ii )
     {
-        SEG seg = arcSpine.GetSegment( ii );
+        VECTOR2I offset = arcSpine.GetPoint( ii ) - center;
 
-        // Note that the error here is only for the rounded ends; we still need to shrink or
-        // expand the width above for the segments themselves.
-        TransformOvalToPolygon( aCornerBuffer, (wxPoint) seg.A, (wxPoint) seg.B, aWidth, aError,
-                                aErrorLoc );
+        polyshape.Append( offset.Resize( radius - radial_offset ) + center );
+        outside_pts.emplace_back( offset.Resize( radius + radial_offset ) + center );
     }
+
+    for( auto it = outside_pts.rbegin(); it != outside_pts.rend(); ++it )
+        polyshape.Append( *it );
+
+    aCornerBuffer.Append( polyshape );
+
 }