convert_basic_shapes_to_polygon.cpp

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/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2018 Jean-Pierre Charras, jp.charras at wanadoo.fr
 * Copyright (C) 1992-2022 KiCad Developers, see AUTHORS.txt for contributors.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, you may find one here:
 * http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
 * or you may search the http://www.gnu.org website for the version 2 license,
 * or you may write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
 */
 
#include <algorithm> // for max, min
#include <bitset> // for bitset::count
#include <math.h> // for atan2
 
#include <convert_basic_shapes_to_polygon.h>
#include <geometry/geometry_utils.h>
#include <geometry/shape_line_chain.h> // for SHAPE_LINE_CHAIN
#include <geometry/shape_poly_set.h> // for SHAPE_POLY_SET, SHAPE_POLY_SE...
#include <math/util.h>
#include <math/vector2d.h> // for VECTOR2I
#include <trigo.h>
 
 
void TransformCircleToPolygon( SHAPE_LINE_CHAIN& aBuffer, const VECTOR2I& aCenter, int aRadius,
 int aError, ERROR_LOC aErrorLoc, int aMinSegCount )
{
 VECTOR2I corner_position;
 int numSegs = GetArcToSegmentCount( aRadius, aError, FULL_CIRCLE );
 numSegs = std::max( aMinSegCount, numSegs );
 
 // 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++;
 
 EDA_ANGLE delta = ANGLE_360 / numSegs;
 int radius = aRadius;
 
 if( aErrorLoc == ERROR_OUTSIDE )
 {
 // 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( EDA_ANGLE angle = ANGLE_0; angle < ANGLE_360; angle += delta )
 {
 corner_position.x = radius;
 corner_position.y = 0;
 RotatePoint( corner_position, angle );
 corner_position += aCenter;
 aBuffer.Append( corner_position.x, corner_position.y );
 }
 
 aBuffer.SetClosed( true );
}
 
 
void TransformCircleToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aCenter, int aRadius,
 int aError, ERROR_LOC aErrorLoc, int aMinSegCount )
{
 VECTOR2I corner_position;
 int numSegs = GetArcToSegmentCount( aRadius, aError, FULL_CIRCLE );
 numSegs = std::max( aMinSegCount, numSegs );
 
 // 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++;
 
 EDA_ANGLE delta = ANGLE_360 / numSegs;
 int radius = aRadius;
 
 if( aErrorLoc == ERROR_OUTSIDE )
 {
 // 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 );
 }
 
 aBuffer.NewOutline();
 
 for( EDA_ANGLE angle = ANGLE_0; angle < ANGLE_360; angle += delta )
 {
 corner_position.x = radius;
 corner_position.y = 0;
 RotatePoint( corner_position, angle );
 corner_position += aCenter;
 aBuffer.Append( corner_position.x, corner_position.y );
 }
 
 // Finish circle
 corner_position.x = radius;
 corner_position.y = 0;
 corner_position += aCenter;
 aBuffer.Append( corner_position.x, corner_position.y );
}
 
 
void TransformOvalToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aStart, const VECTOR2I& aEnd,
 int aWidth, int aError, ERROR_LOC aErrorLoc, int aMinSegCount )
{
 // To build the polygonal shape outside the actual shape, we use a bigger
 // radius to build rounded ends.
 // However, the width of the segment is too big.
 // so, later, we will clamp the polygonal shape with the bounding box
 // of the segment.
 int radius = aWidth / 2;
 int numSegs = GetArcToSegmentCount( radius, aError, FULL_CIRCLE );
 numSegs = std::max( aMinSegCount, numSegs );
 
 // Round up to 8 to make segment approximations align properly at 45-degrees
 numSegs = ( numSegs + 7 ) / 8 * 8;
 
 EDA_ANGLE delta = ANGLE_360 / numSegs;
 
 if( aErrorLoc == ERROR_OUTSIDE )
 {
 // 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 );
 int correction = GetCircleToPolyCorrection( actual_delta_radius );
 radius += correction;
 }
 
 // end point is the coordinate relative to aStart
 VECTOR2I endp = aEnd - aStart;
 VECTOR2I startp = aStart;
 VECTOR2I corner;
 SHAPE_POLY_SET polyshape;
 
 polyshape.NewOutline();
 
