2010-06-10 18:43:12 +00:00
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/*
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* This program source code file is part of KICAD, a free EDA CAD application.
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*
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* Copyright (C) 1992-2010 jean-pierre.charras
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* Copyright (C) 1992-2010 Kicad Developers, see change_log.txt for contributors.
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program 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
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, you may find one here:
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* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
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* or you may search the http://www.gnu.org website for the version 2 license,
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* or you may write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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*/
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#include "kbool/booleng.h"
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#include <stdio.h>
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#include <string.h>
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#include <errno.h>
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#include <stdlib.h>
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#include <math.h>
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#include <vector>
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#include "potracelib.h"
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#include "auxiliary.h"
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#ifndef max
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#define max( a, b ) ( ( (a) > (b) ) ? (a) : (b) )
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#endif
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#ifndef min
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#define min( a, b ) ( ( (a) < (b) ) ? (a) : (b) )
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#endif
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enum output_format {
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POSTSCRIPT_FMT = 1,
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PCBNEW_FMT,
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EESCHEMA_FMT
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};
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2010-06-15 18:27:41 +00:00
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/* free a potrace bitmap */
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static void bm_free(potrace_bitmap_t *bm) {
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if (bm != NULL) {
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free(bm->map);
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}
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free(bm);
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}
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2010-06-10 18:43:12 +00:00
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/* Helper class th handle useful info to convert a bitmpa to
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* a polygonal object description
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*/
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class BITMAPCONV_INFO
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{
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public:
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enum output_format m_Format;
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int m_PixmapWidth;
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int m_PixmapHeight; // the bitmap size in pixels
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double m_ScaleX;
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double m_ScaleY; // the conversion scale
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potrace_path_t* m_Paths; // the list of paths, from potrace (list of lines and bezier curves)
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FILE* m_Outfile;
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public:
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BITMAPCONV_INFO();
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};
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static void BezierToPolyline( std::vector <potrace_dpoint_t>& aCornersBuffer,
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potrace_dpoint_t p1,
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potrace_dpoint_t p2,
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potrace_dpoint_t p3,
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potrace_dpoint_t p4 );
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static void CreateOutputFile( BITMAPCONV_INFO& aInfo );
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static const char* CmpName = "LOGO";
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BITMAPCONV_INFO::BITMAPCONV_INFO()
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{
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m_Format = POSTSCRIPT_FMT;
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m_PixmapWidth = 0;
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m_PixmapHeight = 0;
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m_ScaleX = 1.0;
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m_ScaleY = 1.0;
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m_Paths = NULL;
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m_Outfile = NULL;
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}
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2010-11-12 16:36:43 +00:00
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/**
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* Function ArmBoolEng
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2010-06-10 18:43:12 +00:00
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* Initialise parameters used in kbool
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* @param aBooleng = pointer to the Bool_Engine to initialise
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* @param aConvertHoles = mode for holes when a boolean operation is made
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* true: in resulting polygon, holes are linked into outer contours by double overlapping segments
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* false: in resulting polygons, holes are not linked: they are separate polygons
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*/
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void ArmBoolEng( Bool_Engine* aBooleng, bool aConvertHoles )
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{
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// set some global vals to arm the boolean engine
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// input points are scaled up with GetDGrid() * GetGrid()
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// DGRID is only meant to make fractional parts of input data which
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/*
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* The input data scaled up with DGrid is related to the accuracy the user has in his input data.
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* User data with a minimum accuracy of 0.001, means set the DGrid to 1000.
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* The input data may contain data with a minimum accuracy much smaller, but by setting the DGrid
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* everything smaller than 1/DGrid is rounded.
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*
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* DGRID is only meant to make fractional parts of input data which can be
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* doubles, part of the integers used in vertexes within the boolean algorithm.
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* And therefore DGRID bigger than 1 is not usefull, you would only loose accuracy.
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* Within the algorithm all input data is multiplied with DGRID, and the result
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* is rounded to an integer.
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*/
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double DGRID = 1000.0; // round coordinate X or Y value in calculations to this (initial value = 1000.0 in kbool example)
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// kbool uses DGRID to convert float user units to integer
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// kbool unit = (int)(user unit * DGRID)
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// Note: in kicad, coordinates are already integer so DGRID could be set to 1
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// we can choose 1.0,
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// but choose DGRID = 1000.0 solves some filling problems
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// (perhaps because this allows a better precision in kbool internal calculations
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double MARGE = 1.0 / DGRID; // snap with in this range points to lines in the intersection routines
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// should always be >= 1/DGRID a MARGE >= 10/DGRID is ok
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// this is also used to remove small segments and to decide when
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// two segments are in line. ( initial value = 0.001 )
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// For kicad we choose MARGE = 1/DGRID
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double CORRECTIONFACTOR = 0.0; // correct the polygons by this number: used in BOOL_CORRECTION operation
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// this operation shrinks a polygon if CORRECTIONFACTOR < 0
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// or stretch it if CORRECTIONFACTOR > 0
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// the size change is CORRECTIONFACTOR (holes are correctly handled)
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double CORRECTIONABER = 1.0; // the accuracy for the rounded shapes used in correction
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double ROUNDFACTOR = 1.5; // when will we round the correction shape to a circle
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double SMOOTHABER = 10.0; // accuracy when smoothing a polygon
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double MAXLINEMERGE = 1000.0; // leave as is, segments of this length in smoothen
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/*
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* Grid makes sure that the integer data used within the algorithm has room for extra intersections
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* smaller than the smallest number within the input data.
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* The input data scaled up with DGrid is related to the accuracy the user has in his input data.
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* Another scaling with Grid is applied on top of it to create space in the integer number for
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* even smaller numbers.
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*/
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2010-10-08 20:40:57 +00:00
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int GRID = (int) ( 10000 / DGRID ); // initial value = 10000 in kbool example
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2010-06-10 18:43:12 +00:00
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// But we use 10000/DGRID because the scalling is made
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// by DGRID on integer pcbnew units and
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// the global scalling ( GRID*DGRID) must be < 30000 to avoid
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// overflow in calculations (made in long long in kbool)
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if( GRID <= 1 ) // Cannot be null!
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GRID = 1;
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aBooleng->SetMarge( MARGE );
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aBooleng->SetGrid( GRID );
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aBooleng->SetDGrid( DGRID );
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aBooleng->SetCorrectionFactor( CORRECTIONFACTOR );
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aBooleng->SetCorrectionAber( CORRECTIONABER );
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aBooleng->SetSmoothAber( SMOOTHABER );
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aBooleng->SetMaxlinemerge( MAXLINEMERGE );
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aBooleng->SetRoundfactor( ROUNDFACTOR );
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aBooleng->SetWindingRule( true ); // This is the default kbool value
