Subversion Repositories Scribus

Rev

Rev 15347 | Details | Compare with Previous | Last modification | View Log | RSS feed

Rev Author Line No. Line
15347 fschmid 1
/*
2
 * SVG Elliptical Path Support Class
12065 fschmid 3
 *
15347 fschmid 4
 * Copyright 2008  Marco Cecchetti <mrcekets at gmail.com>
12065 fschmid 5
 *
6
 * This library is free software; you can redistribute it and/or
7
 * modify it either under the terms of the GNU Lesser General Public
8
 * License version 2.1 as published by the Free Software Foundation
9
 * (the "LGPL") or, at your option, under the terms of the Mozilla
10
 * Public License Version 1.1 (the "MPL"). If you do not alter this
11
 * notice, a recipient may use your version of this file under either
12
 * the MPL or the LGPL.
13
 *
14
 * You should have received a copy of the LGPL along with this library
15
 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
18122 mrdocs 16
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
12065 fschmid 17
 * You should have received a copy of the MPL along with this library
18
 * in the file COPYING-MPL-1.1
19
 *
20
 * The contents of this file are subject to the Mozilla Public License
21
 * Version 1.1 (the "License"); you may not use this file except in
22
 * compliance with the License. You may obtain a copy of the License at
23
 * http://www.mozilla.org/MPL/
24
 *
25
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
26
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
27
 * the specific language governing rights and limitations.
28
 */
29
 
30
 
15347 fschmid 31
#ifndef _SVG_ELLIPTICAL_ARC_H_
32
#define _SVG_ELLIPTICAL_ARC_H_
12065 fschmid 33
 
15347 fschmid 34
 
12065 fschmid 35
#include "angle.h"
15347 fschmid 36
#include "matrix.h"
37
#include "sbasis.h"
38
#include "d2.h"
12065 fschmid 39
 
15347 fschmid 40
 
12065 fschmid 41
namespace Geom
42
{
43
 
15347 fschmid 44
class EllipticalArc
45
{
46
  public:
47
    EllipticalArc( Point _initial_point, Point _final_point,
48
                   double _rx,         double _ry,
49
                   bool _large_arc,    bool _sweep,
50
                   double _rot_angle = 0.0
51
                 )
52
        : m_initial_point(_initial_point), m_final_point(_final_point),
53
          m_rx(_rx), m_ry(_ry), m_rot_angle(_rot_angle),
54
          m_large_arc(_large_arc), m_sweep(_sweep)
55
    {
56
        assert( (ray(X) >= 0) && (ray(Y) >= 0) );
57
        if ( are_near(initialPoint(), finalPoint()) )
58
        {
59
            m_start_angle = m_end_angle = 0;
60
            m_center = initialPoint();
61
        }
62
        else
63
        {
64
            calculate_center_and_extreme_angles();
65
        }
12065 fschmid 66
 
15347 fschmid 67
        std::cerr << "start_angle: " << decimal_round(rad_to_deg(m_start_angle),2) << " ( " << m_start_angle << " )" << std::endl
68
                  << "end_angle: " << decimal_round(rad_to_deg(m_end_angle),2) << " ( " << m_end_angle << " )" << std::endl
69
                  << "center: " << m_center << std::endl;
12065 fschmid 70
    }
15347 fschmid 71
 
72
  public:
73
    double center(Geom::Dim2 i) const
74
    {
75
        return m_center[i];
12065 fschmid 76
    }
15347 fschmid 77
 
78
    Point center() const
79
    {
80
        return m_center;
12065 fschmid 81
    }
15347 fschmid 82
 
83
    Point initialPoint() const
84
    {
85
        return m_initial_point;
12065 fschmid 86
    }
15347 fschmid 87
 
88
    Point finalPoint() const
89
    {
90
        return m_final_point;
12065 fschmid 91
    }
15347 fschmid 92
 
93
    double start_angle() const
94
    {
95
        return m_start_angle;
12065 fschmid 96
    }
97
 
15347 fschmid 98
    double end_angle() const
99
    {
100
        return m_end_angle;
12065 fschmid 101
    }
102
 
15347 fschmid 103
    double ray(Geom::Dim2 i) const
104
    {
105
        return (i == 0) ? m_rx : m_ry;
12065 fschmid 106
    }
15347 fschmid 107
 
108
    bool large_arc_flag() const
109
    {
110
        return m_large_arc;
12065 fschmid 111
    }
112
 
