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/*************************************************************************
*
* $RCSfile: b2dbeziertools.cxx,v $
*
* $Revision: 1.1 $
*
* last change: $Author: thb $ $Date: 2003-11-10 13:32:04 $
*
* The Contents of this file are made available subject to the terms of
* either of the following licenses
*
* - GNU Lesser General Public License Version 2.1
* - Sun Industry Standards Source License Version 1.1
*
* Sun Microsystems Inc., October, 2000
*
* GNU Lesser General Public License Version 2.1
* =============================================
* Copyright 2000 by Sun Microsystems, Inc.
* 901 San Antonio Road, Palo Alto, CA 94303, USA
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License version 2.1, as published by the Free Software Foundation.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston,
* MA 02111-1307 USA
*
*
* Sun Industry Standards Source License Version 1.1
* =================================================
* The contents of this file are subject to the Sun Industry Standards
* Source License Version 1.1 (the "License"); You may not use this file
* except in compliance with the License. You may obtain a copy of the
* License at http://www.openoffice.org/license.html.
*
* Software provided under this License is provided on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
* WITHOUT LIMITATION, WARRANTIES THAT THE SOFTWARE IS FREE OF DEFECTS,
* MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE, OR NON-INFRINGING.
* See the License for the specific provisions governing your rights and
* obligations concerning the Software.
*
* The Initial Developer of the Original Code is: Sun Microsystems, Inc.
*
* Copyright: 2000 by Sun Microsystems, Inc.
*
* All Rights Reserved.
*
* Contributor(s): _______________________________________
*
*
************************************************************************/
#include <limits>
#include <algorithm>
#include <basegfx/curve/b2dbeziertools.hxx>
#ifndef _BGFX_CURVE_B2DCUBICBEZIER_HXX
#include <basegfx/curve/b2dcubicbezier.hxx>
#endif
#ifndef _BGFX_CURVE_B2DQUADRATICBEZIER_HXX
#include <basegfx/curve/b2dquadraticbezier.hxx>
#endif
#ifndef _BGFX_POLYGON_B2DPOLYGON_HXX
#include <basegfx/polygon/b2dpolygon.hxx>
#endif
#ifndef _BGFX_POINT_B2DPOINT_HXX
#include <basegfx/point/b2dpoint.hxx>
#endif
namespace basegfx
{
namespace curve
{
namespace
{
/* Recursively subdivide cubic bezier curve via deCasteljau.
@param rPoly
Polygon to append generated points to
@param d2
Maximal squared difference of curve to a straight line
@param P*
Exactly four points, interpreted as support and control points of
a cubic bezier curve.
@param old_distance2
Last squared distance to line for this recursion
path. Used as an end condition, if it is no longer
improving.
@param recursionDepth
Depth of recursion. Used as a termination criterion, to
prevent endless looping.
*/
int ImplAdaptiveSubdivide( polygon::B2DPolygon& rPoly,
const double d2,
const double P1x, const double P1y,
const double P2x, const double P2y,
const double P3x, const double P3y,
const double P4x, const double P4y,
const double old_distance2,
int recursionDepth )
{
// Hard limit on recursion depth, empiric number.
enum {maxRecursionDepth=128};
// Perform bezier flatness test (lecture notes from R. Schaback,
// Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
//
// ||P(t) - L(t)|| <= max ||b_j - b_0 - j/n(b_n - b_0)||
// 0<=j<=n
//
// What is calculated here is an upper bound to the distance from
// a line through b_0 and b_3 (P1 and P4 in our notation) and the
// curve. We can drop 0 and n from the running indices, since the
// argument of max becomes zero for those cases.
const double fJ1x( P2x - P1x - 1.0/3.0*(P4x - P1x) );
const double fJ1y( P2y - P1y - 1.0/3.0*(P4y - P1y) );
const double fJ2x( P3x - P1x - 2.0/3.0*(P4x - P1x) );
const double fJ2y( P3y - P1y - 2.0/3.0*(P4y - P1y) );
const double distance2( ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
fJ2x*fJ2x + fJ2y*fJ2y) );
// stop if error measure does not improve anymore. This is a
// safety guard against floating point inaccuracies.
// stop at recursion level 128. This is a safety guard against
// floating point inaccuracies.
// stop if distance from line is guaranteed to be bounded by d
if( old_distance2 > d2 &&
recursionDepth < maxRecursionDepth &&
distance2 >= d2 )
{
// deCasteljau bezier arc, split at t=0.5
// Foley/vanDam, p. 508
const double L1x( P1x ), L1y( P1y );
const double L2x( (P1x + P2x)*0.5 ), L2y( (P1y + P2y)*0.5 );
const double Hx ( (P2x + P3x)*0.5 ), Hy ( (P2y + P3y)*0.5 );
const double L3x( (L2x + Hx)*0.5 ), L3y( (L2y + Hy)*0.5 );
const double R4x( P4x ), R4y( P4y );
const double R3x( (P3x + P4x)*0.5 ), R3y( (P3y + P4y)*0.5 );
const double R2x( (Hx + R3x)*0.5 ), R2y( (Hy + R3y)*0.5 );
const double R1x( (L3x + R2x)*0.5 ), R1y( (L3y + R2y)*0.5 );
const double L4x( R1x ), L4y( R1y );
// subdivide further
++recursionDepth;
int nGeneratedPoints(0);
nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, L1x, L1y, L2x, L2y, L3x, L3y, L4x, L4y, distance2, recursionDepth);
nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, R1x, R1y, R2x, R2y, R3x, R3y, R4x, R4y, distance2, recursionDepth);
// return number of points generated in this
// recursion branch
return nGeneratedPoints;
}
else
{
// requested resolution reached. Add end points to
// output iterator. order is preserved, since
// this is so to say depth first traversal.
rPoly.append( point::B2DPoint( P1x, P1y ) );
// return number of points generated in this
// recursion branch
return 1;
}
}
}
int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
const B2DCubicBezier& rCurve,
double distanceBounds )
{
const double distance2( distanceBounds*distanceBounds );
const point::B2DPoint start( rCurve.getStartPoint() );
const point::B2DPoint control1( rCurve.getControlPointA() );
const point::B2DPoint control2( rCurve.getControlPointB() );
const point::B2DPoint end( rCurve.getEndPoint() );
return ImplAdaptiveSubdivide( rPoly,
distance2,
start.getX(), start.getY(),
control1.getX(), control1.getY(),
control2.getX(), control2.getY(),
end.getX(), end.getY(),
::std::numeric_limits<double>::max(),
0 );
}
int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
const B2DQuadraticBezier& rCurve,
double distanceBounds )
{
// TODO
return 0;
}
}
}
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