kicad/libs/kimath/src/convert_basic_shapes_to_pol...

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/**
* @file convert_basic_shapes_to_polygon.cpp
*/
/*
* 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) 1992-2021 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 <type_traits> // for swap
#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& aCornerBuffer, wxPoint aCenter, int aRadius,
int aError, ERROR_LOC aErrorLoc, int aMinSegCount )
{
wxPoint corner_position;
int numSegs = GetArcToSegmentCount( aRadius, aError, 360.0 );
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++;
int delta = 3600 / numSegs; // rotate angle in 0.1 degree
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( int angle = 0; angle < 3600; angle += delta )
{
corner_position.x = radius;
corner_position.y = 0;
RotatePoint( &corner_position, angle );
corner_position += aCenter;
aCornerBuffer.Append( corner_position.x, corner_position.y );
}
aCornerBuffer.SetClosed( true );
}
void TransformCircleToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aCenter, int aRadius,
int aError, ERROR_LOC aErrorLoc, int aMinSegCount )
{
wxPoint corner_position;
int numSegs = GetArcToSegmentCount( aRadius, aError, 360.0 );
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++;
int delta = 3600 / numSegs; // rotate angle in 0.1 degree
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 );
}
aCornerBuffer.NewOutline();
for( int angle = 0; angle < 3600; angle += delta )
{
corner_position.x = radius;
corner_position.y = 0;
RotatePoint( &corner_position, angle );
corner_position += aCenter;
aCornerBuffer.Append( corner_position.x, corner_position.y );
}
// Finish circle
corner_position.x = radius;
corner_position.y = 0;
corner_position += aCenter;
aCornerBuffer.Append( corner_position.x, corner_position.y );
}
void TransformOvalToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aStart, wxPoint 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, 360.0 );
numSegs = std::max( aMinSegCount, numSegs );
int delta = 3600 / numSegs; // rotate angle in 0.1 degree
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
wxPoint endp = aEnd - aStart;
wxPoint startp = aStart;
wxPoint 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;
}
// delta_angle is in radian
double delta_angle = atan2( (double)endp.y, (double)endp.x );
int seg_len = KiROUND( EuclideanNorm( endp ) );
// 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:
for( int angle = 0; angle < 1800; angle += delta )
{
corner = wxPoint( 0, radius );
RotatePoint( &corner, angle );
corner.x += seg_len;
polyshape.Append( corner.x, corner.y );
}
// Finish arc:
corner = wxPoint( seg_len, -radius );
polyshape.Append( corner.x, corner.y );
// add left rounded end:
for( int angle = 0; angle < 1800; angle += delta )
{
corner = wxPoint( 0, -radius );
RotatePoint( &corner, angle );
polyshape.Append( corner.x, corner.y );
}
// Finish arc:
corner = wxPoint( 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, VECTOR2I( 0, 0 ) );
polyshape.Move( startp );
aCornerBuffer.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 endAngle, radius = cur.m_radius;
double tanAngle2;
if( ( incoming.x == 0 && outgoing.y == 0 ) || ( incoming.y == 0 && outgoing.x == 0 ) )
{
endAngle = 900;
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 = RAD2DECIDEG( angle );
}
if( aInflate )
{
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, 360.0 ) );
int angDelta = 3600 / numSegs;
int lastSegLen = endAngle % angDelta; // or 0 if last seg length is angDelta
int angPos = lastSegLen ? ( angDelta + lastSegLen ) / 2 : angDelta;
double arcTransitionDistance = radius / tanAngle2;