15347 fschmid 113
//    void large_arc_flag(bool v)
114
//    {
115
//        m_large_arc = v;
116
//    }
12065 fschmid 117
 
15347 fschmid 118
    bool sweep_flag() const
119
    {
120
        return m_sweep;
121
    }
12065 fschmid 122
 
15347 fschmid 123
//    void sweep_flag(bool v)
124
//    {
125
//        m_sweep = v;
126
//    }
12065 fschmid 127
 
15347 fschmid 128
    double rotation_angle() const
129
    {
130
        return m_rot_angle;
131
    }
12065 fschmid 132
 
15347 fschmid 133
    void setInitial( const Point _point)
134
    {
135
        m_initial_point = _point;
136
        calculate_center_and_extreme_angles();
137
    }
12065 fschmid 138
 
15347 fschmid 139
    void setFinal( const Point _point)
140
    {
141
        m_final_point = _point;
142
        calculate_center_and_extreme_angles();
143
    }
12065 fschmid 144
 
15347 fschmid 145
    void setExtremes( const Point& _initial_point, const Point& _final_point )
146
    {
147
        m_initial_point = _initial_point;
148
        m_final_point = _final_point;
149
        calculate_center_and_extreme_angles();
150
    }
12065 fschmid 151
 
15347 fschmid 152
    bool isDegenerate() const
153
    {
154
        return are_near(initialPoint(), finalPoint());
155
    }
12065 fschmid 156
 
15347 fschmid 157
    double valueAt(Coord t, Dim2 d) const
158
    {
159
        Coord tt = from_01_to_02PI(t);
160
        double sin_rot_angle = std::sin(rotation_angle());
161
        double cos_rot_angle = std::cos(rotation_angle());
162
        if ( d == X )
163
        {
164
            return    ray(X) * cos_rot_angle * std::cos(tt)
165
                    - ray(Y) * sin_rot_angle * std::sin(tt)
166
                    + center(X);
167
        }
168
        else
169
        {
170
            return    ray(X) * sin_rot_angle * std::cos(tt)
171
                    + ray(Y) * cos_rot_angle * std::sin(tt)
172
                    + center(X);
173
        }
174
    }
12065 fschmid 175
 
15347 fschmid 176
    Point pointAt(Coord t) const
177
    {
178
        Coord tt = from_01_to_02PI(t);
179
        double sin_rot_angle = std::sin(rotation_angle());
180
        double cos_rot_angle = std::cos(rotation_angle());
181
        Matrix m( ray(X) * cos_rot_angle, ray(X) * sin_rot_angle,
182
                 -ray(Y) * sin_rot_angle, ray(Y) * cos_rot_angle,
183
                  center(X),              center(Y) );
184
        Point p( std::cos(tt), std::sin(tt) );
185
        return p * m;
186
    }
12065 fschmid 187
 
15347 fschmid 188
    D2<SBasis> toSBasis() const
189
    {
190
        // the interval of parametrization has to be [0,1]
191
        Coord et = start_angle() + ( sweep_flag() ? sweep_angle() : -sweep_angle() );
192
        Linear param(start_angle(), et);
193
        // std::cerr << "param : " << param << std::endl;
194
        Coord cos_rot_angle = std::cos(rotation_angle());
195
        Coord sin_rot_angle = std::sin(rotation_angle());
196
        // order = 4 seems to be enough to get perfect looking elliptical arc
197
        // should it be choosen in function of the arc length anyway ?
198
        // a user settable parameter: toSBasis(unsigned int order) ?
199
        SBasis arc_x = ray(X) * cos(param,4);
200
        SBasis arc_y = ray(Y) * sin(param,4);
201
        D2<SBasis> arc;
202
        arc[0] = arc_x * cos_rot_angle - arc_y * sin_rot_angle + Linear(center(X),center(X));
203
        arc[1] = arc_x * sin_rot_angle + arc_y * cos_rot_angle + Linear(center(Y),center(Y));
204
        return arc;
205
    }
12065 fschmid 206
 
15347 fschmid 207
    std::pair<EllipticalArc, EllipticalArc>
208
    subdivide(Coord t) const
209
    {
210
        EllipticalArc* arc1 = portion(0, t);
211
        EllipticalArc* arc2 = portion(t, 1);
212
        assert( arc1 != NULL && arc2 != NULL);
213
        std::pair<EllipticalArc, EllipticalArc> arc_pair(*arc1, *arc2);        
214
        delete arc1;
215
        delete arc2;
216
        return arc_pair;
217
    }
12065 fschmid 218
 