 // normalize the position in order to have endp.x >= 0
 // it makes calculations more easy to understand
 if( endp.x < 0 )
 {
 endp = aStart - aEnd;
 startp = aEnd;
 }
 
 EDA_ANGLE delta_angle( endp );
 int seg_len = endp.EuclideanNorm();
 
 // Compute the outlines of the segment, and creates a polygon
 // Note: the polygonal shape is built from the equivalent horizontal
 // segment starting at {0,0}, and ending at {seg_len,0}
 
 // add right rounded end:
 
 // Right arc start:
 corner = VECTOR2I( seg_len, radius );
 polyshape.Append( corner.x, corner.y );
 
 for( EDA_ANGLE angle = delta / 2; angle < ANGLE_180; angle += delta )
 {
 corner = VECTOR2I( 0, radius );
 RotatePoint( corner, angle );
 corner.x += seg_len;
 polyshape.Append( corner.x, corner.y );
 }
 
 // Finish right arc:
 corner = VECTOR2I( seg_len, -radius );
 polyshape.Append( corner.x, corner.y );
 
 // Left arc start:
 corner = VECTOR2I( 0, -radius );
 polyshape.Append( corner.x, corner.y );
 
 // add left rounded end:
 for( EDA_ANGLE angle = delta / 2; angle < ANGLE_180; angle += delta )
 {
 corner = VECTOR2I( 0, -radius );
 RotatePoint( corner, angle );
 polyshape.Append( corner.x, corner.y );
 }
 
 // Finish left arc:
 corner = VECTOR2I( 0, radius );
 polyshape.Append( corner.x, corner.y );
 
 // Now trim the edges of the polygonal shape which will be slightly outside the
 // track width.
 SHAPE_POLY_SET bbox;
 bbox.NewOutline();
 // Build the bbox (a horizontal rectangle).
 int halfwidth = aWidth / 2; // Use the exact segment width for the bbox height
 corner.x = -radius - 2; // use a bbox width slightly bigger to avoid
 // creating useless corner at segment ends
 corner.y = halfwidth;
 bbox.Append( corner.x, corner.y );
 corner.y = -halfwidth;
 bbox.Append( corner.x, corner.y );
 corner.x = radius + seg_len + 2;
 bbox.Append( corner.x, corner.y );
 corner.y = halfwidth;
 bbox.Append( corner.x, corner.y );
 
 // Now, clamp the shape
 polyshape.BooleanIntersection( bbox, SHAPE_POLY_SET::PM_STRICTLY_SIMPLE );
 // Note the final polygon is a simple, convex polygon with no hole
 // due to the shape of initial polygons
 
 // Rotate and move the polygon to its right location
 polyshape.Rotate( -delta_angle );
 polyshape.Move( startp );
 
 aBuffer.Append( polyshape);
}
 
 
struct ROUNDED_CORNER
{
 VECTOR2I m_position;
 int m_radius;
 ROUNDED_CORNER( int x, int y ) : m_position( VECTOR2I( x, y ) ), m_radius( 0 ) {}
 ROUNDED_CORNER( int x, int y, int radius ) : m_position( VECTOR2I( x, y ) ), m_radius( radius ) {}
};
 
 
// Corner List requirements: no concave shape, corners in clockwise order, no duplicate corners
void CornerListToPolygon( SHAPE_POLY_SET& outline, std::vector<ROUNDED_CORNER>& aCorners,
 int aInflate, int aError, ERROR_LOC aErrorLoc )
{
 assert( aInflate >= 0 );
 outline.NewOutline();
 VECTOR2I incoming = aCorners[0].m_position - aCorners.back().m_position;
 
 for( int n = 0, count = aCorners.size(); n < count; n++ )
 {
 ROUNDED_CORNER& cur = aCorners[n];
 ROUNDED_CORNER& next = aCorners[( n + 1 ) % count];
 VECTOR2I outgoing = next.m_position - cur.m_position;
 
 if( !( aInflate || cur.m_radius ) )
 {
 outline.Append( cur.m_position );
 }
 else
 {
 VECTOR2I cornerPosition = cur.m_position;
 int radius = cur.m_radius;
 EDA_ANGLE endAngle;
 double tanAngle2;
 