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 )
{
VECTOR2I intersect = outlineIn.IntersectLines( SEG( prevPt, pt ) ).get();
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& aCornerBuffer, const wxPoint& aPosition,
const wxSize& aSize, double aRotation, int aDeltaX, int aDeltaY,
int aInflate, int aError, ERROR_LOC aErrorLoc )
{
SHAPE_POLY_SET outline;
wxSize size( aSize / 2 );
std::vector<ROUNDED_CORNER> corners;
corners.reserve( 4 );
corners.push_back( ROUNDED_CORNER( -size.x + aDeltaY, -size.y - aDeltaX ) );
corners.push_back( ROUNDED_CORNER( size.x - aDeltaY, -size.y + aDeltaX ) );
corners.push_back( ROUNDED_CORNER( size.x + aDeltaY, size.y - aDeltaX ) );
corners.push_back( ROUNDED_CORNER( -size.x - aDeltaY, size.y + aDeltaX ) );
if( aDeltaY == size.x || aDeltaX == size.y )
CornerListRemoveDuplicates( corners );
CornerListToPolygon( outline, corners, aInflate, aError, aErrorLoc );
if( aRotation != 0.0 )
outline.Rotate( DECIDEG2RAD( -aRotation ), VECTOR2I( 0, 0 ) );
outline.Move( VECTOR2I( aPosition ) );
aCornerBuffer.Append( outline );
}
void TransformRoundChamferedRectToPolygon( SHAPE_POLY_SET& aCornerBuffer, const wxPoint& aPosition,
const wxSize& aSize, double aRotation, int aCornerRadius,
double aChamferRatio, int aChamferCorners, int aInflate,
int aError, ERROR_LOC aErrorLoc )
{
SHAPE_POLY_SET outline;
wxSize size( aSize / 2 );
int chamferCnt = std::bitset<8>( aChamferCorners ).count();
// Ensure size is > 0, to avoid generating unusable shapes which can crash kicad.
size.x = std::max( 1, size.x );
size.y = std::max( 1, size.y );
std::vector<ROUNDED_CORNER> corners;
corners.reserve( 4 + chamferCnt );
corners.push_back( ROUNDED_CORNER( -size.x, -size.y, aCornerRadius ) );
corners.push_back( ROUNDED_CORNER( size.x, -size.y, aCornerRadius ) );
corners.push_back( ROUNDED_CORNER( size.x, size.y, aCornerRadius ) );
corners.push_back( ROUNDED_CORNER( -size.x, size.y, aCornerRadius ) );
if( aChamferCorners )
{
int shorterSide = std::min( aSize.x, aSize.y );
int chamfer = aChamferRatio * shorterSide;
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 != 0.0 )
outline.Rotate( DECIDEG2RAD( -aRotation ), VECTOR2I( 0, 0 ) );
outline.Move( VECTOR2I( aPosition ) );
aCornerBuffer.Append( outline );
}
int ConvertArcToPolyline( SHAPE_LINE_CHAIN& aPolyline, VECTOR2I aCenter, int aRadius,
double aStartAngleDeg, double aArcAngleDeg, double aAccuracy,
ERROR_LOC aErrorLoc )
{
double endAngle = aStartAngleDeg + aArcAngleDeg;
int n = 2;
if( aRadius >= aAccuracy )
n = GetArcToSegmentCount( aRadius, aAccuracy, aArcAngleDeg )+1; // n >= 3
if( aErrorLoc == ERROR_OUTSIDE )
{
int seg360 = std::abs( KiROUND( n * 360.0 / aArcAngleDeg ) );
int actual_delta_radius = CircleToEndSegmentDeltaRadius( aRadius, seg360 );
aRadius += actual_delta_radius;
}
for( int i = 0; i <= n ; i++ )
{
double rot = aStartAngleDeg;
rot += ( aArcAngleDeg * i ) / n;
double x = aCenter.x + aRadius * cos( rot * M_PI / 180.0 );
double y = aCenter.y + aRadius * sin( rot * M_PI / 180.0 );
aPolyline.Append( KiROUND( x ), KiROUND( y ) );
}
return n;
}
void TransformArcToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint aStart, wxPoint aMid,
wxPoint aEnd, int aWidth, int aError, ERROR_LOC aErrorLoc )
{
SHAPE_ARC arc( aStart, aMid, aEnd, aWidth );
// Currentlye have currently 2 algos:
// the first approximates the thick arc from its outlines
// the second approximates the thick arc from segments given by SHAPE_ARC
// using SHAPE_ARC::ConvertToPolyline
// The actual approximation errors are similar but not exactly the same.
//
// For now, both algorithms are kept, the second is the initial algo used in Kicad.