15347 fschmid 219
    EllipticalArc* portion(double f, double t) const
12065 fschmid 220
    {
15347 fschmid 221
        static const double M_2PI = 2*M_PI;
222
        EllipticalArc* arc = new EllipticalArc( *this );
223
        arc->m_initial_point = pointAt(f);
224
        arc->m_final_point = pointAt(t);
225
        //std::cerr << "initial point: " << arc->m_initial_point << std::endl;
226
        //std::cerr << "final point: " << arc->m_final_point << std::endl;
227
        double sa = sweep_angle();
228
        //std::cerr << "sa: " << sa << std::endl;
229
        arc->m_start_angle = m_start_angle + sa * f;
230
        if ( arc->m_start_angle > M_2PI || are_near(arc->m_start_angle, M_2PI) )
231
            arc->m_start_angle -= M_2PI;
232
        arc->m_end_angle = m_start_angle + sa * t;
233
        if ( arc->m_end_angle > M_2PI || are_near(arc->m_end_angle, M_2PI) )
234
            arc->m_end_angle -= M_2PI;
235
        //std::cerr << "start angle: " << arc->m_start_angle << std::endl;
236
        //std::cerr << "end angle: " << arc->m_end_angle << std::endl;
237
        //std::cerr << "sweep angle: " << arc->sweep_angle() << std::endl;
238
        if (f > t) arc->m_sweep = !m_sweep;
239
        if ( m_large_arc && (arc->sweep_angle() < M_PI) )
240
            arc->m_large_arc = false;
241
        return arc;
12065 fschmid 242
    }
243
 
15347 fschmid 244
    // the arc is the same but traversed in the opposite direction
245
    EllipticalArc* reverse() const
12065 fschmid 246
    {
15347 fschmid 247
        EllipticalArc* rarc = new EllipticalArc( *this );
248
        rarc->m_sweep = !m_sweep;
249
        rarc->m_initial_point = m_final_point;
250
        rarc->m_final_point = m_initial_point;
251
        rarc->m_start_angle = m_end_angle;
252
        rarc->m_end_angle = m_start_angle;
253
        return rarc;
12065 fschmid 254
    }
255
 
15347 fschmid 256
  private:
257
 
258
    double sweep_angle() const
12065 fschmid 259
    {
15347 fschmid 260
        Coord d = end_angle() - start_angle();
261
        if ( !sweep_flag() ) d = -d;
262
        if ( d < 0 || are_near(d, 0) )
263
            d += 2*M_PI;
264
        return d;
12065 fschmid 265
    }
266
 
15347 fschmid 267
    Coord from_01_to_02PI(Coord t) const
12065 fschmid 268
    {
15347 fschmid 269
        if ( sweep_flag() )
270
        {
271
            Coord angle = start_angle() + sweep_angle() * t;
272
            if ( (angle > 2*M_PI) || are_near(angle, 2*M_PI) )
273
                angle -= 2*M_PI;
274
            return angle;
275
        }
276
        else
277
        {
278
            Coord angle = start_angle() - sweep_angle() * t;
279
            if ( angle < 0 ) angle += 2*M_PI;
280
            return angle;
281
        }
12065 fschmid 282
    }
283
 
15347 fschmid 284
    // NOTE: doesn't work with 360 deg arcs
285
    void calculate_center_and_extreme_angles()
286
    {
287
        const double M_HALF_PI = M_PI/2;
288
        const double M_2PI = 2*M_PI;
289
 
290
        double sin_rot_angle = std::sin(rotation_angle());
291
        double cos_rot_angle = std::cos(rotation_angle());
292
 
293
        Point sp = sweep_flag() ? initialPoint() : finalPoint();
294
        Point ep = sweep_flag() ? finalPoint() : initialPoint();
295
 
