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Thorsten Behrens
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131
basegfx/inc/basegfx/curve/b2dbeziertools.hxx
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131
basegfx/inc/basegfx/curve/b2dbeziertools.hxx
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/*************************************************************************
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*
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* $RCSfile: b2dbeziertools.hxx,v $
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*
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* $Revision: 1.1 $
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*
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* last change: $Author: thb $ $Date: 2003-11-10 13:33:07 $
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*
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* The Contents of this file are made available subject to the terms of
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* either of the following licenses
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*
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* - GNU Lesser General Public License Version 2.1
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* - Sun Industry Standards Source License Version 1.1
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*
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* Sun Microsystems Inc., October, 2000
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*
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* GNU Lesser General Public License Version 2.1
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* =============================================
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* Copyright 2000 by Sun Microsystems, Inc.
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* 901 San Antonio Road, Palo Alto, CA 94303, USA
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License version 2.1, as published by the Free Software Foundation.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston,
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* MA 02111-1307 USA
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*
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*
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* Sun Industry Standards Source License Version 1.1
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* =================================================
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* The contents of this file are subject to the Sun Industry Standards
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* Source License Version 1.1 (the "License"); You may not use this file
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* except in compliance with the License. You may obtain a copy of the
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* License at http://www.openoffice.org/license.html.
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*
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* Software provided under this License is provided on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
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* WITHOUT LIMITATION, WARRANTIES THAT THE SOFTWARE IS FREE OF DEFECTS,
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* MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE, OR NON-INFRINGING.
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* See the License for the specific provisions governing your rights and
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* obligations concerning the Software.
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*
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* The Initial Developer of the Original Code is: Sun Microsystems, Inc.
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*
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* Copyright: 2000 by Sun Microsystems, Inc.
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*
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* All Rights Reserved.
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*
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* Contributor(s): _______________________________________
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*
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*
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************************************************************************/
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#ifndef _BGFX_CURVE_B2DBEZIERTOOLS_HXX
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#define _BGFX_CURVE_B2DBEZIERTOOLS_HXX
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//////////////////////////////////////////////////////////////////////////////
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namespace basegfx
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{
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namespace polygon
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{
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class B2DPolygon;
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}
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namespace curve
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{
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class B2DCubicBezier;
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class B2DQuadraticBezier;
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/** Subdivide given cubic bezier segment.
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This function adaptively subdivides the given bezier
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segment into as much straight line segments, such that the
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maximal orthogonal distance from any of the segments to
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the true curve is less than the given error value.
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@param rPoly
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Output polygon. The subdivided bezier segment is added to
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this polygon via B2DPolygon::append().
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@param rCurve
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The cubic bezier curve to subdivide
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@param distanceBounds
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Bounds on the maximal distance of the approximation to the
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true curve
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@return the number of line segments created
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*/
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int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
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const B2DCubicBezier& rCurve,
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double distanceBounds );
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/** Subdivide given quadratic bezier segment.
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This function adaptively subdivides the given bezier
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segment into as much straight line segments, such that the
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maximal orthogonal distance from any of the segments to
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the true curve is less than the given error value.
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@param rPoly
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Output polygon. The subdivided bezier segment is added to
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this polygon via B2DPolygon::append().
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@param rCurve
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The cubic bezier curve to subdivide
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@param distanceBounds
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Bounds on the maximal distance of the approximation to the
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true curve
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@return the number of line segments created
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*/
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int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
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const B2DQuadraticBezier& rCurve,
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double distanceBounds );
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}
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}
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#endif // _BGFX_CURVE_B2DBEZIERTOOLS_HXX2
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216
basegfx/source/curve/b2dbeziertools.cxx
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216
basegfx/source/curve/b2dbeziertools.cxx
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/*************************************************************************
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*
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* $RCSfile: b2dbeziertools.cxx,v $
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*
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* $Revision: 1.1 $
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*
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* last change: $Author: thb $ $Date: 2003-11-10 13:32:04 $
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*
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* The Contents of this file are made available subject to the terms of
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* either of the following licenses
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*
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* - GNU Lesser General Public License Version 2.1
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* - Sun Industry Standards Source License Version 1.1
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*
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* Sun Microsystems Inc., October, 2000
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*
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* GNU Lesser General Public License Version 2.1
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* =============================================
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* Copyright 2000 by Sun Microsystems, Inc.
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* 901 San Antonio Road, Palo Alto, CA 94303, USA
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License version 2.1, as published by the Free Software Foundation.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston,
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* MA 02111-1307 USA
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*
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*
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* Sun Industry Standards Source License Version 1.1
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* =================================================
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* The contents of this file are subject to the Sun Industry Standards
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* Source License Version 1.1 (the "License"); You may not use this file
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* except in compliance with the License. You may obtain a copy of the
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* License at http://www.openoffice.org/license.html.
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*
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* Software provided under this License is provided on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
|
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* WITHOUT LIMITATION, WARRANTIES THAT THE SOFTWARE IS FREE OF DEFECTS,
|
||||
* MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE, OR NON-INFRINGING.
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* See the License for the specific provisions governing your rights and
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* obligations concerning the Software.
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*
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* The Initial Developer of the Original Code is: Sun Microsystems, Inc.
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*
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* Copyright: 2000 by Sun Microsystems, Inc.
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*
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* All Rights Reserved.
