direction_45.cpp

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/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2019 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 3 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, see <http://www.gnu.or/licenses/>.
 */

#include <geometry/direction45.h>


const SHAPE_LINE_CHAIN DIRECTION_45::BuildInitialTrace( const VECTOR2I& aP0, const VECTOR2I& aP1,
 bool aStartDiagonal,
 CORNER_MODE aMode ) const

{
 bool startDiagonal;

 if( m_dir == UNDEFINED )
 startDiagonal = aStartDiagonal;
 else
 startDiagonal = IsDiagonal();

 int w = abs( aP1.x - aP0.x );
 int h = abs( aP1.y - aP0.y );
 int sw = sign( aP1.x - aP0.x );
 int sh = sign( aP1.y - aP0.y );

 bool is90mode = aMode == CORNER_MODE::ROUNDED_90 || aMode == CORNER_MODE::MITERED_90;
 SHAPE_LINE_CHAIN pl;

 // Shortcut where we can generate just one segment and quit. Avoids more complicated handling
 // of precision errors if filleting is enabled
 if( w == 0 || h == 0 || ( !is90mode && h == w ) )
 {
 pl.Append( aP0 );
 pl.Append( aP1 );
 return pl;
 }

 VECTOR2I mp0, mp1;
 int tangentLength;

 if( is90mode )
 {
 if( startDiagonal == ( h >= w ) )
 {
 mp0 = VECTOR2I( w * sw, 0 ); // direction: E
 }
 else
 {
 mp0 = VECTOR2I( 0, sh * h ); // direction: N
 }
 }
 else
 {
 if( w > h )
 {
 mp0 = VECTOR2I( ( w - h ) * sw, 0 ); // direction: E
 mp1 = VECTOR2I( h * sw, h * sh ); // direction: NE
 tangentLength = ( w - h ) - mp1.EuclideanNorm();
 }
 else
 {
 mp0 = VECTOR2I( 0, sh * ( h - w ) ); // direction: N
 mp1 = VECTOR2I( sw * w, sh * w ); // direction: NE
 tangentLength = ( h - w ) - mp1.EuclideanNorm();
 }
 }

 SHAPE_ARC arc;
 VECTOR2I arcEndpoint;

 switch( aMode )
 {
 case CORNER_MODE::MITERED_45:
 /*
 * For width greater than height, we're calculating something like this.
 * mp0 will be used if we start straight; mp1 if we start diagonal.
 *
 * aP0 ----------------- mp0
 * . \
 * . \
 * . \
 * mp1 . . . . . . . . aP1
 *
 */
 pl.Append( aP0 );
 pl.Append( startDiagonal ? ( aP0 + mp1 ) : ( aP0 + mp0 ) );
 pl.Append( aP1 );
 break;

 case CORNER_MODE::ROUNDED_45:
 {
 /*
 * For a fillet, we need to know the arc start point (A in the diagram below)
 * A straight segment will be needed between aP0 and A if we are starting straight,
 * or between the arc end and aP1 if we are starting diagonally.
 *
 * aP0 -- A --___ mp0
 * . ---
 * . --
 * . --
 * mp1 . . . . . . . . aP1
 *
 * For the length of this segment (tangentLength), we subtract the length of the "diagonal"
 * line from the "straight" line (i.e. dist(aP0, mp0) - dist(mp0, aP1))
 * In the example above, we will have a straight segment from aP0 to A, and then we can use
 * the distance from A to aP1 (diagLength) to calculate the radius of the arc.
 */
 if( w == h )
 {
 pl.Append( aP0 );
 pl.Append( aP1 );
 break;
 }

 double diag2 = tangentLength >= 0 ? mp1.SquaredEuclideanNorm() : mp0.SquaredEuclideanNorm();
 double diagLength = std::sqrt( ( 2 * diag2 ) - ( 2 * diag2 * std::cos( 3 * M_PI_4 ) ) );
 int arcRadius = KiROUND( diagLength / ( 2.0 * std::cos( 67.5 * M_PI / 180.0 ) ) );

 // There are four different ways to build an arc, depending on whether or not we are
 // starting diagonally and whether or not we have a negative tangent length (meaning the
 // arc has to be on the opposite end of the line from normal). This math could probably
 // be condensed and optimized but I'm tired of staring at it for now (and it works!)

 if( startDiagonal )
 {
 int rotationSign = ( w > h ) ? ( sw * sh * -1 ) : ( sw * sh );

 if( tangentLength >= 0 )
 {
 // Positive tangentLength, diagonal start: arc goes at the start
 arcEndpoint = aP1 - mp0.Resize( tangentLength );
 arc.ConstructFromStartEndAngle( aP0, arcEndpoint, 45 * rotationSign );

 if( arc.GetP0() == arc.GetP1() )
 pl.Append( aP0 );
 else
 pl.Append( arc );

 pl.Append( aP1 );
 }
 else
 {
 // Negative tangentLength, diagonal start: arc goes at the end
 arcEndpoint = aP0 + mp1.Resize( std::abs( tangentLength ) );
 arc.ConstructFromStartEndAngle( arcEndpoint, aP1, 45 * rotationSign );