 if( ( incoming.x == 0 && outgoing.y == 0 ) || ( incoming.y == 0 && outgoing.x == 0 ) )
 {
 endAngle = ANGLE_90;
 tanAngle2 = 1.0;
 }
 else
 {
 double cosNum = (double) incoming.x * outgoing.x + (double) incoming.y * outgoing.y;
 double cosDen = (double) incoming.EuclideanNorm() * outgoing.EuclideanNorm();
 double angle = acos( cosNum / cosDen );
 tanAngle2 = tan( ( M_PI - angle ) / 2 );
 endAngle = EDA_ANGLE( angle, RADIANS_T );
 }
 
 if( aInflate && tanAngle2 )
 {
 radius += aInflate;
 cornerPosition += incoming.Resize( aInflate / tanAngle2 )
 + incoming.Perpendicular().Resize( -aInflate );
 }
 
 // Ensure 16+ segments per 360deg and ensure first & last segment are the same size
 int numSegs = std::max( 16, GetArcToSegmentCount( radius, aError, FULL_CIRCLE ) );
 EDA_ANGLE angDelta = ANGLE_360 / numSegs;
 EDA_ANGLE lastSeg = endAngle;
 
 if( lastSeg > ANGLE_0 )
 {
 while( lastSeg > angDelta )
 lastSeg -= angDelta;
 }
 else
 {
 while( lastSeg < -angDelta )
 lastSeg += angDelta;
 }
 
 EDA_ANGLE angPos = lastSeg.IsZero() ? angDelta : ( angDelta + lastSeg ) / 2;
 
 double arcTransitionDistance = ( tanAngle2 > 0 ) ? ( radius / tanAngle2 ) : 0;
 VECTOR2I arcStart = cornerPosition - incoming.Resize( arcTransitionDistance );
 VECTOR2I arcCenter = arcStart + incoming.Perpendicular().Resize( radius );
 VECTOR2I arcEnd, arcStartOrigin;
 
 if( aErrorLoc == ERROR_INSIDE )
 {
 arcEnd = SEG( cornerPosition, arcCenter ).ReflectPoint( arcStart );
 arcStartOrigin = arcStart - arcCenter;
 outline.Append( arcStart );
 }
 else
 {
 // The outer radius should be radius+aError, recalculate because numSegs is clamped
 int actualDeltaRadius = CircleToEndSegmentDeltaRadius( radius, numSegs );
 int radiusExtend = GetCircleToPolyCorrection( actualDeltaRadius );
 arcStart += incoming.Perpendicular().Resize( -radiusExtend );
 arcStartOrigin = arcStart - arcCenter;
 
 // To avoid "ears", we only add segments crossing/within the non-rounded outline
 // Note: outlineIn is short and must be treated as defining an infinite line
 SEG outlineIn( cornerPosition - incoming, cornerPosition );
 VECTOR2I prevPt = arcStart;
 arcEnd = cornerPosition; // default if no points within the outline are found
 
 while( angPos < endAngle )
 {
 VECTOR2I pt = arcStartOrigin;
 RotatePoint( pt, -angPos );
 pt += arcCenter;
 angPos += angDelta;
 
 if( outlineIn.Side( pt ) > 0 )
 {
 OPT_VECTOR2I intersect = outlineIn.IntersectLines( SEG( prevPt, pt ) );
 
 wxCHECK_RET( intersect, wxT( "No solutions exist!" ) );
 outline.Append( *intersect );
 outline.Append( pt );
 arcEnd = SEG( cornerPosition, arcCenter ).ReflectPoint( *intersect );
 break;
 }
 
 endAngle -= angDelta; // if skipping first, also skip last
 prevPt = pt;
 }
 }
 
 for( ; angPos < endAngle; angPos += angDelta )
 {
 VECTOR2I pt = arcStartOrigin;
 RotatePoint( pt, -angPos );
 outline.Append( pt + arcCenter );
 }
 
 outline.Append( arcEnd );
 }
 
 incoming = outgoing;
 }
}
 
 
void CornerListRemoveDuplicates( std::vector<ROUNDED_CORNER>& aCorners )
{
 VECTOR2I prev = aCorners[0].m_position;
 