#if 1
// This appproximation convert the 2 ends to polygons, arc outer to polyline
// and arc inner to polyline and merge shapes.
int radial_offset = ( aWidth + 1 ) / 2;
SHAPE_POLY_SET polyshape;
std::vector<VECTOR2I> outside_pts;
/// We start by making rounded ends on the arc
TransformCircleToPolygon( polyshape, aStart, radial_offset, aError, aErrorLoc );
TransformCircleToPolygon( polyshape, aEnd, 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_start_deg = arc.GetStartAngle();
double arc_angle = arc.GetCentralAngle();
double arc_angle_end_deg = arc_angle_start_deg + arc_angle;
if( arc_angle_start_deg != 0 && arc_angle_start_deg != 180.0 )
polyshape.Outline(0).Rotate( arc_angle_start_deg * M_PI/180.0, aStart );
if( arc_angle_end_deg != 0 && arc_angle_end_deg != 180.0 )
polyshape.Outline(1).Rotate( arc_angle_end_deg * M_PI/180.0, aEnd );
VECTOR2I center = arc.GetCenter();
int radius = arc.GetRadius();
int arc_outer_radius = radius + radial_offset;
int arc_inner_radius = radius - radial_offset;
ERROR_LOC errorLocInner = ERROR_OUTSIDE;
ERROR_LOC errorLocOuter = ERROR_INSIDE;
if( aErrorLoc == ERROR_OUTSIDE )
{
errorLocInner = ERROR_INSIDE;
errorLocOuter = ERROR_OUTSIDE;
}
polyshape.NewOutline();
ConvertArcToPolyline( polyshape.Outline(2), center, arc_outer_radius,
arc_angle_start_deg, arc_angle, aError, errorLocOuter );
if( arc_inner_radius > 0 )
ConvertArcToPolyline( polyshape.Outline(2), center, arc_inner_radius,
arc_angle_end_deg, -arc_angle, aError, errorLocInner );
else
polyshape.Append( center );
#else
// This appproximation use SHAPE_ARC to convert the 2 ends to polygons,
// approximate arc to polyline, convert the polyline corners to outer and inner
// corners of outer and inner utliners and merge shapes.
double defaultErr;
SHAPE_LINE_CHAIN arcSpine = arc.ConvertToPolyline( SHAPE_ARC::DefaultAccuracyForPCB(),
&defaultErr);
int radius = arc.GetRadius();
int radial_offset = ( aWidth + 1 ) / 2;
SHAPE_POLY_SET polyshape;
std::vector<VECTOR2I> outside_pts;
// delta is the effective error approximation to build a polyline from an arc
int segCnt360 = arcSpine.GetSegmentCount()*360.0/arc.GetCentralAngle();;
int delta = CircleToEndSegmentDeltaRadius( radius+radial_offset, std::abs(segCnt360) );
/// We start by making rounded ends on the arc
TransformCircleToPolygon( polyshape, aStart, radial_offset, aError, aErrorLoc );
TransformCircleToPolygon( polyshape, aEnd, 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 += delta + defaultErr/2;
else
radial_offset -= defaultErr/2;
if( radial_offset < 0 )
radial_offset = 0;
polyshape.NewOutline();
VECTOR2I center = arc.GetCenter();
int last_index = arcSpine.GetPointCount() -1;
for( std::size_t ii = 0; ii <= last_index; ++ii )
{
VECTOR2I offset = arcSpine.GetPoint( ii ) - center;
int curr_rd = radius;
polyshape.Append( offset.Resize( curr_rd - radial_offset ) + center );
outside_pts.emplace_back( offset.Resize( curr_rd + radial_offset ) + center );
}
for( auto it = outside_pts.rbegin(); it != outside_pts.rend(); ++it )
polyshape.Append( *it );
#endif
// Can be removed, but usefull to display the outline:
polyshape.Simplify( SHAPE_POLY_SET::PM_FAST );
aCornerBuffer.Append( polyshape );
}
void TransformRingToPolygon( SHAPE_POLY_SET& aCornerBuffer, wxPoint 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( aCornerBuffer, 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 );
aCornerBuffer.Append( buffer );
}