 pl.Append( aP0 );

 if( arc.GetP0() == arc.GetP1() )
 pl.Append( aP1 );
 else
 pl.Append( arc );
 }
 }
 else
 {
 int rotationSign = ( w > h ) ? ( sw * sh ) : ( sw * sh * -1 );
 VECTOR2D centerDir( mp0.Rotate( M_PI_2 * rotationSign ) );

 if( tangentLength >= 0 )
 {
 // Positive tangentLength: arc goes at the end
 arcEndpoint = aP0 + mp0.Resize( tangentLength );
 arc.ConstructFromStartEndAngle( arcEndpoint, aP1, 45 * rotationSign );

 pl.Append( aP0 );

 if( arc.GetP0() == arc.GetP1() )
 pl.Append( aP1 );
 else
 pl.Append( arc );
 }
 else
 {
 // Negative tangentLength: arc goes at the start
 VECTOR2I arcCenter = aP0 + centerDir.Resize( arcRadius );
 SHAPE_ARC ca( arcCenter, aP0, 45 * rotationSign );

 // Constructing with a center can lead to imprecise endpoint. We need to guarantee
 // tangency of the endpoint.
 // TODO: update the math above to calculate the proper endpoint directly
 VECTOR2I endpoint( ca.GetP1() );

 if( std::abs( endpoint.y - aP1.y ) < SHAPE_ARC::MIN_PRECISION_IU )
 {
 VECTOR2I fixedEnd( endpoint.x, aP1.y );
 ca.ConstructFromStartEndAngle( ca.GetP0(), fixedEnd, 45 * rotationSign );
 }
 else if( std::abs( endpoint.x - aP1.x ) < SHAPE_ARC::MIN_PRECISION_IU )
 {
 VECTOR2I fixedEnd( aP1.x, endpoint.y );
 ca.ConstructFromStartEndAngle( ca.GetP0(), fixedEnd, 45 * rotationSign );
 }

 if( ca.GetP0() == ca.GetP1() )
 pl.Append( aP0 );
 else
 pl.Append( ca );

 pl.Append( aP1 );
 }
 }
 break;
 }
 case CORNER_MODE::MITERED_90:
 /*
 * For width greater than height, we're calculating something like this.
 *
 *  <-mp0->
 * aP0 -------------------+
 * |
 * |
 * |
 * aP1
 */
 pl.Append( aP0 );
 pl.Append( aP0 + mp0 );
 pl.Append( aP1 );
 break;

 case CORNER_MODE::ROUNDED_90:
 /*
 * For a fillet, we need to know the arc end point
 * A straight segment will be needed between aP0 and arcEnd in case distance aP0,mp0 is bigger
 * than the distance mp0,aP1, if the distance is shorter the straigth segment is between
 * arcEnd and aP1. If both distances are equal, we don't need a straight segment.
 *
 * aP0 ----- arcEnd ---__
 * --
 * \
 * |
 * arcCenter aP1
 *
 * For the length of the radius we use the shorter of the horizontal and vertical distance.
  */
 SHAPE_ARC arc;

 if( w == h ) // we only need one arc without a straigth line.
 {
 arc.ConstructFromStartEndCenter( aP0, aP1, aP1 - mp0, sh == sw != startDiagonal );
 pl.Append( arc );
 return pl;
 }

 VECTOR2I arcEnd; // Arc position that is not at aP0 nor aP1
 VECTOR2I arcCenter;

 if( startDiagonal ) //Means start with the arc first
 {
 if( h > w ) // Arc followed by a vertical line
 {
 int y = aP0.y + ( w * sh );
 arcEnd = VECTOR2I( aP1.x, y );
 arcCenter = VECTOR2I( aP0.x, y );
 arc.ConstructFromStartEndCenter( aP0, arcEnd, arcCenter, sh != sw );
 pl.Append( arc );
 pl.Append( aP1 );
 }
 else // Arc followed by a horizontal line
 {
 int x = aP0.x + ( h * sw );
 arcEnd = VECTOR2I( x, aP1.y );
 arcCenter = VECTOR2I( x, aP0.y );
 arc.ConstructFromStartEndCenter( aP0, arcEnd, arcCenter, sh == sw );
 pl.Append( arc );
 pl.Append( aP1 );
 }
 }
 else
 {
 if( w > h ) // Horizontal line followed by the arc
 {
 int x = aP1.x - ( h * sw );
 arcEnd = VECTOR2I( x, aP0.y );
 arcCenter = VECTOR2I( x, aP1.y );
 pl.Append( aP0 );
 arc.ConstructFromStartEndCenter( arcEnd, aP1, arcCenter, sh != sw );
 pl.Append( arc );
 }
 else // Vertical line followed by the arc
 {
 int y = aP1.y - ( w * sh );
 arcEnd = VECTOR2I( aP0.x, y );
 arcCenter = VECTOR2I( aP1.x, y );
 pl.Append( aP0 );
 arc.ConstructFromStartEndCenter( arcEnd, aP1, arcCenter, sh == sw );
 pl.Append( arc );
 }
 }
 break;
 }

 pl.Simplify();
 return pl;
}