 for( int pos = aCorners.size() - 1; pos >= 0; pos-- )
 {
 if( aCorners[pos].m_position == prev )
 aCorners.erase( aCorners.begin() + pos );
 else
 prev = aCorners[pos].m_position;
 }
}
 
 
void TransformTrapezoidToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aPosition,
 const VECTOR2I& aSize, const EDA_ANGLE& aRotation, int aDeltaX,
 int aDeltaY, int aInflate, int aError, ERROR_LOC aErrorLoc )
{
 SHAPE_POLY_SET outline;
 VECTOR2I size( aSize / 2 );
 std::vector<ROUNDED_CORNER> corners;
 
 if( aInflate < 0 )
 {
 if( !aDeltaX && !aDeltaY ) // rectangle
 {
 size.x = std::max( 1, size.x + aInflate );
 size.y = std::max( 1, size.y + aInflate );
 }
 else if( aDeltaX ) // horizontal trapezoid
 {
 double slope = (double) aDeltaX / size.x;
 int yShrink = KiROUND( ( std::hypot( size.x, aDeltaX ) * aInflate ) / size.x );
 size.y = std::max( 1, size.y + yShrink );
 size.x = std::max( 1, size.x + aInflate );
 aDeltaX = KiROUND( size.x * slope );
 
 if( aDeltaX > size.y ) // shrinking turned the trapezoid into a triangle
 {
 corners.reserve( 3 );
 corners.emplace_back( -size.x, -size.y - aDeltaX );
 corners.emplace_back( KiROUND( size.y / slope ), 0 );
 corners.emplace_back( -size.x, size.y + aDeltaX );
 }
 }
 else // vertical trapezoid
 {
 double slope = (double) aDeltaY / size.y;
 int xShrink = KiROUND( ( std::hypot( size.y, aDeltaY ) * aInflate ) / size.y );
 size.x = std::max( 1, size.x + xShrink );
 size.y = std::max( 1, size.y + aInflate );
 aDeltaY = KiROUND( size.y * slope );
 
 if( aDeltaY > size.x )
 {
 corners.reserve( 3 );
 corners.emplace_back( 0, -KiROUND( size.x / slope ) );
 corners.emplace_back( size.x + aDeltaY, size.y );
 corners.emplace_back( -size.x - aDeltaY, size.y );
 }
 }
 
 aInflate = 0;
 }
 
 if( corners.empty() )
 {
 corners.reserve( 4 );
 corners.emplace_back( -size.x + aDeltaY, -size.y - aDeltaX );
 corners.emplace_back( size.x - aDeltaY, -size.y + aDeltaX );
 corners.emplace_back( size.x + aDeltaY, size.y - aDeltaX );
 corners.emplace_back( -size.x - aDeltaY, size.y + aDeltaX );
 
 if( std::abs( aDeltaY ) == std::abs( size.x ) || std::abs( aDeltaX ) == std::abs( size.y ) )
 CornerListRemoveDuplicates( corners );
 }
 
 CornerListToPolygon( outline, corners, aInflate, aError, aErrorLoc );
 
 if( !aRotation.IsZero() )
 outline.Rotate( aRotation );
 
 outline.Move( VECTOR2I( aPosition ) );
 aBuffer.Append( outline );
}
 
 
void TransformRoundChamferedRectToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aPosition,
 const VECTOR2I& aSize, const EDA_ANGLE& aRotation,
 int aCornerRadius, double aChamferRatio,
 int aChamferCorners, int aInflate, int aError,
 ERROR_LOC aErrorLoc )
{
 SHAPE_POLY_SET outline;
 VECTOR2I size( aSize / 2 );
 int chamferCnt = std::bitset<8>( aChamferCorners ).count();
 double chamferDeduct = 0;
 
 if( aInflate < 0 )
 {
 size.x = std::max( 1, size.x + aInflate );
 size.y = std::max( 1, size.y + aInflate );
 chamferDeduct = aInflate * ( 2.0 - M_SQRT2 );
 aCornerRadius = std::max( 0, aCornerRadius + aInflate );
 aInflate = 0;
 }
 