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*
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* Contributor(s): _______________________________________
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*
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*
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************************************************************************/
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#include <limits>
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#include <algorithm>
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#include <basegfx/curve/b2dbeziertools.hxx>
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#ifndef _BGFX_CURVE_B2DCUBICBEZIER_HXX
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#include <basegfx/curve/b2dcubicbezier.hxx>
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#endif
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#ifndef _BGFX_CURVE_B2DQUADRATICBEZIER_HXX
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#include <basegfx/curve/b2dquadraticbezier.hxx>
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#endif
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#ifndef _BGFX_POLYGON_B2DPOLYGON_HXX
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#include <basegfx/polygon/b2dpolygon.hxx>
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#endif
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#ifndef _BGFX_POINT_B2DPOINT_HXX
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#include <basegfx/point/b2dpoint.hxx>
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#endif
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namespace basegfx
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{
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namespace curve
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{
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namespace
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{
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/* Recursively subdivide cubic bezier curve via deCasteljau.
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@param rPoly
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Polygon to append generated points to
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@param d2
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Maximal squared difference of curve to a straight line
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@param P*
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Exactly four points, interpreted as support and control points of
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a cubic bezier curve.
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@param old_distance2
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Last squared distance to line for this recursion
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path. Used as an end condition, if it is no longer
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improving.
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@param recursionDepth
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Depth of recursion. Used as a termination criterion, to
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prevent endless looping.
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*/
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int ImplAdaptiveSubdivide( polygon::B2DPolygon& rPoly,
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const double d2,
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const double P1x, const double P1y,
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const double P2x, const double P2y,
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const double P3x, const double P3y,
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const double P4x, const double P4y,
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const double old_distance2,
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int recursionDepth )
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{
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// Hard limit on recursion depth, empiric number.
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enum {maxRecursionDepth=128};
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// Perform bezier flatness test (lecture notes from R. Schaback,
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// Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
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//
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// ||P(t) - L(t)|| <= max ||b_j - b_0 - j/n(b_n - b_0)||
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// 0<=j<=n
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//
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// What is calculated here is an upper bound to the distance from
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// a line through b_0 and b_3 (P1 and P4 in our notation) and the
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// curve. We can drop 0 and n from the running indices, since the
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// argument of max becomes zero for those cases.
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const double fJ1x( P2x - P1x - 1.0/3.0*(P4x - P1x) );
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const double fJ1y( P2y - P1y - 1.0/3.0*(P4y - P1y) );
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const double fJ2x( P3x - P1x - 2.0/3.0*(P4x - P1x) );
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const double fJ2y( P3y - P1y - 2.0/3.0*(P4y - P1y) );
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const double distance2( ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
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fJ2x*fJ2x + fJ2y*fJ2y) );
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// stop if error measure does not improve anymore. This is a
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// safety guard against floating point inaccuracies.
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// stop at recursion level 128. This is a safety guard against
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// floating point inaccuracies.
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// stop if distance from line is guaranteed to be bounded by d
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if( old_distance2 > d2 &&
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recursionDepth < maxRecursionDepth &&
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distance2 >= d2 )
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{
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// deCasteljau bezier arc, split at t=0.5
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// Foley/vanDam, p. 508
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const double L1x( P1x ), L1y( P1y );
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const double L2x( (P1x + P2x)*0.5 ), L2y( (P1y + P2y)*0.5 );
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const double Hx ( (P2x + P3x)*0.5 ), Hy ( (P2y + P3y)*0.5 );
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const double L3x( (L2x + Hx)*0.5 ), L3y( (L2y + Hy)*0.5 );
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const double R4x( P4x ), R4y( P4y );
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const double R3x( (P3x + P4x)*0.5 ), R3y( (P3y + P4y)*0.5 );
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const double R2x( (Hx + R3x)*0.5 ), R2y( (Hy + R3y)*0.5 );
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const double R1x( (L3x + R2x)*0.5 ), R1y( (L3y + R2y)*0.5 );
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const double L4x( R1x ), L4y( R1y );
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// subdivide further
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++recursionDepth;
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int nGeneratedPoints(0);
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nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, L1x, L1y, L2x, L2y, L3x, L3y, L4x, L4y, distance2, recursionDepth);
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nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, R1x, R1y, R2x, R2y, R3x, R3y, R4x, R4y, distance2, recursionDepth);
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// return number of points generated in this
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// recursion branch
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return nGeneratedPoints;
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}
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else
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{
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// requested resolution reached. Add end points to
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// output iterator. order is preserved, since
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// this is so to say depth first traversal.
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rPoly.append( point::B2DPoint( P1x, P1y ) );
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// return number of points generated in this
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// recursion branch
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return 1;
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}
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}
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}
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int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
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const B2DCubicBezier& rCurve,
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double distanceBounds )
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{
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const double distance2( distanceBounds*distanceBounds );
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const point::B2DPoint start( rCurve.getStartPoint() );
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const point::B2DPoint control1( rCurve.getControlPointA() );
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const point::B2DPoint control2( rCurve.getControlPointB() );
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const point::B2DPoint end( rCurve.getEndPoint() );
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return ImplAdaptiveSubdivide( rPoly,
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distance2,
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start.getX(), start.getY(),
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control1.getX(), control1.getY(),
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control2.getX(), control2.getY(),
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end.getX(), end.getY(),
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::std::numeric_limits<double>::max(),
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0 );
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}
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int adaptiveSubdivide( polygon::B2DPolygon& rPoly,
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const B2DQuadraticBezier& rCurve,
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double distanceBounds )
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{
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// TODO
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return 0;
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}
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}
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}
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