296
        Matrix m( ray(X) * cos_rot_angle, ray(X) * sin_rot_angle,
297
                 -ray(Y) * sin_rot_angle, ray(Y) * cos_rot_angle,
298
                  0,                      0 );
299
        Matrix im = m.inverse();
300
        Point sol = (ep - sp) * im;
301
        std::cerr << "sol : " << sol << std::endl;
302
        double half_sum_angle = std::atan2(-sol[X], sol[Y]);
303
        double half_diff_angle;
304
        if ( are_near(std::fabs(half_sum_angle), M_HALF_PI) )
305
        {
306
            double anti_sgn_hsa = (half_sum_angle > 0) ? -1 : 1;
307
            double arg = anti_sgn_hsa * sol[X] / 2;
308
            // if |arg| is a little bit > 1 acos returns nan
309
            if ( are_near(arg, 1) )
310
                half_diff_angle = 0;
311
            else if ( are_near(arg, -1) )
312
                half_diff_angle = M_PI;
313
            else
314
            {
315
                assert( -1 < arg && arg < 1 );
316
                //  if it fails => there is no ellipse that satisfies the given constraints
317
                half_diff_angle = std::acos( arg );
318
            }
319
 
320
            half_diff_angle = M_HALF_PI - half_diff_angle;
321
        }
322
        else
323
        {
324
            double  arg = sol[Y] / ( 2 * std::cos(half_sum_angle) );
325
            // if |arg| is a little bit > 1 asin returns nan
326
            if ( are_near(arg, 1) )
327
                half_diff_angle = M_HALF_PI;
328
            else if ( are_near(arg, -1) )
329
                half_diff_angle = -M_HALF_PI;
330
            else
331
            {
332
                assert( -1 < arg && arg < 1 );  
333
                // if it fails => there is no ellipse that satisfies the given constraints
334
                half_diff_angle = std::asin( arg );
335
            }
336
        }
337
        std::cerr << "half_sum_angle : " << decimal_round(rad_to_deg(half_sum_angle),2) << " ( " << half_sum_angle << " )" << std::endl;
338
        std::cerr << "half_diff_angle : " << decimal_round(rad_to_deg(half_diff_angle),2) << " ( " << half_diff_angle << " )" << std::endl;
339
        //std::cerr << "cos(half_sum_angle) : " << std::cos(half_sum_angle) << std::endl;
340
        //std::cerr << "sol[Y] / ( 2 * std::cos(half_sum_angle) ) : " << sol[Y] / ( 2 * std::cos(half_sum_angle) ) << std::endl;        
341
 
342
        if (   ( m_large_arc && half_diff_angle > 0 )
343
            || (!m_large_arc && half_diff_angle < 0 ) )
344
        {
345
            half_diff_angle = -half_diff_angle;
346
        }
347
        if ( half_sum_angle < 0 ) half_sum_angle += M_2PI;
348
        if ( half_diff_angle < 0 ) half_diff_angle += M_PI;
349
        std::cerr << "half_sum_angle : " << decimal_round(rad_to_deg(half_sum_angle),2) << " ( " << half_sum_angle << " )" << std::endl;
350
        std::cerr << "half_diff_angle : " << decimal_round(rad_to_deg(half_diff_angle),2) << " ( " << half_diff_angle << " )" << std::endl;
351
 
352
        m_start_angle = half_sum_angle - half_diff_angle;
353
        m_end_angle =  half_sum_angle + half_diff_angle;
354
        // 0 <= m_start_angle, m_end_angle < 2PI
355
        if ( m_start_angle < 0 ) m_start_angle += M_2PI;
356
        if ( m_end_angle > M_2PI || are_near(m_end_angle, M_2PI) ) m_end_angle -= M_2PI;
357
        sol[0] = std::cos(m_start_angle);
358
        sol[1] = std::sin(m_start_angle);
359
        m_center = sp - sol * m;
360
        if ( !sweep_flag() )
361
        {
362
            double angle = m_start_angle;
363
            m_start_angle = m_end_angle;
364
            m_end_angle = angle;
365
        }
366
    }
367
 
12065 fschmid 368
  private:
15347 fschmid 369
    Point m_initial_point, m_final_point;
370
    double m_rx, m_ry, m_rot_angle;
371
    bool m_large_arc, m_sweep;
372
 
373
    double m_start_angle, m_end_angle;
374
    Point m_center;
12065 fschmid 375
};
376
 
377
 
15347 fschmid 378
}
12065 fschmid 379
 
380
 
15347 fschmid 381
#endif /*_SVG_ELLIPTICAL_ARC_H_*/
12065 fschmid 382
 
383
 
384
/*
385
  Local Variables:
386
  mode:c++
387
  c-file-style:"stroustrup"
388
  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
389
  indent-tabs-mode:nil
390
  fill-column:99
391
  End:
392
*/
393
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :