1 | // Copyright (C) 2021 The Qt Company Ltd. |
---|---|
2 | // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only |
3 | #include "qtransform.h" |
4 | |
5 | #include "qdatastream.h" |
6 | #include "qdebug.h" |
7 | #include "qhashfunctions.h" |
8 | #include "qregion.h" |
9 | #include "qpainterpath.h" |
10 | #include "qpainterpath_p.h" |
11 | #include "qvariant.h" |
12 | #include "qmath_p.h" |
13 | #include <qnumeric.h> |
14 | |
15 | #include <private/qbezier_p.h> |
16 | |
17 | QT_BEGIN_NAMESPACE |
18 | |
19 | #ifndef QT_NO_DEBUG |
20 | Q_NEVER_INLINE |
21 | static void nanWarning(const char *func) |
22 | { |
23 | qWarning(msg: "QTransform::%s with NaN called", func); |
24 | } |
25 | #endif // QT_NO_DEBUG |
26 | |
27 | #define Q_NEAR_CLIP (sizeof(qreal) == sizeof(double) ? 0.000001 : 0.0001) |
28 | |
29 | void QTransform::do_map(qreal x, qreal y, qreal &nx, qreal &ny) const |
30 | { |
31 | const TransformationType t = inline_type(); |
32 | switch (t) { |
33 | case QTransform::TxNone: |
34 | nx = x; |
35 | ny = y; |
36 | return; |
37 | case QTransform::TxTranslate: |
38 | nx = x + m_matrix[2][0]; |
39 | ny = y + m_matrix[2][1]; |
40 | return; |
41 | case QTransform::TxScale: |
42 | nx = m_matrix[0][0] * x + m_matrix[2][0]; |
43 | ny = m_matrix[1][1] * y + m_matrix[2][1]; |
44 | return; |
45 | case QTransform::TxRotate: |
46 | case QTransform::TxShear: |
47 | case QTransform::TxProject: |
48 | nx = m_matrix[0][0] * x + m_matrix[1][0] * y + m_matrix[2][0]; |
49 | ny = m_matrix[0][1] * x + m_matrix[1][1] * y + m_matrix[2][1]; |
50 | if (t == QTransform::TxProject) { |
51 | qreal w = (m_matrix[0][2] * x + m_matrix[1][2] * y + m_matrix[2][2]); |
52 | if (w < qreal(Q_NEAR_CLIP)) w = qreal(Q_NEAR_CLIP); |
53 | w = qreal(1.)/w; |
54 | nx *= w; |
55 | ny *= w; |
56 | } |
57 | return; |
58 | } |
59 | Q_UNREACHABLE_RETURN(); |
60 | } |
61 | |
62 | /*! |
63 | \class QTransform |
64 | \brief The QTransform class specifies 2D transformations of a coordinate system. |
65 | \since 4.3 |
66 | \ingroup painting |
67 | \inmodule QtGui |
68 | |
69 | A transformation specifies how to translate, scale, shear, rotate |
70 | or project the coordinate system, and is typically used when |
71 | rendering graphics. |
72 | |
73 | A QTransform object can be built using the setMatrix(), scale(), |
74 | rotate(), translate() and shear() functions. Alternatively, it |
75 | can be built by applying \l {QTransform#Basic Matrix |
76 | Operations}{basic matrix operations}. The matrix can also be |
77 | defined when constructed, and it can be reset to the identity |
78 | matrix (the default) using the reset() function. |
79 | |
80 | The QTransform class supports mapping of graphic primitives: A given |
81 | point, line, polygon, region, or painter path can be mapped to the |
82 | coordinate system defined by \e this matrix using the map() |
83 | function. In case of a rectangle, its coordinates can be |
84 | transformed using the mapRect() function. A rectangle can also be |
85 | transformed into a \e polygon (mapped to the coordinate system |
86 | defined by \e this matrix), using the mapToPolygon() function. |
87 | |
88 | QTransform provides the isIdentity() function which returns \c true if |
89 | the matrix is the identity matrix, and the isInvertible() function |
90 | which returns \c true if the matrix is non-singular (i.e. AB = BA = |
91 | I). The inverted() function returns an inverted copy of \e this |
92 | matrix if it is invertible (otherwise it returns the identity |
93 | matrix), and adjoint() returns the matrix's classical adjoint. |
94 | In addition, QTransform provides the determinant() function which |
95 | returns the matrix's determinant. |
96 | |
97 | Finally, the QTransform class supports matrix multiplication, addition |
98 | and subtraction, and objects of the class can be streamed as well |
99 | as compared. |
100 | |
101 | \section1 Rendering Graphics |
102 | |
103 | When rendering graphics, the matrix defines the transformations |
104 | but the actual transformation is performed by the drawing routines |
105 | in QPainter. |
106 | |
107 | By default, QPainter operates on the associated device's own |
108 | coordinate system. The standard coordinate system of a |
109 | QPaintDevice has its origin located at the top-left position. The |
110 | \e x values increase to the right; \e y values increase |
111 | downward. For a complete description, see the \l {Coordinate |
112 | System} {coordinate system} documentation. |
113 | |
114 | QPainter has functions to translate, scale, shear and rotate the |
115 | coordinate system without using a QTransform. For example: |
116 | |
117 | \table 100% |
118 | \row |
119 | \li \inlineimage qtransform-simpletransformation.png |
120 | \li |
121 | \snippet transform/main.cpp 0 |
122 | \endtable |
123 | |
124 | Although these functions are very convenient, it can be more |
125 | efficient to build a QTransform and call QPainter::setTransform() if you |
126 | want to perform more than a single transform operation. For |
127 | example: |
128 | |
129 | \table 100% |
130 | \row |
131 | \li \inlineimage qtransform-combinedtransformation.png |
132 | \li |
133 | \snippet transform/main.cpp 1 |
134 | \endtable |
135 | |
136 | \section1 Basic Matrix Operations |
137 | |
138 | \image qtransform-representation.png |
139 | |
140 | A QTransform object contains a 3 x 3 matrix. The \c m31 (\c dx) and |
141 | \c m32 (\c dy) elements specify horizontal and vertical translation. |
142 | The \c m11 and \c m22 elements specify horizontal and vertical scaling. |
143 | The \c m21 and \c m12 elements specify horizontal and vertical \e shearing. |
144 | And finally, the \c m13 and \c m23 elements specify horizontal and vertical |
145 | projection, with \c m33 as an additional projection factor. |
146 | |
147 | QTransform transforms a point in the plane to another point using the |
148 | following formulas: |
149 | |
150 | \snippet code/src_gui_painting_qtransform.cpp 0 |
151 | |
152 | The point \e (x, y) is the original point, and \e (x', y') is the |
153 | transformed point. \e (x', y') can be transformed back to \e (x, |
154 | y) by performing the same operation on the inverted() matrix. |
155 | |
156 | The various matrix elements can be set when constructing the |
157 | matrix, or by using the setMatrix() function later on. They can also |
158 | be manipulated using the translate(), rotate(), scale() and |
159 | shear() convenience functions. The currently set values can be |
160 | retrieved using the m11(), m12(), m13(), m21(), m22(), m23(), |
161 | m31(), m32(), m33(), dx() and dy() functions. |
162 | |
163 | Translation is the simplest transformation. Setting \c dx and \c |
164 | dy will move the coordinate system \c dx units along the X axis |
165 | and \c dy units along the Y axis. Scaling can be done by setting |
166 | \c m11 and \c m22. For example, setting \c m11 to 2 and \c m22 to |
167 | 1.5 will double the height and increase the width by 50%. The |
168 | identity matrix has \c m11, \c m22, and \c m33 set to 1 (all others are set |
169 | to 0) mapping a point to itself. Shearing is controlled by \c m12 |
170 | and \c m21. Setting these elements to values different from zero |
171 | will twist the coordinate system. Rotation is achieved by |
172 | setting both the shearing factors and the scaling factors. Perspective |
173 | transformation is achieved by setting both the projection factors and |
174 | the scaling factors. |
175 | |
176 | \section2 Combining Transforms |
177 | Here's the combined transformations example using basic matrix |
178 | operations: |
179 | |
180 | \table 100% |
181 | \row |
182 | \li \inlineimage qtransform-combinedtransformation2.png |
183 | \li |
184 | \snippet transform/main.cpp 2 |
185 | \endtable |
186 | |
187 | The combined transform first scales each operand, then rotates it, and |
188 | finally translates it, just as in the order in which the product of its |
189 | factors is written. This means the point to which the transforms are |
190 | applied is implicitly multiplied on the left with the transform |
191 | to its right. |
192 | |
193 | \section2 Relation to Matrix Notation |
194 | The matrix notation in QTransform is the transpose of a commonly-taught |
195 | convention which represents transforms and points as matrices and vectors. |
196 | That convention multiplies its matrix on the left and column vector to the |
197 | right. In other words, when several transforms are applied to a point, the |
198 | right-most matrix acts directly on the vector first. Then the next matrix |
199 | to the left acts on the result of the first operation - and so on. As a |
200 | result, that convention multiplies the matrices that make up a composite |
201 | transform in the reverse of the order in QTransform, as you can see in |
202 | \l {Combining Transforms}. Transposing the matrices, and combining them to |
203 | the right of a row vector that represents the point, lets the matrices of |
204 | transforms appear, in their product, in the order in which we think of the |
205 | transforms being applied to the point. |
206 | |
207 | \sa QPainter, {Coordinate System}, {painting/affine}{Affine |
208 | Transformations Example}, {Transformations Example} |