 std::vector<ROUNDED_CORNER> corners;
 corners.reserve( 4 + chamferCnt );
 corners.emplace_back( -size.x, -size.y, aCornerRadius );
 corners.emplace_back( size.x, -size.y, aCornerRadius );
 corners.emplace_back( size.x, size.y, aCornerRadius );
 corners.emplace_back( -size.x, size.y, aCornerRadius );
 
 if( aChamferCorners )
 {
 int shorterSide = std::min( aSize.x, aSize.y );
 int chamfer = std::max( 0, KiROUND( aChamferRatio * shorterSide + chamferDeduct ) );
 int chamId[4] = { RECT_CHAMFER_TOP_LEFT, RECT_CHAMFER_TOP_RIGHT,
 RECT_CHAMFER_BOTTOM_RIGHT, RECT_CHAMFER_BOTTOM_LEFT };
 int sign[8] = { 0, 1, -1, 0, 0, -1, 1, 0 };
 
 for( int cc = 0, pos = 0; cc < 4; cc++, pos++ )
 {
 if( !( aChamferCorners & chamId[cc] ) )
 continue;
 
 corners[pos].m_radius = 0;
 
 if( chamfer == 0 )
 continue;
 
 corners.insert( corners.begin() + pos + 1, corners[pos] );
 corners[pos].m_position.x += sign[( 2 * cc ) & 7] * chamfer;
 corners[pos].m_position.y += sign[( 2 * cc - 2 ) & 7] * chamfer;
 corners[pos + 1].m_position.x += sign[( 2 * cc + 1 ) & 7] * chamfer;
 corners[pos + 1].m_position.y += sign[( 2 * cc - 1 ) & 7] * chamfer;
 pos++;
 }
 
 if( chamferCnt > 1 && 2 * chamfer >= shorterSide )
 CornerListRemoveDuplicates( corners );
 }
 
 CornerListToPolygon( outline, corners, aInflate, aError, aErrorLoc );
 
 if( !aRotation.IsZero() )
 outline.Rotate( aRotation );
 
 outline.Move( aPosition );
 aBuffer.Append( outline );
}
 
 
int ConvertArcToPolyline( SHAPE_LINE_CHAIN& aPolyline, VECTOR2I aCenter, int aRadius,
 const EDA_ANGLE& aStartAngle, const EDA_ANGLE& aArcAngle,
 double aAccuracy, ERROR_LOC aErrorLoc )
{
 int n = 2;
 
 if( aRadius >= aAccuracy )
 n = GetArcToSegmentCount( aRadius, aAccuracy, aArcAngle ) + 1;
 
 EDA_ANGLE delta = aArcAngle / n;
 
 if( aErrorLoc == ERROR_INSIDE )
 {
 // This is the easy case: with the error on the inside the endpoints of each segment
 // are error-free.
 
 EDA_ANGLE rot = aStartAngle;
 
 for( int i = 0; i <= n; i++, rot += delta )
 {
 double x = aCenter.x + aRadius * rot.Cos();
 double y = aCenter.y + aRadius * rot.Sin();
 
 aPolyline.Append( KiROUND( x ), KiROUND( y ) );
 }
 }
 else
 {
 // This is the hard case: with the error on the outside it's the segment midpoints
 // that are error-free. So we need to add a half-segment at each end of the arc to get
 // them correct.
 
 int seg360 = std::abs( KiROUND( n * 360.0 / aArcAngle.AsDegrees() ) );
 int actual_delta_radius = CircleToEndSegmentDeltaRadius( aRadius, seg360 );
 int errorRadius = aRadius + actual_delta_radius;
 
 double x = aCenter.x + aRadius * aStartAngle.Cos();
 double y = aCenter.y + aRadius * aStartAngle.Sin();
 
 aPolyline.Append( KiROUND( x ), KiROUND( y ) );
 
 EDA_ANGLE rot = aStartAngle + delta / 2;
 
 for( int i = 0; i < n; i++, rot += delta )
 {
 x = aCenter.x + errorRadius * rot.Cos();
 y = aCenter.y + errorRadius * rot.Sin();
 
 aPolyline.Append( KiROUND( x ), KiROUND( y ) );
 }
 
 x = aCenter.x + aRadius * ( aStartAngle + aArcAngle ).Cos();
 y = aCenter.y + aRadius * ( aStartAngle + aArcAngle ).Sin();
 
 aPolyline.Append( KiROUND( x ), KiROUND( y ) );
 }
 
 return n;
}
 
 
void TransformArcToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aStart, const VECTOR2I& aMid,
 const VECTOR2I& aEnd, int aWidth, int aError, ERROR_LOC aErrorLoc )
{
 SEG startToEnd( aStart, aEnd );
 int distanceToMid = startToEnd.Distance( aMid );
 
 if( distanceToMid <= 1 )
 {
 // Not an arc but essentially a straight line with a small error
 TransformOvalToPolygon( aBuffer, aStart, aEnd, aWidth + distanceToMid, aError, aErrorLoc );
 return;
 }
 
 // This appproximation builds a single polygon by starting with a 180 degree arc at one
 // end, then the outer edge of the arc, then a 180 degree arc at the other end, and finally
 // the inner edge of the arc.
 SHAPE_ARC arc( aStart, aMid, aEnd, aWidth );
 EDA_ANGLE arc_angle_start = arc.GetStartAngle();
 EDA_ANGLE arc_angle = arc.GetCentralAngle();
 EDA_ANGLE arc_angle_end = arc_angle_start + arc_angle;
 
 if( arc_angle < ANGLE_0 )
 {
 std::swap( arc_angle_start, arc_angle_end );
 arc = SHAPE_ARC( aEnd, aMid, aStart, aWidth );
 arc_angle = -arc_angle;
 }
 
 int radial_offset = arc.GetWidth() / 2;
 int arc_outer_radius = arc.GetRadius() + radial_offset;
 int arc_inner_radius = arc.GetRadius() - radial_offset;
 ERROR_LOC errorLocInner = ( aErrorLoc == ERROR_INSIDE ) ? ERROR_OUTSIDE : ERROR_INSIDE;
 ERROR_LOC errorLocOuter = ( aErrorLoc == ERROR_INSIDE ) ? ERROR_INSIDE : ERROR_OUTSIDE;
 
 SHAPE_POLY_SET polyshape;
 polyshape.NewOutline();
 
 SHAPE_LINE_CHAIN& outline = polyshape.Outline( 0 );
 
 // Starting end
 ConvertArcToPolyline( outline, arc.GetP0(), radial_offset, arc_angle_start - ANGLE_180,
 ANGLE_180, aError, aErrorLoc );
 
 // Outside edge
 ConvertArcToPolyline( outline, arc.GetCenter(), arc_outer_radius, arc_angle_start, arc_angle,
 aError, errorLocOuter );
 
 // Other end
 ConvertArcToPolyline( outline, arc.GetP1(), radial_offset, arc_angle_end, ANGLE_180, aError,
 aErrorLoc );
 
 // Inside edge
 if( arc_inner_radius > 0 )
 {
 ConvertArcToPolyline( outline, arc.GetCenter(), arc_inner_radius, arc_angle_end,
 -arc_angle, aError, errorLocInner );
 }
 
 aBuffer.Append( polyshape );
}
 
 
void TransformRingToPolygon( SHAPE_POLY_SET& aBuffer, const VECTOR2I& aCentre, int aRadius,
 int aWidth, int aError, ERROR_LOC aErrorLoc )
{
 int inner_radius = aRadius - ( aWidth / 2 );
 int outer_radius = inner_radius + aWidth;
 
 if( inner_radius <= 0 )
 {
 //In this case, the ring is just a circle (no hole inside)
 TransformCircleToPolygon( aBuffer, aCentre, aRadius + ( aWidth / 2 ), aError, aErrorLoc );
 return;
 }
 
 SHAPE_POLY_SET buffer;
 
 TransformCircleToPolygon( buffer, aCentre, outer_radius, aError, aErrorLoc );
 
 // Build the hole:
 buffer.NewHole();
 // The circle is the hole, so the approximation error location is the opposite of aErrorLoc
 ERROR_LOC inner_err_loc = aErrorLoc == ERROR_OUTSIDE ? ERROR_INSIDE : ERROR_OUTSIDE;
 TransformCircleToPolygon( buffer.Hole( 0, 0 ), aCentre, inner_radius,
 aError, inner_err_loc );
 
 buffer.Fracture( SHAPE_POLY_SET::PM_FAST );
 aBuffer.Append( buffer );
}