/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright (C) 2014 Jean-Pierre Charras, jp.charras at wanadoo.fr
* Copyright (C) 2014-2017 KiCad Developers, see CHANGELOG.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
*/
/************************************/
/* routines to handle bezier curves */
/************************************/
#include <fctsys.h>
#include <bezier_curves.h>
static inline double calc_sq_distance( int x1, int y1, int x2, int y2 )
{
int dx = x2 - x1;
int dy = y2 - y1;
return (double)dx * dx + (double)dy * dy;
}
static inline double sqrt_len( int dx, int dy )
{
return ((double)dx * dx) + ((double)dy * dy);
}
void BEZIER_POLY::GetPoly( std::vector<wxPoint>& aOutput )
{
wxCHECK( !m_ctrlPts.empty(), /* void */ );
m_output = &aOutput;
m_output->clear();
m_output->push_back( wxPoint( m_ctrlPts.front() ) );
// Only quadratic and cubic Bezier curves are handled
if( m_ctrlPts.size() == 3 )
recursiveBezier( m_ctrlPts[0].x, m_ctrlPts[0].y,
m_ctrlPts[1].x, m_ctrlPts[1].y,
m_ctrlPts[2].x, m_ctrlPts[2].y, 0 );
else if( m_ctrlPts.size() == 4 )
recursiveBezier( m_ctrlPts[0].x, m_ctrlPts[0].y,
m_ctrlPts[1].x, m_ctrlPts[1].y,
m_ctrlPts[2].x, m_ctrlPts[2].y,
m_ctrlPts[3].x, m_ctrlPts[3].y, 0 );
m_output->push_back( wxPoint( m_ctrlPts.back() ) );
}
void BEZIER_POLY::recursiveBezier( int x1, int y1, int x2, int y2, int x3, int y3, unsigned int level )
{
if( level > recursion_limit )
return;
// Calculate all the mid-points of the line segments
//----------------------
int x12 = (x1 + x2) / 2;
int y12 = (y1 + y2) / 2;
int x23 = (x2 + x3) / 2;
int y23 = (y2 + y3) / 2;
int x123 = (x12 + x23) / 2;
int y123 = (y12 + y23) / 2;
int dx = x3 - x1;
int dy = y3 - y1;
double d = fabs( ((double) (x2 - x3) * dy) - ((double) (y2 - y3) * dx ) );
double da;
if( d > curve_collinearity_epsilon )
{
// Regular case
//-----------------
if( d * d <= distance_tolerance_square * (dx * dx + dy * dy) )
{
// If the curvature doesn't exceed the distance_tolerance value
// we tend to finish subdivisions.
//----------------------
if( angle_tolerance < curve_angle_tolerance_epsilon )
{
addSegment( wxPoint( x123, y123 ) );
return;
}
// Angle & Cusp Condition
//----------------------
da = fabs( atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) -
atan2( (double) ( y2 - y1 ), (double) ( x2 - x1 ) ) );
if( da >=M_PI )
da = 2 * M_PI - da;
if( da < angle_tolerance )
{
// Finally we can stop the recursion
//----------------------
addSegment( wxPoint( x123, y123 ) );
return;
}
}
}
else
{
// Collinear case
//------------------
da = sqrt_len(dx, dy);
if( da == 0 )
{
d = calc_sq_distance( x1, y1, x2, y2 );
}
else
{
d = ( (double)(x2 - x1) * dx + (double)(y2 - y1) * dy ) / da;
if( d > 0 && d < 1 )
{
// Simple collinear case, 1---2---3
// We can leave just two endpoints
return;
}
if( d <= 0 )
d = calc_sq_distance( x2, y2, x1, y1 );
else if( d >= 1 )
d = calc_sq_distance( x2, y2, x3, y3 );
else
d = calc_sq_distance( x2, y2, x1 + (int) d * dx,
y1 + (int) d * dy );
}
if( d < distance_tolerance_square )
{
addSegment( wxPoint( x2, y2 ) );
return;
}
}
// Continue subdivision
//----------------------
recursiveBezier( x1, y1, x12, y12, x123, y123, level + 1 );
recursiveBezier( x123, y123, x23, y23, x3, y3, -(level + 1) );
}
void BEZIER_POLY::recursiveBezier( int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4, unsigned int level )
{
if( level > recursion_limit )
return;
// Calculate all the mid-points of the line segments
//----------------------
int x12 = (x1 + x2) / 2;
int y12 = (y1 + y2) / 2;
int x23 = (x2 + x3) / 2;
int y23 = (y2 + y3) / 2;
int x34 = (x3 + x4) / 2;
int y34 = (y3 + y4) / 2;
int x123 = (x12 + x23) / 2;
int y123 = (y12 + y23) / 2;
int x234 = (x23 + x34) / 2;
int y234 = (y23 + y34) / 2;
int x1234 = (x123 + x234) / 2;
int y1234 = (y123 + y234) / 2;
// Try to approximate the full cubic curve by a single straight line