209 | */ |
210 | |
211 | /*! |
212 | \enum QTransform::TransformationType |
213 | |
214 | \value TxNone |
215 | \value TxTranslate |
216 | \value TxScale |
217 | \value TxRotate |
218 | \value TxShear |
219 | \value TxProject |
220 | */ |
221 | |
222 | /*! |
223 | \fn QTransform::QTransform(Qt::Initialization) |
224 | \internal |
225 | */ |
226 | |
227 | /*! |
228 | \fn QTransform::QTransform() |
229 | |
230 | Constructs an identity matrix. |
231 | |
232 | All elements are set to zero except \c m11 and \c m22 (specifying |
233 | the scale) and \c m33 which are set to 1. |
234 | |
235 | \sa reset() |
236 | */ |
237 | |
238 | /*! |
239 | \fn QTransform::QTransform(qreal m11, qreal m12, qreal m13, qreal m21, qreal m22, qreal m23, qreal m31, qreal m32, qreal m33) |
240 | |
241 | Constructs a matrix with the elements, \a m11, \a m12, \a m13, |
242 | \a m21, \a m22, \a m23, \a m31, \a m32, \a m33. |
243 | |
244 | \sa setMatrix() |
245 | */ |
246 | |
247 | /*! |
248 | \fn QTransform::QTransform(qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy) |
249 | |
250 | Constructs a matrix with the elements, \a m11, \a m12, \a m21, \a m22, \a dx and \a dy. |
251 | |
252 | \sa setMatrix() |
253 | */ |
254 | |
255 | /*! |
256 | Returns the adjoint of this matrix. |
257 | */ |
258 | QTransform QTransform::adjoint() const |
259 | { |
260 | qreal h11, h12, h13, |
261 | h21, h22, h23, |
262 | h31, h32, h33; |
263 | h11 = m_matrix[1][1] * m_matrix[2][2] - m_matrix[1][2] * m_matrix[2][1]; |
264 | h21 = m_matrix[1][2] * m_matrix[2][0] - m_matrix[1][0] * m_matrix[2][2]; |
265 | h31 = m_matrix[1][0] * m_matrix[2][1] - m_matrix[1][1] * m_matrix[2][0]; |
266 | h12 = m_matrix[0][2] * m_matrix[2][1] - m_matrix[0][1] * m_matrix[2][2]; |
267 | h22 = m_matrix[0][0] * m_matrix[2][2] - m_matrix[0][2] * m_matrix[2][0]; |
268 | h32 = m_matrix[0][1] * m_matrix[2][0] - m_matrix[0][0] * m_matrix[2][1]; |
269 | h13 = m_matrix[0][1] * m_matrix[1][2] - m_matrix[0][2] * m_matrix[1][1]; |
270 | h23 = m_matrix[0][2] * m_matrix[1][0] - m_matrix[0][0] * m_matrix[1][2]; |
271 | h33 = m_matrix[0][0] * m_matrix[1][1] - m_matrix[0][1] * m_matrix[1][0]; |
272 | |
273 | return QTransform(h11, h12, h13, |
274 | h21, h22, h23, |
275 | h31, h32, h33); |
276 | } |
277 | |
278 | /*! |
279 | Returns the transpose of this matrix. |
280 | */ |
281 | QTransform QTransform::transposed() const |
282 | { |
283 | QTransform t(m_matrix[0][0], m_matrix[1][0], m_matrix[2][0], |
284 | m_matrix[0][1], m_matrix[1][1], m_matrix[2][1], |
285 | m_matrix[0][2], m_matrix[1][2], m_matrix[2][2]); |
286 | return t; |
287 | } |
288 | |
289 | /*! |
290 | Returns an inverted copy of this matrix. |
291 | |
292 | If the matrix is singular (not invertible), the returned matrix is |
293 | the identity matrix. If \a invertible is valid (i.e. not 0), its |
294 | value is set to true if the matrix is invertible, otherwise it is |
295 | set to false. |
296 | |
297 | \sa isInvertible() |
298 | */ |
299 | QTransform QTransform::inverted(bool *invertible) const |
300 | { |
301 | QTransform invert; |
302 | bool inv = true; |
303 | |
304 | switch(inline_type()) { |
305 | case TxNone: |
306 | break; |
307 | case TxTranslate: |
308 | invert.m_matrix[2][0] = -m_matrix[2][0]; |
309 | invert.m_matrix[2][1] = -m_matrix[2][1]; |
310 | break; |
311 | case TxScale: |
312 | inv = !qFuzzyIsNull(d: m_matrix[0][0]); |
313 | inv &= !qFuzzyIsNull(d: m_matrix[1][1]); |
314 | if (inv) { |
315 | invert.m_matrix[0][0] = 1. / m_matrix[0][0]; |
316 | invert.m_matrix[1][1] = 1. / m_matrix[1][1]; |
317 | invert.m_matrix[2][0] = -m_matrix[2][0] * invert.m_matrix[0][0]; |
318 | invert.m_matrix[2][1] = -m_matrix[2][1] * invert.m_matrix[1][1]; |
319 | } |
320 | break; |
321 | // case TxRotate: |
322 | // case TxShear: |
323 | // invert.affine = affine.inverted(&inv); |
324 | // break; |
325 | default: |
326 | // general case |
327 | qreal det = determinant(); |
328 | inv = !qFuzzyIsNull(d: det); |
329 | if (inv) |
330 | invert = adjoint() / det; |
331 | break; |
332 | } |
333 | |
334 | if (invertible) |
335 | *invertible = inv; |
336 | |
337 | if (inv) { |
338 | // inverting doesn't change the type |
339 | invert.m_type = m_type; |
340 | invert.m_dirty = m_dirty; |
341 | } |
342 | |
343 | return invert; |
344 | } |
345 | |
346 | /*! |
347 | Moves the coordinate system \a dx along the x axis and \a dy along |
348 | the y axis, and returns a reference to the matrix. |
349 | |
350 | \sa setMatrix() |
351 | */ |
352 | QTransform &QTransform::translate(qreal dx, qreal dy) |
353 | { |
354 | if (dx == 0 && dy == 0) |
355 | return *this; |
356 | #ifndef QT_NO_DEBUG |
357 | if (qIsNaN(d: dx) || qIsNaN(d: dy)) { |
358 | nanWarning(func: "translate"); |
359 | return *this; |
360 | } |
361 | #endif |
362 | |
363 | switch(inline_type()) { |
364 | case TxNone: |
365 | m_matrix[2][0] = dx; |
366 | m_matrix[2][1] = dy; |
367 | break; |
368 | case TxTranslate: |
369 | m_matrix[2][0] += dx; |
370 | m_matrix[2][1] += dy; |
371 | break; |
372 | case TxScale: |
373 | m_matrix[2][0] += dx * m_matrix[0][0]; |
374 | m_matrix[2][1] += dy * m_matrix[1][1]; |
375 | break; |
376 | case TxProject: |
377 | m_matrix[2][2] += dx * m_matrix[0][2] + dy * m_matrix[1][2]; |
378 | Q_FALLTHROUGH(); |
379 | case TxShear: |
380 | case TxRotate: |
381 | m_matrix[2][0] += dx * m_matrix[0][0] + dy * m_matrix[1][0]; |
382 | m_matrix[2][1] += dy * m_matrix[1][1] + dx * m_matrix[0][1]; |
383 | break; |
384 | } |
385 | if (m_dirty < TxTranslate) |
386 | m_dirty = TxTranslate; |
387 | return *this; |
388 | } |
389 | |
390 | /*! |
391 | Creates a matrix which corresponds to a translation of \a dx along |
392 | the x axis and \a dy along the y axis. This is the same as |
393 | QTransform().translate(dx, dy) but slightly faster. |
394 | |
395 | \since 4.5 |
396 | */ |
397 | QTransform QTransform::fromTranslate(qreal dx, qreal dy) |
398 | { |
399 | #ifndef QT_NO_DEBUG |
400 | if (qIsNaN(d: dx) || qIsNaN(d: dy)) { |
401 | nanWarning(func: "fromTranslate"); |
402 | return QTransform(); |
403 | } |
404 | #endif |
405 | QTransform transform(1, 0, 0, 0, 1, 0, dx, dy, 1); |
406 | if (dx == 0 && dy == 0) |
407 | transform.m_type = TxNone; |
408 | else |
409 | transform.m_type = TxTranslate; |
410 | transform.m_dirty = TxNone; |
411 | return transform; |
412 | } |
413 | |
414 | /*! |
415 | Scales the coordinate system by \a sx horizontally and \a sy |
416 | vertically, and returns a reference to the matrix. |
417 | |
418 | \sa setMatrix() |
419 | */ |
420 | QTransform & QTransform::scale(qreal sx, qreal sy) |
421 | { |
422 | if (sx == 1 && sy == 1) |
423 | return *this; |
424 | #ifndef QT_NO_DEBUG |
425 | if (qIsNaN(d: sx) || qIsNaN(d: sy)) { |
426 | nanWarning(func: "scale"); |
427 | return *this; |
428 | } |
429 | #endif |
430 | |
431 | switch(inline_type()) { |
432 | case TxNone: |
433 | case TxTranslate: |
434 | m_matrix[0][0] = sx; |
435 | m_matrix[1][1] = sy; |
436 | break; |
437 | case TxProject: |
438 | m_matrix[0][2] *= sx; |
439 | m_matrix[1][2] *= sy; |
440 | Q_FALLTHROUGH(); |
441 | case TxRotate: |
442 | case TxShear: |
443 | m_matrix[0][1] *= sx; |
444 | m_matrix[1][0] *= sy; |
445 | Q_FALLTHROUGH(); |
446 | case TxScale: |
447 | m_matrix[0][0] *= sx; |
448 | m_matrix[1][1] *= sy; |
449 | break; |
450 | } |
451 | if (m_dirty < TxScale) |
452 | m_dirty = TxScale; |
453 | return *this; |
454 | } |
455 | |
456 | /*! |
457 | Creates a matrix which corresponds to a scaling of |
458 | \a sx horizontally and \a sy vertically. |
459 | This is the same as QTransform().scale(sx, sy) but slightly faster. |
460 | |
461 | \since 4.5 |
462 | */ |
463 | QTransform QTransform::fromScale(qreal sx, qreal sy) |
464 | { |
465 | #ifndef QT_NO_DEBUG |
466 | if (qIsNaN(d: sx) || qIsNaN(d: sy)) { |
467 | nanWarning(func: "fromScale"); |
468 | return QTransform(); |
469 | } |
470 | #endif |
471 | QTransform transform(sx, 0, 0, 0, sy, 0, 0, 0, 1); |
472 | if (sx == 1. && sy == 1.) |
473 | transform.m_type = TxNone; |
474 | else |
475 | transform.m_type = TxScale; |
476 | transform.m_dirty = TxNone; |
477 | return transform; |
478 | } |
479 | |
480 | /*! |
481 | Shears the coordinate system by \a sh horizontally and \a sv |
482 | vertically, and returns a reference to the matrix. |
483 | |
484 | \sa setMatrix() |
485 | */ |
486 | QTransform & QTransform::shear(qreal sh, qreal sv) |
487 | { |
488 | if (sh == 0 && sv == 0) |
489 | return *this; |
490 | #ifndef QT_NO_DEBUG |
491 | if (qIsNaN(d: sh) || qIsNaN(d: sv)) { |
492 | nanWarning(func: "shear"); |
493 | return *this; |
494 | } |
495 | #endif |
496 | |
497 | switch(inline_type()) { |
498 | case TxNone: |
499 | case TxTranslate: |
500 | m_matrix[0][1] = sv; |
501 | m_matrix[1][0] = sh; |
502 | break; |
503 | case TxScale: |
504 | m_matrix[0][1] = sv*m_matrix[1][1]; |
505 | m_matrix[1][0] = sh*m_matrix[0][0]; |
506 | break; |
507 | case TxProject: { |
508 | qreal tm13 = sv * m_matrix[1][2]; |
509 | qreal tm23 = sh * m_matrix[0][2]; |
510 | m_matrix[0][2] += tm13; |
511 | m_matrix[1][2] += tm23; |
512 | } |
513 | Q_FALLTHROUGH(); |
514 | case TxRotate: |
515 | case TxShear: { |
516 | qreal tm11 = sv * m_matrix[1][0]; |
517 | qreal tm22 = sh * m_matrix[0][1]; |
518 | qreal tm12 = sv * m_matrix[1][1]; |
519 | qreal tm21 = sh * m_matrix[0][0]; |
520 | m_matrix[0][0] += tm11; |
521 | m_matrix[0][1] += tm12; |
522 | m_matrix[1][0] += tm21; |
523 | m_matrix[1][1] += tm22; |
524 | break; |
525 | } |
526 | } |
527 | if (m_dirty < TxShear) |
528 | m_dirty = TxShear; |
529 | return *this; |
530 | } |
531 | |
532 | /*! |
533 | \since 6.5 |
534 | |
535 | Rotates the coordinate system counterclockwise by the given angle \a a |
536 | about the specified \a axis at distance \a distanceToPlane from the |
537 | screen and returns a reference to the matrix. |
538 | |
539 | //! [transform-rotate-note] |
540 | Note that if you apply a QTransform to a point defined in widget |
541 | coordinates, the direction of the rotation will be clockwise |
542 | because the y-axis points downwards. |
543 | |
544 | The angle is specified in degrees. |
545 | //! [transform-rotate-note] |
546 | |
547 | If \a distanceToPlane is zero, it will be ignored. This is suitable |
548 | for implementing orthographic projections where the z coordinate should |
549 | be dropped rather than projected. |
550 | |
551 | \sa setMatrix() |
552 | */ |
553 | QTransform & QTransform::rotate(qreal a, Qt::Axis axis, qreal distanceToPlane) |
554 | { |
555 | if (a == 0) |
556 | return *this; |
557 | #ifndef QT_NO_DEBUG |
558 | if (qIsNaN(d: a) || qIsNaN(d: distanceToPlane)) { |
559 | nanWarning(func: "rotate"); |
560 | return *this; |
561 | } |
562 | #endif |
563 | |
564 | qreal sina = 0; |
565 | qreal cosa = 0; |
566 | if (a == 90. || a == -270.) |
567 | sina = 1.; |
568 | else if (a == 270. || a == -90.) |
569 | sina = -1.; |
570 | else if (a == 180.) |
571 | cosa = -1.; |
572 | else{ |
573 | qreal b = qDegreesToRadians(degrees: a); |
574 | sina = qSin(v: b); // fast and convenient |
575 | cosa = qCos(v: b); |
576 | } |
577 | |
578 | if (axis == Qt::ZAxis) { |
579 | switch(inline_type()) { |
580 | case TxNone: |
581 | case TxTranslate: |
582 | m_matrix[0][0] = cosa; |
583 | m_matrix[0][1] = sina; |
584 | m_matrix[1][0] = -sina; |
585 | m_matrix[1][1] = cosa; |
586 | break; |
587 | case TxScale: { |
588 | qreal tm11 = cosa * m_matrix[0][0]; |
589 | qreal tm12 = sina * m_matrix[1][1]; |
590 | qreal tm21 = -sina * m_matrix[0][0]; |
591 | qreal tm22 = cosa * m_matrix[1][1]; |
592 | m_matrix[0][0] = tm11; |
593 | m_matrix[0][1] = tm12; |
594 | m_matrix[1][0] = tm21; |
595 | m_matrix[1][1] = tm22; |
596 | break; |
597 | } |
598 | case TxProject: { |
599 | qreal tm13 = cosa * m_matrix[0][2] + sina * m_matrix[1][2]; |
600 | qreal tm23 = -sina * m_matrix[0][2] + cosa * m_matrix[1][2]; |
601 | m_matrix[0][2] = tm13; |
602 | m_matrix[1][2] = tm23; |
603 | Q_FALLTHROUGH(); |
604 | } |
605 | case TxRotate: |
606 | case TxShear: { |
607 | qreal tm11 = cosa * m_matrix[0][0] + sina * m_matrix[1][0]; |
608 | qreal tm12 = cosa * m_matrix[0][1] + sina * m_matrix[1][1]; |
609 | qreal tm21 = -sina * m_matrix[0][0] + cosa * m_matrix[1][0]; |
610 | qreal tm22 = -sina * m_matrix[0][1] + cosa * m_matrix[1][1]; |
611 | m_matrix[0][0] = tm11; |
612 | m_matrix[0][1] = tm12; |
613 | m_matrix[1][0] = tm21; |
614 | m_matrix[1][1] = tm22; |
615 | break; |
616 | } |
617 | } |
618 | if (m_dirty < TxRotate) |
619 | m_dirty = TxRotate; |
620 | } else { |
621 | if (!qIsNull(d: distanceToPlane)) |
622 | sina /= distanceToPlane; |
623 | |
624 | QTransform result; |
625 | if (axis == Qt::YAxis) { |
626 | result.m_matrix[0][0] = cosa; |
627 | result.m_matrix[0][2] = -sina; |
628 | } else { |
629 | result.m_matrix[1][1] = cosa; |
630 | result.m_matrix[1][2] = -sina; |
631 | } |
632 | result.m_type = TxProject; |
633 | *this = result * *this; |
634 | } |
635 | |
636 | return *this; |
637 | } |
638 | |
639 | #if QT_VERSION < QT_VERSION_CHECK(7, 0, 0) |
640 | /*! |
641 | \overload |
642 | |
643 | Rotates the coordinate system counterclockwise by the given angle \a a |
644 | about the specified \a axis at distance 1024.0 from the screen and |
645 | returns a reference to the matrix. |
646 | |
647 | \include qtransform.cpp transform-rotate-note |
648 | |
649 | \sa setMatrix |
650 | */ |
651 | QTransform &QTransform::rotate(qreal a, Qt::Axis axis) |
652 | { |
653 | return rotate(a, axis, distanceToPlane: 1024.0); |
654 | } |
655 | #endif |
656 | |
657 | /*! |
658 | \since 6.5 |
659 | |
660 | Rotates the coordinate system counterclockwise by the given angle \a a |
661 | about the specified \a axis at distance \a distanceToPlane from the |
662 | screen and returns a reference to the matrix. |
663 | |
664 | //! [transform-rotate-radians-note] |
665 | Note that if you apply a QTransform to a point defined in widget |
666 | coordinates, the direction of the rotation will be clockwise |
667 | because the y-axis points downwards. |
668 | |
669 | The angle is specified in radians. |
670 | //! [transform-rotate-radians-note] |
671 | |
672 | If \a distanceToPlane is zero, it will be ignored. This is suitable |
673 | for implementing orthographic projections where the z coordinate should |
674 | be dropped rather than projected. |
675 | |
676 | \sa setMatrix() |
677 | */ |
678 | QTransform & QTransform::rotateRadians(qreal a, Qt::Axis axis, qreal distanceToPlane) |
679 | { |
680 | #ifndef QT_NO_DEBUG |
681 | if (qIsNaN(d: a) || qIsNaN(d: distanceToPlane)) { |
682 | nanWarning(func: "rotateRadians"); |
683 | return *this; |
684 | } |
685 | #endif |
686 | qreal sina = qSin(v: a); |
687 | qreal cosa = qCos(v: a); |
688 | |
689 | if (axis == Qt::ZAxis) { |
690 | switch(inline_type()) { |
691 | case TxNone: |
692 | case TxTranslate: |
693 | m_matrix[0][0] = cosa; |
694 | m_matrix[0][1] = sina; |
695 | m_matrix[1][0] = -sina; |
696 | m_matrix[1][1] = cosa; |
697 | break; |
698 | case TxScale: { |
699 | qreal tm11 = cosa * m_matrix[0][0]; |
700 | qreal tm12 = sina * m_matrix[1][1]; |
701 | qreal tm21 = -sina * m_matrix[0][0]; |
702 | qreal tm22 = cosa * m_matrix[1][1]; |
703 | m_matrix[0][0] = tm11; |
704 | m_matrix[0][1] = tm12; |
705 | m_matrix[1][0] = tm21; |
706 | m_matrix[1][1] = tm22; |
707 | break; |
708 | } |
709 | case TxProject: { |
710 | qreal tm13 = cosa * m_matrix[0][2] + sina * m_matrix[1][2]; |
711 | qreal tm23 = -sina * m_matrix[0][2] + cosa * m_matrix[1][2]; |
712 | m_matrix[0][2] = tm13; |
713 | m_matrix[1][2] = tm23; |
714 | Q_FALLTHROUGH(); |
715 | } |
716 | case TxRotate: |
717 | case TxShear: { |
718 | qreal tm11 = cosa * m_matrix[0][0] + sina * m_matrix[1][0]; |
719 | qreal tm12 = cosa * m_matrix[0][1] + sina * m_matrix[1][1]; |
720 | qreal tm21 = -sina * m_matrix[0][0] + cosa * m_matrix[1][0]; |
721 | qreal tm22 = -sina * m_matrix[0][1] + cosa * m_matrix[1][1]; |
722 | m_matrix[0][0] = tm11; |
723 | m_matrix[0][1] = tm12; |
724 | m_matrix[1][0] = tm21; |
725 | m_matrix[1][1] = tm22; |
726 | break; |
727 | } |
728 | } |
729 | if (m_dirty < TxRotate) |
730 | m_dirty = TxRotate; |
731 | } else { |
732 | if (!qIsNull(d: distanceToPlane)) |
733 | sina /= distanceToPlane; |
734 | |
735 | QTransform result; |
736 | if (axis == Qt::YAxis) { |
737 | result.m_matrix[0][0] = cosa; |
738 | result.m_matrix[0][2] = -sina; |
739 | } else { |
740 | result.m_matrix[1][1] = cosa; |
741 | result.m_matrix[1][2] = -sina; |
742 | } |
743 | result.m_type = TxProject; |
744 | *this = result * *this; |
745 | } |
746 | return *this; |
747 | } |
748 | |
749 | #if QT_VERSION < QT_VERSION_CHECK(7, 0, 0) |
750 | /*! |
751 | \overload |
752 | |
753 | Rotates the coordinate system counterclockwise by the given angle \a a |
754 | about the specified \a axis at distance 1024.0 from the screen and |
755 | returns a reference to the matrix. |
756 | |
757 | \include qtransform.cpp transform-rotate-radians-note |
758 | |
759 | \sa setMatrix() |
760 | */ |
761 | QTransform &QTransform::rotateRadians(qreal a, Qt::Axis axis) |
762 | { |
763 | return rotateRadians(a, axis, distanceToPlane: 1024.0); |
764 | } |
765 | #endif |
766 | |
767 | /*! |
768 | \fn bool QTransform::operator==(const QTransform &matrix) const |
769 | Returns \c true if this matrix is equal to the given \a matrix, |
770 | otherwise returns \c false. |
771 | */ |
772 | bool QTransform::operator==(const QTransform &o) const |
773 | { |
774 | return m_matrix[0][0] == o.m_matrix[0][0] && |
775 | m_matrix[0][1] == o.m_matrix[0][1] && |
776 | m_matrix[1][0] == o.m_matrix[1][0] && |
777 | m_matrix[1][1] == o.m_matrix[1][1] && |
778 | m_matrix[2][0] == o.m_matrix[2][0] && |
779 | m_matrix[2][1] == o.m_matrix[2][1] && |
780 | m_matrix[0][2] == o.m_matrix[0][2] && |
781 | m_matrix[1][2] == o.m_matrix[1][2] && |
782 | m_matrix[2][2] == o.m_matrix[2][2]; |
783 | } |
784 | |
785 | /*! |
786 | \since 5.6 |
787 | \qhashold{QTransform} |
788 | */ |
789 | size_t qHash(const QTransform &key, size_t seed) noexcept |
790 | { |
791 | QtPrivate::QHashCombine hash; |
792 | seed = hash(seed, key.m11()); |
793 | seed = hash(seed, key.m12()); |
794 | seed = hash(seed, key.m21()); |
795 | seed = hash(seed, key.m22()); |
796 | seed = hash(seed, key.dx()); |
797 | seed = hash(seed, key.dy()); |
798 | seed = hash(seed, key.m13()); |
799 | seed = hash(seed, key.m23()); |
800 | seed = hash(seed, key.m33()); |
801 | return seed; |
802 | } |
803 | |
804 | |
805 | /*! |
806 | \fn bool QTransform::operator!=(const QTransform &matrix) const |
807 | Returns \c true if this matrix is not equal to the given \a matrix, |
808 | otherwise returns \c false. |
809 | */ |
810 | bool QTransform::operator!=(const QTransform &o) const |
811 | { |
812 | return !operator==(o); |
813 | } |
814 | |
815 | /*! |
816 | \fn QTransform & QTransform::operator*=(const QTransform &matrix) |
817 | \overload |
818 | |
819 | Returns the result of multiplying this matrix by the given \a |
820 | matrix. |
821 | */ |
822 | QTransform & QTransform::operator*=(const QTransform &o) |
823 | { |
824 | const TransformationType otherType = o.inline_type(); |
825 | if (otherType == TxNone) |
826 | return *this; |
827 | |
828 | const TransformationType thisType = inline_type(); |
829 | if (thisType == TxNone) |
830 | return operator=(o); |
831 | |
832 | TransformationType t = qMax(a: thisType, b: otherType); |
833 | switch(t) { |
834 | case TxNone: |
835 | break; |
836 | case TxTranslate: |
837 | m_matrix[2][0] += o.m_matrix[2][0]; |
838 | m_matrix[2][1] += o.m_matrix[2][1]; |
839 | break; |
840 | case TxScale: |
841 | { |
842 | qreal m11 = m_matrix[0][0] * o.m_matrix[0][0]; |
843 | qreal m22 = m_matrix[1][1] * o.m_matrix[1][1]; |
844 | |
845 | qreal m31 = m_matrix[2][0] * o.m_matrix[0][0] + o.m_matrix[2][0]; |
846 | qreal m32 = m_matrix[2][1] * o.m_matrix[1][1] + o.m_matrix[2][1]; |
847 | |
848 | m_matrix[0][0] = m11; |
849 | m_matrix[1][1] = m22; |
850 | m_matrix[2][0] = m31; m_matrix[2][1] = m32; |
851 | break; |
852 | } |
853 | case TxRotate: |
854 | case TxShear: |
855 | { |
856 | qreal m11 = m_matrix[0][0] * o.m_matrix[0][0] + m_matrix[0][1] * o.m_matrix[1][0]; |
857 | qreal m12 = m_matrix[0][0] * o.m_matrix[0][1] + m_matrix[0][1] * o.m_matrix[1][1]; |
858 | |
859 | qreal m21 = m_matrix[1][0] * o.m_matrix[0][0] + m_matrix[1][1] * o.m_matrix[1][0]; |
860 | qreal m22 = m_matrix[1][0] * o.m_matrix[0][1] + m_matrix[1][1] * o.m_matrix[1][1]; |
861 | |
862 | qreal m31 = m_matrix[2][0] * o.m_matrix[0][0] + m_matrix[2][1] * o.m_matrix[1][0] + o.m_matrix[2][0]; |
863 | qreal m32 = m_matrix[2][0] * o.m_matrix[0][1] + m_matrix[2][1] * o.m_matrix[1][1] + o.m_matrix[2][1]; |
864 | |
865 | m_matrix[0][0] = m11; |
866 | m_matrix[0][1] = m12; |
867 | m_matrix[1][0] = m21; |
868 | m_matrix[1][1] = m22; |
869 | m_matrix[2][0] = m31; |
870 | m_matrix[2][1] = m32; |
871 | break; |
872 | } |
873 | case TxProject: |
874 | { |
875 | qreal m11 = m_matrix[0][0] * o.m_matrix[0][0] + m_matrix[0][1] * o.m_matrix[1][0] + m_matrix[0][2] * o.m_matrix[2][0]; |
876 | qreal m12 = m_matrix[0][0] * o.m_matrix[0][1] + m_matrix[0][1] * o.m_matrix[1][1] + m_matrix[0][2] * o.m_matrix[2][1]; |
877 | qreal m13 = m_matrix[0][0] * o.m_matrix[0][2] + m_matrix[0][1] * o.m_matrix[1][2] + m_matrix[0][2] * o.m_matrix[2][2]; |
878 | |
879 | qreal m21 = m_matrix[1][0] * o.m_matrix[0][0] + m_matrix[1][1] * o.m_matrix[1][0] + m_matrix[1][2] * o.m_matrix[2][0]; |
880 | qreal m22 = m_matrix[1][0] * o.m_matrix[0][1] + m_matrix[1][1] * o.m_matrix[1][1] + m_matrix[1][2] * o.m_matrix[2][1]; |
881 | qreal m23 = m_matrix[1][0] * o.m_matrix[0][2] + m_matrix[1][1] * o.m_matrix[1][2] + m_matrix[1][2] * o.m_matrix[2][2]; |
882 | |
883 | qreal m31 = m_matrix[2][0] * o.m_matrix[0][0] + m_matrix[2][1] * o.m_matrix[1][0] + m_matrix[2][2] * o.m_matrix[2][0]; |
884 | qreal m32 = m_matrix[2][0] * o.m_matrix[0][1] + m_matrix[2][1] * o.m_matrix[1][1] + m_matrix[2][2] * o.m_matrix[2][1]; |
885 | qreal m33 = m_matrix[2][0] * o.m_matrix[0][2] + m_matrix[2][1] * o.m_matrix[1][2] + m_matrix[2][2] * o.m_matrix[2][2]; |
886 | |
887 | m_matrix[0][0] = m11; m_matrix[0][1] = m12; m_matrix[0][2] = m13; |
888 | m_matrix[1][0] = m21; m_matrix[1][1] = m22; m_matrix[1][2] = m23; |
889 | m_matrix[2][0] = m31; m_matrix[2][1] = m32; m_matrix[2][2] = m33; |
890 | } |
891 | } |
892 | |
893 | m_dirty = t; |
894 | m_type = t; |
895 | |
896 | return *this; |
897 | } |
898 | |
899 | /*! |
900 | \fn QTransform QTransform::operator*(const QTransform &matrix) const |
901 | Returns the result of multiplying this matrix by the given \a |
902 | matrix. |
903 | |
904 | Note that matrix multiplication is not commutative, i.e. a*b != |
905 | b*a. |
906 | */ |
907 | QTransform QTransform::operator*(const QTransform &m) const |
908 | { |
909 | const TransformationType otherType = m.inline_type(); |
910 | if (otherType == TxNone) |
911 | return *this; |
912 | |
913 | const TransformationType thisType = inline_type(); |
914 | if (thisType == TxNone) |
915 | return m; |
916 | |
917 | QTransform t; |
918 | TransformationType type = qMax(a: thisType, b: otherType); |
919 | switch(type) { |
920 | case TxNone: |
921 | break; |
922 | case TxTranslate: |
923 | t.m_matrix[2][0] = m_matrix[2][0] + m.m_matrix[2][0]; |
924 | t.m_matrix[2][1] = m_matrix[2][1] + m.m_matrix[2][1]; |
925 | break; |
926 | case TxScale: |
927 | { |
928 | qreal m11 = m_matrix[0][0] * m.m_matrix[0][0]; |
929 | qreal m22 = m_matrix[1][1] * m.m_matrix[1][1]; |
930 | |
931 | qreal m31 = m_matrix[2][0] * m.m_matrix[0][0] + m.m_matrix[2][0]; |
932 | qreal m32 = m_matrix[2][1] * m.m_matrix[1][1] + m.m_matrix[2][1]; |
933 | |
934 | t.m_matrix[0][0] = m11; |
935 | t.m_matrix[1][1] = m22; |
936 | t.m_matrix[2][0] = m31; |
937 | t.m_matrix[2][1] = m32; |
938 | break; |
939 | } |
940 | case TxRotate: |
941 | case TxShear: |
942 | { |
943 | qreal m11 = m_matrix[0][0] * m.m_matrix[0][0] + m_matrix[0][1] * m.m_matrix[1][0]; |
944 | qreal m12 = m_matrix[0][0] * m.m_matrix[0][1] + m_matrix[0][1] * m.m_matrix[1][1]; |
945 | |
946 | qreal m21 = m_matrix[1][0] * m.m_matrix[0][0] + m_matrix[1][1] * m.m_matrix[1][0]; |
947 | qreal m22 = m_matrix[1][0] * m.m_matrix[0][1] + m_matrix[1][1] * m.m_matrix[1][1]; |
948 | |
949 | qreal m31 = m_matrix[2][0] * m.m_matrix[0][0] + m_matrix[2][1] * m.m_matrix[1][0] + m.m_matrix[2][0]; |
950 | qreal m32 = m_matrix[2][0] * m.m_matrix[0][1] + m_matrix[2][1] * m.m_matrix[1][1] + m.m_matrix[2][1]; |
951 | |
952 | t.m_matrix[0][0] = m11; t.m_matrix[0][1] = m12; |
953 | t.m_matrix[1][0] = m21; t.m_matrix[1][1] = m22; |
954 | t.m_matrix[2][0] = m31; t.m_matrix[2][1] = m32; |
955 | break; |
956 | } |
957 | case TxProject: |
958 | { |
959 | qreal m11 = m_matrix[0][0] * m.m_matrix[0][0] + m_matrix[0][1] * m.m_matrix[1][0] + m_matrix[0][2] * m.m_matrix[2][0]; |
960 | qreal m12 = m_matrix[0][0] * m.m_matrix[0][1] + m_matrix[0][1] * m.m_matrix[1][1] + m_matrix[0][2] * m.m_matrix[2][1]; |
961 | qreal m13 = m_matrix[0][0] * m.m_matrix[0][2] + m_matrix[0][1] * m.m_matrix[1][2] + m_matrix[0][2] * m.m_matrix[2][2]; |
962 | |
963 | qreal m21 = m_matrix[1][0] * m.m_matrix[0][0] + m_matrix[1][1] * m.m_matrix[1][0] + m_matrix[1][2] * m.m_matrix[2][0]; |
964 | qreal m22 = m_matrix[1][0] * m.m_matrix[0][1] + m_matrix[1][1] * m.m_matrix[1][1] + m_matrix[1][2] * m.m_matrix[2][1]; |
965 | qreal m23 = m_matrix[1][0] * m.m_matrix[0][2] + m_matrix[1][1] * m.m_matrix[1][2] + m_matrix[1][2] * m.m_matrix[2][2]; |
966 | |
967 | qreal m31 = m_matrix[2][0] * m.m_matrix[0][0] + m_matrix[2][1] * m.m_matrix[1][0] + m_matrix[2][2] * m.m_matrix[2][0]; |
968 | qreal m32 = m_matrix[2][0] * m.m_matrix[0][1] + m_matrix[2][1] * m.m_matrix[1][1] + m_matrix[2][2] * m.m_matrix[2][1]; |
969 | qreal m33 = m_matrix[2][0] * m.m_matrix[0][2] + m_matrix[2][1] * m.m_matrix[1][2] + m_matrix[2][2] * m.m_matrix[2][2]; |
970 | |
971 | t.m_matrix[0][0] = m11; t.m_matrix[0][1] = m12; t.m_matrix[0][2] = m13; |
972 | t.m_matrix[1][0] = m21; t.m_matrix[1][1] = m22; t.m_matrix[1][2] = m23; |
973 | t.m_matrix[2][0] = m31; t.m_matrix[2][1] = m32; t.m_matrix[2][2] = m33; |
974 | } |
975 | } |
976 | |
977 | t.m_dirty = type; |
978 | t.m_type = type; |
979 | |
980 | return t; |
981 | } |
982 | |
983 | /*! |
984 | \fn QTransform & QTransform::operator*=(qreal scalar) |
985 | \overload |
986 | |
987 | Returns the result of performing an element-wise multiplication of this |
988 | matrix with the given \a scalar. |
989 | */ |
990 | |
991 | /*! |
992 | \fn QTransform & QTransform::operator/=(qreal scalar) |
993 | \overload |
994 | |
995 | Returns the result of performing an element-wise division of this |
996 | matrix by the given \a scalar. |
997 | */ |
998 | |
999 | /*! |
1000 | \fn QTransform & QTransform::operator+=(qreal scalar) |
1001 | \overload |
1002 | |
1003 | Returns the matrix obtained by adding the given \a scalar to each |
1004 | element of this matrix. |
1005 | */ |
1006 | |
1007 | /*! |
1008 | \fn QTransform & QTransform::operator-=(qreal scalar) |
1009 | \overload |
1010 | |
1011 | Returns the matrix obtained by subtracting the given \a scalar from each |
1012 | element of this matrix. |
1013 | */ |
1014 | |
1015 | /*! |
1016 | \fn QTransform &QTransform::operator=(const QTransform &matrix) noexcept |
1017 | |
1018 | Assigns the given \a matrix's values to this matrix. |
1019 | */ |
1020 | |
1021 | /*! |
1022 | Resets the matrix to an identity matrix, i.e. all elements are set |
1023 | to zero, except \c m11 and \c m22 (specifying the scale) and \c m33 |
1024 | which are set to 1. |
1025 | |
1026 | \sa QTransform(), isIdentity(), {QTransform#Basic Matrix |
1027 | Operations}{Basic Matrix Operations} |
1028 | */ |
1029 | void QTransform::reset() |
1030 | { |
1031 | *this = QTransform(); |
1032 | } |
1033 | |
1034 | #ifndef QT_NO_DATASTREAM |
1035 | /*! |