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if( aConvertHoles )
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{
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#if 1 // Can be set to 1 for kbool version >= 2.1, must be set to 0 for previous versions
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// SetAllowNonTopHoleLinking() exists only in kbool >= 2.1
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aBooleng->SetAllowNonTopHoleLinking( false ); // Default = , but i have problems (filling errors) when true
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#endif
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aBooleng->SetLinkHoles( true ); // holes will be connected by double overlapping segments
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aBooleng->SetOrientationEntryMode( false ); // all polygons are contours, not holes
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}
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else
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{
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aBooleng->SetLinkHoles( false ); // holes will not be connected by double overlapping segments
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aBooleng->SetOrientationEntryMode( true ); // holes are entered counter clockwise
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}
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}
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2010-06-15 18:27:41 +00:00
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int bitmap2component( potrace_bitmap_t* aPotrace_bitmap, FILE * aOutfile, int aFormat )
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2010-06-10 18:43:12 +00:00
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{
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potrace_param_t* param;
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potrace_state_t* st;
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/* set tracing parameters, starting from defaults */
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param = potrace_param_default();
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if( !param )
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{
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fprintf( stderr, "Error allocating parameters: %s\n", strerror( errno ) );
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return 1;
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}
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param->turdsize = 0;
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/* convert the bitmap to curves */
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2010-06-15 18:27:41 +00:00
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st = potrace_trace( param, aPotrace_bitmap );
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2010-06-10 18:43:12 +00:00
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if( !st || st->status != POTRACE_STATUS_OK )
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{
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fprintf( stderr, "Error tracing bitmap: %s\n", strerror( errno ) );
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return 1;
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}
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BITMAPCONV_INFO info;
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2010-06-15 18:27:41 +00:00
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info.m_PixmapWidth = aPotrace_bitmap->w;
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info.m_PixmapHeight = aPotrace_bitmap->h; // the bitmap size in pixels
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2010-06-10 18:43:12 +00:00
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info.m_Paths = st->plist;
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2010-06-15 18:27:41 +00:00
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info.m_Outfile = aOutfile;
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2010-06-10 18:43:12 +00:00
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2010-06-15 18:27:41 +00:00
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switch( aFormat )
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2010-06-10 18:43:12 +00:00
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{
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2010-06-15 18:27:41 +00:00
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case 2:
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2010-06-10 18:43:12 +00:00
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info.m_Format = POSTSCRIPT_FMT;
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info.m_ScaleX = info.m_ScaleY = 1.0; // the conversion scale
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/* output vector data, e.g. as a rudimentary EPS file */
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2010-06-15 18:27:41 +00:00
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CreateOutputFile( info );
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2010-06-10 18:43:12 +00:00
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break;
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2010-06-15 18:27:41 +00:00
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case 1:
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2010-06-10 18:43:12 +00:00
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info.m_Format = EESCHEMA_FMT;
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2010-06-15 18:27:41 +00:00
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info.m_ScaleX = 1000.0 / 300; // the conversion scale
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info.m_ScaleY = - info.m_ScaleX; // Y axis is bottom to Top for components in libs
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CreateOutputFile( info );
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2010-06-10 18:43:12 +00:00
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break;
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2010-06-15 18:27:41 +00:00
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case 0:
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2010-06-10 18:43:12 +00:00
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info.m_Format = PCBNEW_FMT;
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2010-06-15 18:27:41 +00:00
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info.m_ScaleX = 10000.0 / 300; // the conversion scale
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info.m_ScaleY = info.m_ScaleX; // Y axis is top to bottom in modedit
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CreateOutputFile( info );
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2010-06-10 18:43:12 +00:00
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break;
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default:
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2010-06-15 18:27:41 +00:00
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break;
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2010-06-10 18:43:12 +00:00
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}
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2010-06-15 18:27:41 +00:00
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bm_free( aPotrace_bitmap );
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2010-06-10 18:43:12 +00:00
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potrace_state_free( st );
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potrace_param_free( param );
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return 0;
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}
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static void OuputHeader( BITMAPCONV_INFO& aInfo )
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{
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int Ypos = (int) ( aInfo.m_PixmapHeight / 2 * aInfo.m_ScaleY );
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int fieldSize; // fields text size = 60 mils
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switch( aInfo.m_Format )
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{
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case POSTSCRIPT_FMT:
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/* output vector data, e.g. as a rudimentary EPS file */
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fprintf( aInfo.m_Outfile, "%%!PS-Adobe-3.0 EPSF-3.0\n" );
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fprintf( aInfo.m_Outfile, "%%%%BoundingBox: 0 0 %d %d\n",
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aInfo.m_PixmapWidth, aInfo.m_PixmapHeight );
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fprintf( aInfo.m_Outfile, "gsave\n" );
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break;
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case PCBNEW_FMT:
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#define FIELD_LAYER 21
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fieldSize = 600; // fields text size = 60 mils
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Ypos += fieldSize / 2;
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fprintf( aInfo.m_Outfile, "PCBNEW-LibModule-V1\n" );
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fprintf( aInfo.m_Outfile, "$INDEX\n%s\n$EndINDEX\n", CmpName );
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fprintf( aInfo.m_Outfile, "#\n# %s\n", CmpName );
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fprintf( aInfo.m_Outfile, "# pixmap w = %d, h = %d\n#\n",
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aInfo.m_PixmapWidth, aInfo.m_PixmapHeight );
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fprintf( aInfo.m_Outfile, "$MODULE %s\n", CmpName );
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fprintf( aInfo.m_Outfile, "Po 0 0 0 15 00000000 00000000 ~~\n");
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fprintf( aInfo.m_Outfile, "T0 0 %d %d %d 0 %d N I %d \"G***\"\n",
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Ypos, fieldSize, fieldSize, fieldSize/5, FIELD_LAYER );
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fprintf( aInfo.m_Outfile, "T1 0 %d %d %d 0 %d N I %d \"%s\"\n",
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-Ypos, fieldSize, fieldSize, fieldSize/5, FIELD_LAYER, CmpName );
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break;
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case EESCHEMA_FMT:
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fprintf( aInfo.m_Outfile, "EESchema-LIBRARY Version 2.3\n" );
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fprintf( aInfo.m_Outfile, "#\n# %s\n", CmpName );
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fprintf( aInfo.m_Outfile, "# pixmap size w = %d, h = %d\n#\n",
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aInfo.m_PixmapWidth, aInfo.m_PixmapHeight );
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// print reference and value
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fieldSize = 60; // fields text size = 60 mils
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Ypos += fieldSize / 2;
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fprintf( aInfo.m_Outfile, "DEF %s G 0 40 Y Y 1 F N\n", CmpName );
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fprintf( aInfo.m_Outfile, "F0 \"#G\" 0 %d %d H I C CNN\n", Ypos, fieldSize );
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fprintf( aInfo.m_Outfile, "F1 \"%s\" 0 %d %d H I C CNN\n", CmpName, -Ypos, fieldSize );
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fprintf( aInfo.m_Outfile, "DRAW\n" );
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break;
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}
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}
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static void OuputEnd( BITMAPCONV_INFO& aInfo )
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{
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switch( aInfo.m_Format )
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{
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case POSTSCRIPT_FMT:
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fprintf( aInfo.m_Outfile, "grestore\n" );
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fprintf( aInfo.m_Outfile, "%%EOF\n" );
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break;
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case PCBNEW_FMT:
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fprintf( aInfo.m_Outfile, "$EndMODULE %s\n", CmpName );
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fprintf( aInfo.m_Outfile, "$EndLIBRARY\n" );
|
|
|
|
break;
|
|
|
|
|
|
|
|
case EESCHEMA_FMT:
|
|
|
|
fprintf( aInfo.m_Outfile, "ENDDRAW\n" );
|
|
|
|
fprintf( aInfo.m_Outfile, "ENDDEF\n" );
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
static void OuputOnePolygon( BITMAPCONV_INFO& aInfo,
|
|
|
|
std::vector <potrace_dpoint_t>& aPolygonBuffer )
|
|
|
|
{
|
|
|
|
unsigned ii;
|
|
|
|
|
|
|
|
double offsetX = aInfo.m_PixmapWidth / 2 * aInfo.m_ScaleX;
|
|
|
|
double offsetY = aInfo.m_PixmapHeight / 2 * aInfo.m_ScaleY;
|
|
|
|
|
|
|
|
switch( aInfo.m_Format )
|
|
|
|
{
|
|
|
|
case POSTSCRIPT_FMT:
|
|
|
|
fprintf( aInfo.m_Outfile, "%f %f moveto\n",
|
|
|
|
aPolygonBuffer[0].x * aInfo.m_ScaleX,
|
|
|
|
aPolygonBuffer[0].y * aInfo.m_ScaleY );
|
|
|
|
for( ii = 1; ii < aPolygonBuffer.size(); ii++ )
|
|
|
|
fprintf( aInfo.m_Outfile, "%f %f lineto\n",
|
|
|
|
aPolygonBuffer[ii].x * aInfo.m_ScaleX,
|
|
|
|
aPolygonBuffer[ii].y * aInfo.m_ScaleY );
|
|
|
|
|
|
|
|
fprintf( aInfo.m_Outfile, "0 setgray fill\n" );
|
|
|
|
break;
|
|
|
|
|
|
|
|
case PCBNEW_FMT:
|
|
|
|
{
|
|
|
|
#define SILKSCREEN_N_FRONT 21
|
|
|
|
int layer = SILKSCREEN_N_FRONT;
|
|
|
|
int width = 1;
|
|
|
|
fprintf( aInfo.m_Outfile, "DP %d %d %d %d %d %d %d\n",
|
|
|
|
0, 0, 0, 0,
|
2010-06-12 04:46:34 +00:00
|
|
|
int(aPolygonBuffer.size()+1),
|
2010-06-10 18:43:12 +00:00
|
|
|
width, layer );
|
|
|
|
|
|
|
|
for( ii = 0; ii < aPolygonBuffer.size(); ii++ )
|
|
|
|
fprintf( aInfo.m_Outfile, "Dl %d %d\n",
|
|
|
|
(int) ( aPolygonBuffer[ii].x * aInfo.m_ScaleX - offsetX ),
|
|
|
|
(int) ( aPolygonBuffer[ii].y * aInfo.m_ScaleY - offsetY ) );
|
|
|
|
// Close polygon
|
|
|
|
fprintf( aInfo.m_Outfile, "Dl %d %d\n",
|
|
|
|
(int) ( aPolygonBuffer[0].x * aInfo.m_ScaleX - offsetX ),
|
|
|
|
(int) ( aPolygonBuffer[0].y * aInfo.m_ScaleY - offsetY ) );
|
|
|
|
}
|
|
|
|
break;
|
|
|
|
|
|
|
|
case EESCHEMA_FMT:
|
2010-06-12 04:46:34 +00:00
|
|
|
fprintf( aInfo.m_Outfile, "P %d 0 0 1", int(aPolygonBuffer.size()+1) );
|
2010-06-10 18:43:12 +00:00
|
|
|
for( ii = 0; ii < aPolygonBuffer.size(); ii++ )
|
|
|
|
fprintf( aInfo.m_Outfile, " %d %d",
|
|
|
|
(int) ( aPolygonBuffer[ii].x * aInfo.m_ScaleX - offsetX ),
|
|
|
|
(int) ( aPolygonBuffer[ii].y * aInfo.m_ScaleY - offsetY ) );
|
|
|
|
// Close polygon
|
|
|
|
fprintf( aInfo.m_Outfile, " %d %d",
|
|
|
|
(int) ( aPolygonBuffer[0].x * aInfo.m_ScaleX - offsetX ),
|
|
|
|
(int) ( aPolygonBuffer[0].y * aInfo.m_ScaleY - offsetY ) );
|
|
|
|
|
|
|
|
fprintf( aInfo.m_Outfile, " F\n" );
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
static void CreateOutputFile( BITMAPCONV_INFO& aInfo )
|
|
|
|
{
|
|
|
|
unsigned int i, n;
|
|
|
|
int* tag;
|
|
|
|
|
|
|
|
std::vector <potrace_dpoint_t> cornersBuffer;
|
|
|
|
|
|
|
|
potrace_dpoint_t( *c )[3];
|
|
|
|
OuputHeader( aInfo );
|
|
|
|
|
|
|
|
bool main_outline = true;
|
|
|
|
Bool_Engine* booleng = NULL;
|
|
|
|
|
|
|
|
/* draw each as a polygon with no hole.
|
|
|
|
* Bezier curves are approximated by a polyline
|
|
|
|
*/
|
|
|
|
potrace_path_t* paths = aInfo.m_Paths; // the list of paths
|
|
|
|
while( paths != NULL )
|
|
|
|
{
|
|
|
|
n = paths->curve.n;
|
|
|
|
tag = paths->curve.tag;
|
|
|
|
c = paths->curve.c;
|
|
|
|
potrace_dpoint_t startpoint = c[n - 1][2];
|
|
|
|
cornersBuffer.push_back( startpoint );
|
|
|
|
if( booleng == NULL )
|
|
|
|
{
|
|
|
|
booleng = new Bool_Engine();
|
|
|
|
ArmBoolEng( booleng, true );
|
|
|
|
}
|
|
|
|
for( i = 0; i < n; i++ )
|
|
|
|
{
|
|
|
|
switch( tag[i] )
|
|
|
|
{
|
|
|
|
case POTRACE_CORNER:
|
|
|
|
cornersBuffer.push_back( c[i][1] );
|
|
|
|
cornersBuffer.push_back( c[i][2] );
|
|
|
|
startpoint = c[i][2];
|
|
|
|
break;
|
|
|
|
|
|
|
|
case POTRACE_CURVETO:
|
|
|
|
BezierToPolyline( cornersBuffer, startpoint, c[i][0], c[i][1], c[i][2] );
|
|
|
|
startpoint = c[i][2];
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Store current path
|
|
|
|
if( main_outline )
|
|
|
|
{
|
|
|
|
main_outline = false;
|
|
|
|
booleng->StartPolygonAdd( GROUP_A );
|
|
|
|
for( i = 1; i < cornersBuffer.size(); i++ )
|
|
|
|
booleng->AddPoint( cornersBuffer[i].x, cornersBuffer[i].y );
|
|
|
|
|
|
|
|
booleng->EndPolygonAdd();
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
booleng->StartPolygonAdd( GROUP_B );
|
|
|
|
for( i = 1; i < cornersBuffer.size(); i++ )
|
|
|
|
booleng->AddPoint( cornersBuffer[i].x, cornersBuffer[i].y );
|
|
|
|
|
|
|
|
booleng->EndPolygonAdd();
|
|
|
|
}
|
|
|
|
cornersBuffer.clear();
|
|
|
|
|
|
|
|
/* at the end of a group of a positive path and its negative
|
|
|
|
* children, fill. */
|
|
|
|
if( paths->next == NULL || paths->next->sign == '+' )
|
|
|
|
{
|
|
|
|
booleng->Do_Operation( BOOL_A_SUB_B );
|
|
|
|
std::vector <potrace_dpoint_t> PolygonBuffer;
|
|
|
|
while( booleng->StartPolygonGet() )
|
|
|
|
{
|
|
|
|
potrace_dpoint_t corner;
|
|
|
|
PolygonBuffer.clear();
|
|
|
|
while( booleng->PolygonHasMorePoints() )
|
|
|
|
{
|
|
|
|
corner.x = booleng->GetPolygonXPoint();
|
|
|
|
corner.y = booleng->GetPolygonYPoint();
|
|
|
|
PolygonBuffer.push_back( corner );
|
|
|
|
}
|
|
|
|
|
|
|
|
booleng->EndPolygonGet();
|
|
|
|
OuputOnePolygon( aInfo, PolygonBuffer );
|
|
|
|
PolygonBuffer.clear();
|
|
|
|
}
|
|
|
|
|
|
|
|
delete booleng;
|
|
|
|
booleng = NULL;
|
|
|
|
main_outline = true;
|
|
|
|
}
|
|
|
|
paths = paths->next;
|
|
|
|
}
|
|
|
|
|
|
|
|
OuputEnd( aInfo );
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* render a Bezier curve. */
|
|
|
|
void BezierToPolyline( std::vector <potrace_dpoint_t>& aCornersBuffer,
|
|
|
|
potrace_dpoint_t p1,
|
|
|
|
potrace_dpoint_t p2,
|
|
|
|
potrace_dpoint_t p3,
|
|
|
|
potrace_dpoint_t p4 )
|
|
|
|
{
|
|
|
|
double dd0, dd1, dd, delta, e2, epsilon, t;
|
|
|
|
|
|
|
|
// p1 = starting point
|
|
|
|
|
|
|
|
/* we approximate the curve by small line segments. The interval
|
|
|
|
* size, epsilon, is determined on the fly so that the distance
|
|
|
|
* between the true curve and its approximation does not exceed the
|
|
|
|
* desired accuracy delta. */
|
|
|
|
|
|
|
|
delta = 0.5; /* desired accuracy, in pixels */
|
|
|
|
|
|
|
|
/* let dd = maximal value of 2nd derivative over curve - this must
|
|
|
|
* occur at an endpoint. */
|
|
|
|
dd0 = sq( p1.x - 2 * p2.x + p3.x ) + sq( p1.y - 2 * p2.y + p3.y );
|
|
|
|
dd1 = sq( p2.x - 2 * p3.x + p4.x ) + sq( p2.y - 2 * p3.y + p4.y );
|
|
|
|
dd = 6 * sqrt( max( dd0, dd1 ) );
|
|
|
|
e2 = 8 * delta <= dd ? 8 * delta / dd : 1;
|
|
|
|
epsilon = sqrt( e2 ); /* necessary interval size */
|
|
|
|
|
|
|
|
for( t = epsilon; t<1; t += epsilon )
|
|
|
|
{
|
|
|
|
potrace_dpoint_t intermediate_point;
|
|
|
|
intermediate_point.x = p1.x * cu( 1 - t ) +
|
|
|
|
3* p2.x* sq( 1 - t ) * t +
|
|
|
|
3 * p3.x * (1 - t) * sq( t ) +
|
|
|
|
p4.x* cu( t );
|
|
|
|
|
|
|
|
intermediate_point.y = p1.y * cu( 1 - t ) +
|
|
|
|
3* p2.y* sq( 1 - t ) * t +
|
|
|
|
3 * p3.y * (1 - t) * sq( t ) + p4.y* cu( t );
|
|
|
|
|
|
|
|
aCornersBuffer.push_back( intermediate_point );
|
|
|
|
}
|
|
|
|
|
|
|
|
aCornersBuffer.push_back( p4 );
|
|
|
|
}
|