//------------------
int dx = x4 - x1;
int dy = y4 - y1;
double d2 = fabs( (double) ( (x2 - x4) * dy - (y2 - y4) * dx ) );
double d3 = fabs( (double) ( (x3 - x4) * dy - (y3 - y4) * dx ) );
double da1, da2, k;
switch( (int(d2 > curve_collinearity_epsilon) << 1) +
int(d3 > curve_collinearity_epsilon) )
{
case 0:
// All collinear OR p1==p4
//----------------------
k = dx * dx + dy * dy;
if( k == 0 )
{
d2 = calc_sq_distance( x1, y1, x2, y2 );
d3 = calc_sq_distance( x4, y4, x3, y3 );
}
else
{
k = 1 / k;
da1 = x2 - x1;
da2 = y2 - y1;
d2 = k * (da1 * dx + da2 * dy);
da1 = x3 - x1;
da2 = y3 - y1;
d3 = k * (da1 * dx + da2 * dy);
if( d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1 )
{
// Simple collinear case, 1---2---3---4
// We can leave just two endpoints
return;
}
if( d2 <= 0 )
d2 = calc_sq_distance( x2, y2, x1, y1 );
else if( d2 >= 1 )
d2 = calc_sq_distance( x2, y2, x4, y4 );
else
d2 = calc_sq_distance( x2, y2, x1 + (int) d2 * dx,
y1 + (int) d2 * dy );
if( d3 <= 0 )
d3 = calc_sq_distance( x3, y3, x1, y1 );
else if( d3 >= 1 )
d3 = calc_sq_distance( x3, y3, x4, y4 );
else
d3 = calc_sq_distance( x3, y3, x1 + (int) d3 * dx,
y1 + (int) d3 * dy );
}
if( d2 > d3 )
{
if( d2 < distance_tolerance_square )
{
addSegment( wxPoint( x2, y2 ) );
return;
}
}
else
{
if( d3 < distance_tolerance_square )
{
addSegment( wxPoint( x3, y3 ) );
return;
}
}
break;
case 1:
// p1,p2,p4 are collinear, p3 is significant
//----------------------
if( d3 * d3 <= distance_tolerance_square * sqrt_len(dx, dy) )
{
if( angle_tolerance < curve_angle_tolerance_epsilon )
{
addSegment( wxPoint( x23, y23 ) );
return;
}
// Angle Condition
//----------------------
da1 = fabs( atan2( (double) ( y4 - y3 ), (double) ( x4 - x3 ) ) -
atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) );
if( da1 >= M_PI )
da1 = 2 * M_PI - da1;
if( da1 < angle_tolerance )
{
addSegment( wxPoint( x2, y2 ) );
addSegment( wxPoint( x3, y3 ) );
return;
}
if( cusp_limit != 0.0 )
{
if( da1 > cusp_limit )
{
addSegment( wxPoint( x3, y3 ) );
return;
}
}
}
break;
case 2:
// p1,p3,p4 are collinear, p2 is significant
//----------------------
if( d2 * d2 <= distance_tolerance_square * sqrt_len(dx, dy) )
{
if( angle_tolerance < curve_angle_tolerance_epsilon )
{
addSegment( wxPoint( x23, y23 ) );
return;
}
// Angle Condition
//----------------------
da1 = fabs( atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) ) -
atan2( (double) ( y2 - y1 ), (double) ( x2 - x1 ) ) );
if( da1 >= M_PI )
da1 = 2 * M_PI - da1;
if( da1 < angle_tolerance )
{
addSegment( wxPoint( x2, y2 ) );
addSegment( wxPoint( x3, y3 ) );
return;
}
if( cusp_limit != 0.0 )
{
if( da1 > cusp_limit )
{
addSegment( wxPoint( x2, y2 ) );
return;
}
}
}
break;
case 3:
// Regular case
//-----------------
if( (d2 + d3) * (d2 + d3) <= distance_tolerance_square * sqrt_len(dx, dy) )
{
// If the curvature doesn't exceed the distance_tolerance value
// we tend to finish subdivisions.
//----------------------
if( angle_tolerance < curve_angle_tolerance_epsilon )
{
addSegment( wxPoint( x23, y23 ) );
return;
}
// Angle & Cusp Condition
//----------------------
k = atan2( (double) ( y3 - y2 ), (double) ( x3 - x2 ) );
da1 = fabs( k - atan2( (double) ( y2 - y1 ),
(double) ( x2 - x1 ) ) );
da2 = fabs( atan2( (double) ( y4 - y3 ),
(double) ( x4 - x3 ) ) - k );
if( da1 >= M_PI )
da1 = 2 * M_PI - da1;
if( da2 >= M_PI )
da2 = 2 * M_PI - da2;
if( da1 + da2 < angle_tolerance )
{
// Finally we can stop the recursion
//----------------------
addSegment( wxPoint( x23, y23 ) );
return;
}
if( cusp_limit != 0.0 )
{
if( da1 > cusp_limit )
{
addSegment( wxPoint( x2, y2 ) );
return;
}
if( da2 > cusp_limit )
{
addSegment( wxPoint( x3, y3 ) );
return;
}
}
}
break;
}
// Continue subdivision
//----------------------
recursiveBezier( x1, y1, x12, y12, x123, y123, x1234, y1234, level + 1 );
recursiveBezier( x1234, y1234, x234, y234, x34, y34, x4, y4, level + 1 );
}