1036 | \fn QDataStream &operator<<(QDataStream &stream, const QTransform &matrix) |
1037 | \since 4.3 |
1038 | \relates QTransform |
1039 | |
1040 | Writes the given \a matrix to the given \a stream and returns a |
1041 | reference to the stream. |
1042 | |
1043 | \sa {Serializing Qt Data Types} |
1044 | */ |
1045 | QDataStream & operator<<(QDataStream &s, const QTransform &m) |
1046 | { |
1047 | s << double(m.m11()) |
1048 | << double(m.m12()) |
1049 | << double(m.m13()) |
1050 | << double(m.m21()) |
1051 | << double(m.m22()) |
1052 | << double(m.m23()) |
1053 | << double(m.m31()) |
1054 | << double(m.m32()) |
1055 | << double(m.m33()); |
1056 | return s; |
1057 | } |
1058 | |
1059 | /*! |
1060 | \fn QDataStream &operator>>(QDataStream &stream, QTransform &matrix) |
1061 | \since 4.3 |
1062 | \relates QTransform |
1063 | |
1064 | Reads the given \a matrix from the given \a stream and returns a |
1065 | reference to the stream. |
1066 | |
1067 | \sa {Serializing Qt Data Types} |
1068 | */ |
1069 | QDataStream & operator>>(QDataStream &s, QTransform &t) |
1070 | { |
1071 | double m11, m12, m13, |
1072 | m21, m22, m23, |
1073 | m31, m32, m33; |
1074 | |
1075 | s >> m11; |
1076 | s >> m12; |
1077 | s >> m13; |
1078 | s >> m21; |
1079 | s >> m22; |
1080 | s >> m23; |
1081 | s >> m31; |
1082 | s >> m32; |
1083 | s >> m33; |
1084 | t.setMatrix(m11, m12, m13, |
1085 | m21, m22, m23, |
1086 | m31, m32, m33); |
1087 | return s; |
1088 | } |
1089 | |
1090 | #endif // QT_NO_DATASTREAM |
1091 | |
1092 | #ifndef QT_NO_DEBUG_STREAM |
1093 | QDebug operator<<(QDebug dbg, const QTransform &m) |
1094 | { |
1095 | static const char typeStr[][12] = |
1096 | { |
1097 | "TxNone", |
1098 | "TxTranslate", |
1099 | "TxScale", |
1100 | "", |
1101 | "TxRotate", |
1102 | "", "", "", |
1103 | "TxShear", |
1104 | "", "", "", "", "", "", "", |
1105 | "TxProject" |
1106 | }; |
1107 | |
1108 | QDebugStateSaver saver(dbg); |
1109 | dbg.nospace() << "QTransform(type="<< typeStr[m.type()] << ',' |
1110 | << " 11="<< m.m11() |
1111 | << " 12="<< m.m12() |
1112 | << " 13="<< m.m13() |
1113 | << " 21="<< m.m21() |
1114 | << " 22="<< m.m22() |
1115 | << " 23="<< m.m23() |
1116 | << " 31="<< m.m31() |
1117 | << " 32="<< m.m32() |
1118 | << " 33="<< m.m33() |
1119 | << ')'; |
1120 | |
1121 | return dbg; |
1122 | } |
1123 | #endif |
1124 | |
1125 | /*! |
1126 | \fn QPoint operator*(const QPoint &point, const QTransform &matrix) |
1127 | \relates QTransform |
1128 | |
1129 | This is the same as \a{matrix}.map(\a{point}). |
1130 | |
1131 | \sa QTransform::map() |
1132 | */ |
1133 | QPoint QTransform::map(const QPoint &p) const |
1134 | { |
1135 | qreal fx = p.x(); |
1136 | qreal fy = p.y(); |
1137 | |
1138 | qreal x = 0, y = 0; |
1139 | |
1140 | do_map(x: fx, y: fy, nx&: x, ny&: y); |
1141 | |
1142 | return QPoint(qRound(d: x), qRound(d: y)); |
1143 | } |
1144 | |
1145 | |
1146 | /*! |
1147 | \fn QPointF operator*(const QPointF &point, const QTransform &matrix) |
1148 | \relates QTransform |
1149 | |
1150 | Same as \a{matrix}.map(\a{point}). |
1151 | |
1152 | \sa QTransform::map() |
1153 | */ |
1154 | |
1155 | /*! |
1156 | \overload |
1157 | |
1158 | Creates and returns a QPointF object that is a copy of the given point, |
1159 | \a p, mapped into the coordinate system defined by this matrix. |
1160 | */ |
1161 | QPointF QTransform::map(const QPointF &p) const |
1162 | { |
1163 | qreal fx = p.x(); |
1164 | qreal fy = p.y(); |
1165 | |
1166 | qreal x = 0, y = 0; |
1167 | |
1168 | do_map(x: fx, y: fy, nx&: x, ny&: y); |
1169 | |
1170 | return QPointF(x, y); |
1171 | } |
1172 | |
1173 | /*! |
1174 | \fn QPoint QTransform::map(const QPoint &point) const |
1175 | \overload |
1176 | |
1177 | Creates and returns a QPoint object that is a copy of the given \a |
1178 | point, mapped into the coordinate system defined by this |
1179 | matrix. Note that the transformed coordinates are rounded to the |
1180 | nearest integer. |
1181 | */ |
1182 | |
1183 | /*! |
1184 | \fn QLineF operator*(const QLineF &line, const QTransform &matrix) |
1185 | \relates QTransform |
1186 | |
1187 | This is the same as \a{matrix}.map(\a{line}). |
1188 | |
1189 | \sa QTransform::map() |
1190 | */ |
1191 | |
1192 | /*! |
1193 | \fn QLine operator*(const QLine &line, const QTransform &matrix) |
1194 | \relates QTransform |
1195 | |
1196 | This is the same as \a{matrix}.map(\a{line}). |
1197 | |
1198 | \sa QTransform::map() |
1199 | */ |
1200 | |
1201 | /*! |
1202 | \overload |
1203 | |
1204 | Creates and returns a QLineF object that is a copy of the given line, |
1205 | \a l, mapped into the coordinate system defined by this matrix. |
1206 | */ |
1207 | QLine QTransform::map(const QLine &l) const |
1208 | { |
1209 | qreal fx1 = l.x1(); |
1210 | qreal fy1 = l.y1(); |
1211 | qreal fx2 = l.x2(); |
1212 | qreal fy2 = l.y2(); |
1213 | |
1214 | qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0; |
1215 | |
1216 | do_map(x: fx1, y: fy1, nx&: x1, ny&: y1); |
1217 | do_map(x: fx2, y: fy2, nx&: x2, ny&: y2); |
1218 | |
1219 | return QLine(qRound(d: x1), qRound(d: y1), qRound(d: x2), qRound(d: y2)); |
1220 | } |
1221 | |
1222 | /*! |
1223 | \overload |
1224 | |
1225 | \fn QLineF QTransform::map(const QLineF &line) const |
1226 | |
1227 | Creates and returns a QLine object that is a copy of the given \a |
1228 | line, mapped into the coordinate system defined by this matrix. |
1229 | Note that the transformed coordinates are rounded to the nearest |
1230 | integer. |
1231 | */ |
1232 | |
1233 | QLineF QTransform::map(const QLineF &l) const |
1234 | { |
1235 | qreal fx1 = l.x1(); |
1236 | qreal fy1 = l.y1(); |
1237 | qreal fx2 = l.x2(); |
1238 | qreal fy2 = l.y2(); |
1239 | |
1240 | qreal x1 = 0, y1 = 0, x2 = 0, y2 = 0; |
1241 | |
1242 | do_map(x: fx1, y: fy1, nx&: x1, ny&: y1); |
1243 | do_map(x: fx2, y: fy2, nx&: x2, ny&: y2); |
1244 | |
1245 | return QLineF(x1, y1, x2, y2); |
1246 | } |
1247 | |
1248 | /*! |
1249 | \fn QPolygonF operator *(const QPolygonF &polygon, const QTransform &matrix) |
1250 | \since 4.3 |
1251 | \relates QTransform |
1252 | |
1253 | This is the same as \a{matrix}.map(\a{polygon}). |
1254 | |
1255 | \sa QTransform::map() |
1256 | */ |
1257 | |
1258 | /*! |
1259 | \fn QPolygon operator*(const QPolygon &polygon, const QTransform &matrix) |
1260 | \relates QTransform |
1261 | |
1262 | This is the same as \a{matrix}.map(\a{polygon}). |
1263 | |
1264 | \sa QTransform::map() |
1265 | */ |
1266 | |
1267 | /*! |
1268 | \fn QPolygonF QTransform::map(const QPolygonF &polygon) const |
1269 | \overload |
1270 | |
1271 | Creates and returns a QPolygonF object that is a copy of the given |
1272 | \a polygon, mapped into the coordinate system defined by this |
1273 | matrix. |
1274 | */ |
1275 | QPolygonF QTransform::map(const QPolygonF &a) const |
1276 | { |
1277 | TransformationType t = inline_type(); |
1278 | if (t <= TxTranslate) |
1279 | return a.translated(dx: m_matrix[2][0], dy: m_matrix[2][1]); |
1280 | |
1281 | int size = a.size(); |
1282 | int i; |
1283 | QPolygonF p(size); |
1284 | const QPointF *da = a.constData(); |
1285 | QPointF *dp = p.data(); |
1286 | |
1287 | for(i = 0; i < size; ++i) { |
1288 | do_map(x: da[i].xp, y: da[i].yp, nx&: dp[i].xp, ny&: dp[i].yp); |
1289 | } |
1290 | return p; |
1291 | } |
1292 | |
1293 | /*! |
1294 | \fn QPolygon QTransform::map(const QPolygon &polygon) const |
1295 | \overload |
1296 | |
1297 | Creates and returns a QPolygon object that is a copy of the given |
1298 | \a polygon, mapped into the coordinate system defined by this |
1299 | matrix. Note that the transformed coordinates are rounded to the |
1300 | nearest integer. |
1301 | */ |
1302 | QPolygon QTransform::map(const QPolygon &a) const |
1303 | { |
1304 | TransformationType t = inline_type(); |
1305 | if (t <= TxTranslate) |
1306 | return a.translated(dx: qRound(d: m_matrix[2][0]), dy: qRound(d: m_matrix[2][1])); |
1307 | |
1308 | int size = a.size(); |
1309 | int i; |
1310 | QPolygon p(size); |
1311 | const QPoint *da = a.constData(); |
1312 | QPoint *dp = p.data(); |
1313 | |
1314 | for(i = 0; i < size; ++i) { |
1315 | qreal nx = 0, ny = 0; |
1316 | do_map(x: da[i].xp, y: da[i].yp, nx, ny); |
1317 | dp[i].xp = qRound(d: nx); |
1318 | dp[i].yp = qRound(d: ny); |
1319 | } |
1320 | return p; |
1321 | } |
1322 | |
1323 | /*! |
1324 | \fn QRegion operator*(const QRegion ®ion, const QTransform &matrix) |
1325 | \relates QTransform |
1326 | |
1327 | This is the same as \a{matrix}.map(\a{region}). |
1328 | |
1329 | \sa QTransform::map() |
1330 | */ |
1331 | |
1332 | extern QPainterPath qt_regionToPath(const QRegion ®ion); |
1333 | |
1334 | /*! |
1335 | \fn QRegion QTransform::map(const QRegion ®ion) const |
1336 | \overload |
1337 | |
1338 | Creates and returns a QRegion object that is a copy of the given |
1339 | \a region, mapped into the coordinate system defined by this matrix. |
1340 | |
1341 | Calling this method can be rather expensive if rotations or |
1342 | shearing are used. |
1343 | */ |
1344 | QRegion QTransform::map(const QRegion &r) const |
1345 | { |
1346 | TransformationType t = inline_type(); |
1347 | if (t == TxNone) |
1348 | return r; |
1349 | |
1350 | if (t == TxTranslate) { |
1351 | QRegion copy(r); |
1352 | copy.translate(dx: qRound(d: m_matrix[2][0]), dy: qRound(d: m_matrix[2][1])); |
1353 | return copy; |
1354 | } |
1355 | |
1356 | if (t == TxScale) { |
1357 | QRegion res; |
1358 | if (m11() < 0 || m22() < 0) { |
1359 | for (const QRect &rect : r) |
1360 | res += qt_mapFillRect(rect: QRectF(rect), xf: *this); |
1361 | } else { |
1362 | QVarLengthArray<QRect, 32> rects; |
1363 | rects.reserve(sz: r.rectCount()); |
1364 | for (const QRect &rect : r) { |
1365 | QRect nr = qt_mapFillRect(rect: QRectF(rect), xf: *this); |
1366 | if (!nr.isEmpty()) |
1367 | rects.append(t: nr); |
1368 | } |
1369 | res.setRects(rect: rects.constData(), num: rects.size()); |
1370 | } |
1371 | return res; |
1372 | } |
1373 | |
1374 | QPainterPath p = map(p: qt_regionToPath(region: r)); |
1375 | return p.toFillPolygon().toPolygon(); |
1376 | } |
1377 | |
1378 | struct QHomogeneousCoordinate |
1379 | { |
1380 | qreal x; |
1381 | qreal y; |
1382 | qreal w; |
1383 | |
1384 | QHomogeneousCoordinate() {} |
1385 | QHomogeneousCoordinate(qreal x_, qreal y_, qreal w_) : x(x_), y(y_), w(w_) {} |
1386 | |
1387 | const QPointF toPoint() const { |
1388 | qreal iw = 1. / w; |
1389 | return QPointF(x * iw, y * iw); |
1390 | } |
1391 | }; |
1392 | |
1393 | static inline QHomogeneousCoordinate mapHomogeneous(const QTransform &transform, const QPointF &p) |
1394 | { |
1395 | QHomogeneousCoordinate c; |
1396 | c.x = transform.m11() * p.x() + transform.m21() * p.y() + transform.m31(); |
1397 | c.y = transform.m12() * p.x() + transform.m22() * p.y() + transform.m32(); |
1398 | c.w = transform.m13() * p.x() + transform.m23() * p.y() + transform.m33(); |
1399 | return c; |
1400 | } |
1401 | |
1402 | static inline bool lineTo_clipped(QPainterPath &path, const QTransform &transform, const QPointF &a, const QPointF &b, |
1403 | bool needsMoveTo, bool needsLineTo = true) |
1404 | { |
1405 | QHomogeneousCoordinate ha = mapHomogeneous(transform, p: a); |
1406 | QHomogeneousCoordinate hb = mapHomogeneous(transform, p: b); |
1407 | |
1408 | if (ha.w < Q_NEAR_CLIP && hb.w < Q_NEAR_CLIP) |
1409 | return false; |
1410 | |
1411 | if (hb.w < Q_NEAR_CLIP) { |
1412 | const qreal t = (Q_NEAR_CLIP - hb.w) / (ha.w - hb.w); |
1413 | |
1414 | hb.x += (ha.x - hb.x) * t; |
1415 | hb.y += (ha.y - hb.y) * t; |
1416 | hb.w = qreal(Q_NEAR_CLIP); |
1417 | } else if (ha.w < Q_NEAR_CLIP) { |
1418 | const qreal t = (Q_NEAR_CLIP - ha.w) / (hb.w - ha.w); |
1419 | |
1420 | ha.x += (hb.x - ha.x) * t; |
1421 | ha.y += (hb.y - ha.y) * t; |
1422 | ha.w = qreal(Q_NEAR_CLIP); |
1423 | |
1424 | const QPointF p = ha.toPoint(); |
1425 | if (needsMoveTo) { |
1426 | path.moveTo(p); |
1427 | needsMoveTo = false; |
1428 | } else { |
1429 | path.lineTo(p); |
1430 | } |
1431 | } |
1432 | |
1433 | if (needsMoveTo) |
1434 | path.moveTo(p: ha.toPoint()); |
1435 | |
1436 | if (needsLineTo) |
1437 | path.lineTo(p: hb.toPoint()); |
1438 | |
1439 | return true; |
1440 | } |
1441 | Q_GUI_EXPORT bool qt_scaleForTransform(const QTransform &transform, qreal *scale); |
1442 | |
1443 | static inline bool cubicTo_clipped(QPainterPath &path, const QTransform &transform, const QPointF &a, const QPointF &b, const QPointF &c, const QPointF &d, bool needsMoveTo) |
1444 | { |
1445 | // Convert projective xformed curves to line |
1446 | // segments so they can be transformed more accurately |
1447 | |
1448 | qreal scale; |
1449 | qt_scaleForTransform(transform, scale: &scale); |
1450 | |
1451 | qreal curveThreshold = scale == 0 ? qreal(0.25) : (qreal(0.25) / scale); |
1452 | |
1453 | QPolygonF segment = QBezier::fromPoints(p1: a, p2: b, p3: c, p4: d).toPolygon(bezier_flattening_threshold: curveThreshold); |
1454 | |
1455 | for (int i = 0; i < segment.size() - 1; ++i) |
1456 | if (lineTo_clipped(path, transform, a: segment.at(i), b: segment.at(i: i+1), needsMoveTo)) |
1457 | needsMoveTo = false; |
1458 | |
1459 | return !needsMoveTo; |
1460 | } |
1461 | |
1462 | static QPainterPath mapProjective(const QTransform &transform, const QPainterPath &path) |
1463 | { |
1464 | QPainterPath result; |
1465 | |
1466 | QPointF last; |
1467 | QPointF lastMoveTo; |
1468 | bool needsMoveTo = true; |
1469 | for (int i = 0; i < path.elementCount(); ++i) { |
1470 | switch (path.elementAt(i).type) { |
1471 | case QPainterPath::MoveToElement: |
1472 | if (i > 0 && lastMoveTo != last) |
1473 | lineTo_clipped(path&: result, transform, a: last, b: lastMoveTo, needsMoveTo); |
1474 | |
1475 | lastMoveTo = path.elementAt(i); |
1476 | last = path.elementAt(i); |
1477 | needsMoveTo = true; |
1478 | break; |
1479 | case QPainterPath::LineToElement: |
1480 | if (lineTo_clipped(path&: result, transform, a: last, b: path.elementAt(i), needsMoveTo)) |
1481 | needsMoveTo = false; |
1482 | last = path.elementAt(i); |
1483 | break; |
1484 | case QPainterPath::CurveToElement: |
1485 | if (cubicTo_clipped(path&: result, transform, a: last, b: path.elementAt(i), c: path.elementAt(i: i+1), d: path.elementAt(i: i+2), needsMoveTo)) |
1486 | needsMoveTo = false; |
1487 | i += 2; |
1488 | last = path.elementAt(i); |
1489 | break; |
1490 | default: |
1491 | Q_ASSERT(false); |
1492 | } |
1493 | } |
1494 | |
1495 | if (path.elementCount() > 0 && lastMoveTo != last) |
1496 | lineTo_clipped(path&: result, transform, a: last, b: lastMoveTo, needsMoveTo, needsLineTo: false); |
1497 | |
1498 | result.setFillRule(path.fillRule()); |
1499 | return result; |
1500 | } |
1501 | |
1502 | /*! |
1503 | \fn QPainterPath operator *(const QPainterPath &path, const QTransform &matrix) |
1504 | \since 4.3 |
1505 | \relates QTransform |
1506 | |
1507 | This is the same as \a{matrix}.map(\a{path}). |
1508 | |
1509 | \sa QTransform::map() |
1510 | */ |
1511 | |
1512 | /*! |
1513 | \overload |
1514 | |
1515 | Creates and returns a QPainterPath object that is a copy of the |
1516 | given \a path, mapped into the coordinate system defined by this |
1517 | matrix. |
1518 | */ |
1519 | QPainterPath QTransform::map(const QPainterPath &path) const |
1520 | { |
1521 | TransformationType t = inline_type(); |
1522 | if (t == TxNone || path.elementCount() == 0) |
1523 | return path; |
1524 | |
1525 | if (t >= TxProject) |
1526 | return mapProjective(transform: *this, path); |
1527 | |
1528 | QPainterPath copy = path; |
1529 | |
1530 | if (t == TxTranslate) { |
1531 | copy.translate(dx: m_matrix[2][0], dy: m_matrix[2][1]); |
1532 | } else { |
1533 | copy.detach(); |
1534 | // Full xform |
1535 | for (int i=0; i<path.elementCount(); ++i) { |
1536 | QPainterPath::Element &e = copy.d_ptr->elements[i]; |
1537 | do_map(x: e.x, y: e.y, nx&: e.x, ny&: e.y); |
1538 | } |
1539 | } |
1540 | |
1541 | return copy; |
1542 | } |
1543 | |
1544 | /*! |
1545 | \fn QPolygon QTransform::mapToPolygon(const QRect &rectangle) const |
1546 | |
1547 | Creates and returns a QPolygon representation of the given \a |
1548 | rectangle, mapped into the coordinate system defined by this |
1549 | matrix. |
1550 | |
1551 | The rectangle's coordinates are transformed using the following |
1552 | formulas: |
1553 | |
1554 | \snippet code/src_gui_painting_qtransform.cpp 1 |
1555 | |
1556 | Polygons and rectangles behave slightly differently when |
1557 | transformed (due to integer rounding), so |
1558 | \c{matrix.map(QPolygon(rectangle))} is not always the same as |
1559 | \c{matrix.mapToPolygon(rectangle)}. |
1560 | |
1561 | \sa mapRect(), {QTransform#Basic Matrix Operations}{Basic Matrix |
1562 | Operations} |
1563 | */ |
1564 | QPolygon QTransform::mapToPolygon(const QRect &rect) const |
1565 | { |
1566 | TransformationType t = inline_type(); |
1567 | |
1568 | QPolygon a(4); |
1569 | qreal x[4] = { 0, 0, 0, 0 }, y[4] = { 0, 0, 0, 0 }; |
1570 | if (t <= TxScale) { |
1571 | x[0] = m_matrix[0][0]*rect.x() + m_matrix[2][0]; |
1572 | y[0] = m_matrix[1][1]*rect.y() + m_matrix[2][1]; |
1573 | qreal w = m_matrix[0][0]*rect.width(); |
1574 | qreal h = m_matrix[1][1]*rect.height(); |
1575 | if (w < 0) { |
1576 | w = -w; |
1577 | x[0] -= w; |
1578 | } |
1579 | if (h < 0) { |
1580 | h = -h; |
1581 | y[0] -= h; |
1582 | } |
1583 | x[1] = x[0]+w; |
1584 | x[2] = x[1]; |
1585 | x[3] = x[0]; |
1586 | y[1] = y[0]; |
1587 | y[2] = y[0]+h; |
1588 | y[3] = y[2]; |
1589 | } else { |
1590 | auto right = rect.x() + rect.width(); |
1591 | auto bottom = rect.y() + rect.height(); |
1592 | do_map(x: rect.x(), y: rect.y(), nx&: x[0], ny&: y[0]); |
1593 | do_map(x: right, y: rect.y(), nx&: x[1], ny&: y[1]); |
1594 | do_map(x: right, y: bottom, nx&: x[2], ny&: y[2]); |
1595 | do_map(x: rect.x(), y: bottom, nx&: x[3], ny&: y[3]); |
1596 | } |
1597 | |
1598 | // all coordinates are correctly, transform to a pointarray |
1599 | // (rounding to the next integer) |
1600 | a.setPoints(nPoints: 4, firstx: qRound(d: x[0]), firsty: qRound(d: y[0]), |
1601 | qRound(d: x[1]), qRound(d: y[1]), |
1602 | qRound(d: x[2]), qRound(d: y[2]), |
1603 | qRound(d: x[3]), qRound(d: y[3])); |
1604 | return a; |
1605 | } |
1606 | |
1607 | /*! |
1608 | Creates a transformation matrix, \a trans, that maps a unit square |
1609 | to a four-sided polygon, \a quad. Returns \c true if the transformation |
1610 | is constructed or false if such a transformation does not exist. |
1611 | |
1612 | \sa quadToSquare(), quadToQuad() |
1613 | */ |
1614 | bool QTransform::squareToQuad(const QPolygonF &quad, QTransform &trans) |
1615 | { |
1616 | if (quad.size() != (quad.isClosed() ? 5 : 4)) |
1617 | return false; |
1618 | |
1619 | qreal dx0 = quad[0].x(); |
1620 | qreal dx1 = quad[1].x(); |
1621 | qreal dx2 = quad[2].x(); |
1622 | qreal dx3 = quad[3].x(); |
1623 | |
1624 | qreal dy0 = quad[0].y(); |
1625 | qreal dy1 = quad[1].y(); |
1626 | qreal dy2 = quad[2].y(); |
1627 | qreal dy3 = quad[3].y(); |
1628 | |
1629 | double ax = dx0 - dx1 + dx2 - dx3; |
1630 | double ay = dy0 - dy1 + dy2 - dy3; |
1631 | |
1632 | if (!ax && !ay) { //afine transform |
1633 | trans.setMatrix(m11: dx1 - dx0, m12: dy1 - dy0, m13: 0, |
1634 | m21: dx2 - dx1, m22: dy2 - dy1, m23: 0, |
1635 | m31: dx0, m32: dy0, m33: 1); |
1636 | } else { |
1637 | double ax1 = dx1 - dx2; |
1638 | double ax2 = dx3 - dx2; |
1639 | double ay1 = dy1 - dy2; |
1640 | double ay2 = dy3 - dy2; |
1641 | |
1642 | /*determinants */ |
1643 | double gtop = ax * ay2 - ax2 * ay; |
1644 | double htop = ax1 * ay - ax * ay1; |
1645 | double bottom = ax1 * ay2 - ax2 * ay1; |
1646 | |
1647 | double a, b, c, d, e, f, g, h; /*i is always 1*/ |
1648 | |
1649 | if (!bottom) |
1650 | return false; |
1651 | |
1652 | g = gtop/bottom; |
1653 | h = htop/bottom; |
1654 | |
1655 | a = dx1 - dx0 + g * dx1; |
1656 | b = dx3 - dx0 + h * dx3; |
1657 | c = dx0; |
1658 | d = dy1 - dy0 + g * dy1; |
1659 | e = dy3 - dy0 + h * dy3; |
1660 | f = dy0; |
1661 | |
1662 | trans.setMatrix(m11: a, m12: d, m13: g, |
1663 | m21: b, m22: e, m23: h, |
1664 | m31: c, m32: f, m33: 1.0); |
1665 | } |
1666 | |
1667 | return true; |
1668 | } |
1669 | |
1670 | /*! |
1671 | \fn bool QTransform::quadToSquare(const QPolygonF &quad, QTransform &trans) |
1672 | |
1673 | Creates a transformation matrix, \a trans, that maps a four-sided polygon, |
1674 | \a quad, to a unit square. Returns \c true if the transformation is constructed |
1675 | or false if such a transformation does not exist. |
1676 | |
1677 | \sa squareToQuad(), quadToQuad() |
1678 | */ |
1679 | bool QTransform::quadToSquare(const QPolygonF &quad, QTransform &trans) |
1680 | { |
1681 | if (!squareToQuad(quad, trans)) |
1682 | return false; |
1683 | |
1684 | bool invertible = false; |
1685 | trans = trans.inverted(invertible: &invertible); |
1686 | |
1687 | return invertible; |
1688 | } |
1689 | |
1690 | /*! |
1691 | Creates a transformation matrix, \a trans, that maps a four-sided |
1692 | polygon, \a one, to another four-sided polygon, \a two. |
1693 | Returns \c true if the transformation is possible; otherwise returns |
1694 | false. |
1695 | |
1696 | This is a convenience method combining quadToSquare() and |
1697 | squareToQuad() methods. It allows the input quad to be |
1698 | transformed into any other quad. |
1699 | |
1700 | \sa squareToQuad(), quadToSquare() |
1701 | */ |
1702 | bool QTransform::quadToQuad(const QPolygonF &one, |
1703 | const QPolygonF &two, |
1704 | QTransform &trans) |
1705 | { |
1706 | QTransform stq; |
1707 | if (!quadToSquare(quad: one, trans)) |
1708 | return false; |
1709 | if (!squareToQuad(quad: two, trans&: stq)) |
1710 | return false; |
1711 | trans *= stq; |
1712 | //qDebug()<<"Final = "<<trans; |
1713 | return true; |
1714 | } |
1715 | |
1716 | /*! |
1717 | Sets the matrix elements to the specified values, \a m11, |
1718 | \a m12, \a m13 \a m21, \a m22, \a m23 \a m31, \a m32 and |
1719 | \a m33. Note that this function replaces the previous values. |
1720 | QTransform provides the translate(), rotate(), scale() and shear() |
1721 | convenience functions to manipulate the various matrix elements |
1722 | based on the currently defined coordinate system. |
1723 | |
1724 | \sa QTransform() |
1725 | */ |
1726 | |
1727 | void QTransform::setMatrix(qreal m11, qreal m12, qreal m13, |
1728 | qreal m21, qreal m22, qreal m23, |
1729 | qreal m31, qreal m32, qreal m33) |
1730 | { |
1731 | m_matrix[0][0] = m11; m_matrix[0][1] = m12; m_matrix[0][2] = m13; |
1732 | m_matrix[1][0] = m21; m_matrix[1][1] = m22; m_matrix[1][2] = m23; |
1733 | m_matrix[2][0] = m31; m_matrix[2][1] = m32; m_matrix[2][2] = m33; |
1734 | m_type = TxNone; |
1735 | m_dirty = TxProject; |
1736 | } |
1737 | |
1738 | QRect QTransform::mapRect(const QRect &rect) const |
1739 | { |
1740 | TransformationType t = inline_type(); |
1741 | if (t <= TxTranslate) |
1742 | return rect.translated(dx: qRound(d: m_matrix[2][0]), dy: qRound(d: m_matrix[2][1])); |
1743 | |
1744 | if (t <= TxScale) { |
1745 | int x = qRound(d: m_matrix[0][0] * rect.x() + m_matrix[2][0]); |
1746 | int y = qRound(d: m_matrix[1][1] * rect.y() + m_matrix[2][1]); |
1747 | int w = qRound(d: m_matrix[0][0] * rect.width()); |
1748 | int h = qRound(d: m_matrix[1][1] * rect.height()); |
1749 | if (w < 0) { |
1750 | w = -w; |
1751 | x -= w; |
1752 | } |
1753 | if (h < 0) { |
1754 | h = -h; |
1755 | y -= h; |
1756 | } |
1757 | return QRect(x, y, w, h); |
1758 | } else { |
1759 | qreal x = 0, y = 0; |
1760 | do_map(x: rect.left(), y: rect.top(), nx&: x, ny&: y); |
1761 | qreal xmin = x; |
1762 | qreal ymin = y; |
1763 | qreal xmax = x; |
1764 | qreal ymax = y; |
1765 | do_map(x: rect.right() + 1, y: rect.top(), nx&: x, ny&: y); |
1766 | xmin = qMin(a: xmin, b: x); |
1767 | ymin = qMin(a: ymin, b: y); |
1768 | xmax = qMax(a: xmax, b: x); |
1769 | ymax = qMax(a: ymax, b: y); |
1770 | do_map(x: rect.right() + 1, y: rect.bottom() + 1, nx&: x, ny&: y); |
1771 | xmin = qMin(a: xmin, b: x); |
1772 | ymin = qMin(a: ymin, b: y); |
1773 | xmax = qMax(a: xmax, b: x); |
1774 | ymax = qMax(a: ymax, b: y); |
1775 | do_map(x: rect.left(), y: rect.bottom() + 1, nx&: x, ny&: y); |
1776 | xmin = qMin(a: xmin, b: x); |
1777 | ymin = qMin(a: ymin, b: y); |
1778 | xmax = qMax(a: xmax, b: x); |
1779 | ymax = qMax(a: ymax, b: y); |
1780 | return QRectF(xmin, ymin, xmax-xmin, ymax-ymin).toRect(); |
1781 | } |
1782 | } |
1783 | |
1784 | /*! |
1785 | \fn QRectF QTransform::mapRect(const QRectF &rectangle) const |
1786 | |
1787 | Creates and returns a QRectF object that is a copy of the given \a |
1788 | rectangle, mapped into the coordinate system defined by this |
1789 | matrix. |
1790 | |
1791 | The rectangle's coordinates are transformed using the following |
1792 | formulas: |
1793 | |
1794 | \snippet code/src_gui_painting_qtransform.cpp 2 |
1795 | |
1796 | If rotation or shearing has been specified, this function returns |
1797 | the \e bounding rectangle. To retrieve the exact region the given |
1798 | \a rectangle maps to, use the mapToPolygon() function instead. |
1799 | |
1800 | \sa mapToPolygon(), {QTransform#Basic Matrix Operations}{Basic Matrix |
1801 | Operations} |
1802 | */ |
1803 | QRectF QTransform::mapRect(const QRectF &rect) const |
1804 | { |
1805 | TransformationType t = inline_type(); |
1806 | if (t <= TxTranslate) |
1807 | return rect.translated(dx: m_matrix[2][0], dy: m_matrix[2][1]); |
1808 | |
1809 | if (t <= TxScale) { |
1810 | qreal x = m_matrix[0][0] * rect.x() + m_matrix[2][0]; |
1811 | qreal y = m_matrix[1][1] * rect.y() + m_matrix[2][1]; |
1812 | qreal w = m_matrix[0][0] * rect.width(); |
1813 | qreal h = m_matrix[1][1] * rect.height(); |
1814 | if (w < 0) { |
1815 | w = -w; |
1816 | x -= w; |
1817 | } |
1818 | if (h < 0) { |
1819 | h = -h; |
1820 | y -= h; |
1821 | } |
1822 | return QRectF(x, y, w, h); |
1823 | } else { |
1824 | qreal x = 0, y = 0; |
1825 | do_map(x: rect.x(), y: rect.y(), nx&: x, ny&: y); |
1826 | qreal xmin = x; |
1827 | qreal ymin = y; |
1828 | qreal xmax = x; |
1829 | qreal ymax = y; |
1830 | do_map(x: rect.x() + rect.width(), y: rect.y(), nx&: x, ny&: y); |
1831 | xmin = qMin(a: xmin, b: x); |
1832 | ymin = qMin(a: ymin, b: y); |
1833 | xmax = qMax(a: xmax, b: x); |
1834 | ymax = qMax(a: ymax, b: y); |
1835 | do_map(x: rect.x() + rect.width(), y: rect.y() + rect.height(), nx&: x, ny&: y); |
1836 | xmin = qMin(a: xmin, b: x); |
1837 | ymin = qMin(a: ymin, b: y); |
1838 | xmax = qMax(a: xmax, b: x); |
1839 | ymax = qMax(a: ymax, b: y); |
1840 | do_map(x: rect.x(), y: rect.y() + rect.height(), nx&: x, ny&: y); |
1841 | xmin = qMin(a: xmin, b: x); |
1842 | ymin = qMin(a: ymin, b: y); |
1843 | xmax = qMax(a: xmax, b: x); |
1844 | ymax = qMax(a: ymax, b: y); |
1845 | return QRectF(xmin, ymin, xmax-xmin, ymax - ymin); |
1846 | } |
1847 | } |
1848 | |
1849 | /*! |
1850 | \fn QRect QTransform::mapRect(const QRect &rectangle) const |
1851 | \overload |
1852 | |
1853 | Creates and returns a QRect object that is a copy of the given \a |
1854 | rectangle, mapped into the coordinate system defined by this |
1855 | matrix. Note that the transformed coordinates are rounded to the |
1856 | nearest integer. |
1857 | */ |
1858 | |
1859 | /*! |
1860 | Maps the given coordinates \a x and \a y into the coordinate |
1861 | system defined by this matrix. The resulting values are put in *\a |
1862 | tx and *\a ty, respectively. |
1863 | |
1864 | The coordinates are transformed using the following formulas: |
1865 | |
1866 | \snippet code/src_gui_painting_qtransform.cpp 3 |
1867 | |
1868 | The point (x, y) is the original point, and (x', y') is the |
1869 | transformed point. |
1870 | |
1871 | \sa {QTransform#Basic Matrix Operations}{Basic Matrix Operations} |
1872 | */ |
1873 | void QTransform::map(qreal x, qreal y, qreal *tx, qreal *ty) const |
1874 | { |
1875 | do_map(x, y, nx&: *tx, ny&: *ty); |
1876 | } |
1877 | |
1878 | /*! |
1879 | \overload |
1880 | |
1881 | Maps the given coordinates \a x and \a y into the coordinate |
1882 | system defined by this matrix. The resulting values are put in *\a |
1883 | tx and *\a ty, respectively. Note that the transformed coordinates |
1884 | are rounded to the nearest integer. |
1885 | */ |
1886 | void QTransform::map(int x, int y, int *tx, int *ty) const |
1887 | { |
1888 | qreal fx = 0, fy = 0; |
1889 | do_map(x, y, nx&: fx, ny&: fy); |
1890 | *tx = qRound(d: fx); |
1891 | *ty = qRound(d: fy); |
1892 | } |
1893 | |
1894 | /*! |
1895 | Returns the transformation type of this matrix. |
1896 | |
1897 | The transformation type is the highest enumeration value |
1898 | capturing all of the matrix's transformations. For example, |
1899 | if the matrix both scales and shears, the type would be \c TxShear, |
1900 | because \c TxShear has a higher enumeration value than \c TxScale. |
1901 | |
1902 | Knowing the transformation type of a matrix is useful for optimization: |
1903 | you can often handle specific types more optimally than handling |
1904 | the generic case. |
1905 | */ |
1906 | QTransform::TransformationType QTransform::type() const |
1907 | { |
1908 | if (m_dirty == TxNone || m_dirty < m_type) |
1909 | return static_cast<TransformationType>(m_type); |
1910 | |
1911 | switch (static_cast<TransformationType>(m_dirty)) { |
1912 | case TxProject: |
1913 | if (!qFuzzyIsNull(d: m_matrix[0][2]) || !qFuzzyIsNull(d: m_matrix[1][2]) || !qFuzzyIsNull(d: m_matrix[2][2] - 1)) { |
1914 | m_type = TxProject; |
1915 | break; |
1916 | } |
1917 | Q_FALLTHROUGH(); |
1918 | case TxShear: |
1919 | case TxRotate: |
1920 | if (!qFuzzyIsNull(d: m_matrix[0][1]) || !qFuzzyIsNull(d: m_matrix[1][0])) { |
1921 | const qreal dot = m_matrix[0][0] * m_matrix[1][0] + m_matrix[0][1] * m_matrix[1][1]; |
1922 | if (qFuzzyIsNull(d: dot)) |
1923 | m_type = TxRotate; |
1924 | else |
1925 | m_type = TxShear; |
1926 | break; |
1927 | } |
1928 | Q_FALLTHROUGH(); |
1929 | case TxScale: |
1930 | if (!qFuzzyIsNull(d: m_matrix[0][0] - 1) || !qFuzzyIsNull(d: m_matrix[1][1] - 1)) { |
1931 | m_type = TxScale; |
1932 | break; |
1933 | } |
1934 | Q_FALLTHROUGH(); |
1935 | case TxTranslate: |
1936 | if (!qFuzzyIsNull(d: m_matrix[2][0]) || !qFuzzyIsNull(d: m_matrix[2][1])) { |
1937 | m_type = TxTranslate; |
1938 | break; |
1939 | } |
1940 | Q_FALLTHROUGH(); |
1941 | case TxNone: |
1942 | m_type = TxNone; |
1943 | break; |
1944 | } |
1945 | |
1946 | m_dirty = TxNone; |
1947 | return static_cast<TransformationType>(m_type); |
1948 | } |
1949 | |
1950 | /*! |
1951 | |
1952 | Returns the transform as a QVariant. |
1953 | */ |
1954 | QTransform::operator QVariant() const |
1955 | { |
1956 | return QVariant::fromValue(value: *this); |
1957 | } |
1958 | |
1959 | |
1960 | /*! |
1961 | \fn bool QTransform::isInvertible() const |
1962 | |
1963 | Returns \c true if the matrix is invertible, otherwise returns \c false. |
1964 | |
1965 | \sa inverted() |
1966 | */ |
1967 | |
1968 | /*! |
1969 | \fn qreal QTransform::m11() const |
1970 | |
1971 | Returns the horizontal scaling factor. |
1972 | |
1973 | \sa scale(), {QTransform#Basic Matrix Operations}{Basic Matrix |
1974 | Operations} |
1975 | */ |
1976 | |
1977 | /*! |
1978 | \fn qreal QTransform::m12() const |
1979 | |
1980 | Returns the vertical shearing factor. |
1981 | |
1982 | \sa shear(), {QTransform#Basic Matrix Operations}{Basic Matrix |
1983 | Operations} |
1984 | */ |
1985 | |
1986 | /*! |
1987 | \fn qreal QTransform::m21() const |
1988 | |
1989 | Returns the horizontal shearing factor. |
1990 | |
1991 | \sa shear(), {QTransform#Basic Matrix Operations}{Basic Matrix |
1992 | Operations} |
1993 | */ |
1994 | |
1995 | /*! |
1996 | \fn qreal QTransform::m22() const |
1997 | |
1998 | Returns the vertical scaling factor. |
1999 | |
2000 | \sa scale(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2001 | Operations} |
2002 | */ |
2003 | |
2004 | /*! |
2005 | \fn qreal QTransform::dx() const |
2006 | |
2007 | Returns the horizontal translation factor. |
2008 | |
2009 | \sa m31(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2010 | Operations} |
2011 | */ |
2012 | |
2013 | /*! |
2014 | \fn qreal QTransform::dy() const |
2015 | |
2016 | Returns the vertical translation factor. |
2017 | |
2018 | \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2019 | Operations} |
2020 | */ |
2021 | |
2022 | |
2023 | /*! |
2024 | \fn qreal QTransform::m13() const |
2025 | |
2026 | Returns the horizontal projection factor. |
2027 | |
2028 | \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2029 | Operations} |
2030 | */ |
2031 | |
2032 | |
2033 | /*! |
2034 | \fn qreal QTransform::m23() const |
2035 | |
2036 | Returns the vertical projection factor. |
2037 | |
2038 | \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2039 | Operations} |
2040 | */ |
2041 | |
2042 | /*! |
2043 | \fn qreal QTransform::m31() const |
2044 | |
2045 | Returns the horizontal translation factor. |
2046 | |
2047 | \sa dx(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2048 | Operations} |
2049 | */ |
2050 | |
2051 | /*! |
2052 | \fn qreal QTransform::m32() const |
2053 | |
2054 | Returns the vertical translation factor. |
2055 | |
2056 | \sa dy(), translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2057 | Operations} |
2058 | */ |
2059 | |
2060 | /*! |
2061 | \fn qreal QTransform::m33() const |
2062 | |
2063 | Returns the division factor. |
2064 | |
2065 | \sa translate(), {QTransform#Basic Matrix Operations}{Basic Matrix |
2066 | Operations} |
2067 | */ |
2068 | |
2069 | /*! |
2070 | \fn qreal QTransform::determinant() const |
2071 | |
2072 | Returns the matrix's determinant. |
2073 | */ |
2074 | |
2075 | /*! |
2076 | \fn bool QTransform::isIdentity() const |
2077 | |
2078 | Returns \c true if the matrix is the identity matrix, otherwise |
2079 | returns \c false. |
2080 | |
2081 | \sa reset() |
2082 | */ |
2083 | |
2084 | /*! |
2085 | \fn bool QTransform::isAffine() const |
2086 | |
2087 | Returns \c true if the matrix represent an affine transformation, |
2088 | otherwise returns \c false. |
2089 | */ |
2090 | |
2091 | /*! |
2092 | \fn bool QTransform::isScaling() const |
2093 | |
2094 | Returns \c true if the matrix represents a scaling |
2095 | transformation, otherwise returns \c false. |
2096 | |
2097 | \sa reset() |
2098 | */ |
2099 | |
2100 | /*! |
2101 | \fn bool QTransform::isRotating() const |
2102 | |
2103 | Returns \c true if the matrix represents some kind of a |
2104 | rotating transformation, otherwise returns \c false. |
2105 | |
2106 | \note A rotation transformation of 180 degrees and/or 360 degrees is treated as a scaling transformation. |
2107 | |
2108 | \sa reset() |
2109 | */ |
2110 | |
2111 | /*! |
2112 | \fn bool QTransform::isTranslating() const |
2113 | |
2114 | Returns \c true if the matrix represents a translating |
2115 | transformation, otherwise returns \c false. |
2116 | |
2117 | \sa reset() |
2118 | */ |
2119 | |
2120 | /*! |
2121 | \fn bool qFuzzyCompare(const QTransform& t1, const QTransform& t2) |
2122 | |
2123 | \relates QTransform |
2124 | \since 4.6 |
2125 | |
2126 | Returns \c true if \a t1 and \a t2 are equal, allowing for a small |
2127 | fuzziness factor for floating-point comparisons; false otherwise. |
2128 | */ |
2129 | |
2130 | |
2131 | // returns true if the transform is uniformly scaling |
2132 | // (same scale in x and y direction) |
2133 | // scale is set to the max of x and y scaling factors |
2134 | Q_GUI_EXPORT |
2135 | bool qt_scaleForTransform(const QTransform &transform, qreal *scale) |
2136 | { |
2137 | const QTransform::TransformationType type = transform.type(); |
2138 | if (type <= QTransform::TxTranslate) { |
2139 | if (scale) |
2140 | *scale = 1; |
2141 | return true; |
2142 | } else if (type == QTransform::TxScale) { |
2143 | const qreal xScale = qAbs(t: transform.m11()); |
2144 | const qreal yScale = qAbs(t: transform.m22()); |
2145 | if (scale) |
2146 | *scale = qMax(a: xScale, b: yScale); |
2147 | return qFuzzyCompare(p1: xScale, p2: yScale); |
2148 | } |
2149 | |
2150 | // rotate then scale: compare columns |
2151 | const qreal xScale1 = transform.m11() * transform.m11() |
2152 | + transform.m21() * transform.m21(); |
2153 | const qreal yScale1 = transform.m12() * transform.m12() |
2154 | + transform.m22() * transform.m22(); |
2155 | |
2156 | // scale then rotate: compare rows |
2157 | const qreal xScale2 = transform.m11() * transform.m11() |
2158 | + transform.m12() * transform.m12(); |
2159 | const qreal yScale2 = transform.m21() * transform.m21() |
2160 | + transform.m22() * transform.m22(); |
2161 | |
2162 | // decide the order of rotate and scale operations |
2163 | if (qAbs(t: xScale1 - yScale1) > qAbs(t: xScale2 - yScale2)) { |
2164 | if (scale) |
2165 | *scale = qSqrt(v: qMax(a: xScale1, b: yScale1)); |
2166 | |
2167 | return type == QTransform::TxRotate && qFuzzyCompare(p1: xScale1, p2: yScale1); |
2168 | } else { |
2169 | if (scale) |
2170 | *scale = qSqrt(v: qMax(a: xScale2, b: yScale2)); |
2171 | |
2172 | return type == QTransform::TxRotate && qFuzzyCompare(p1: xScale2, p2: yScale2); |
2173 | } |
2174 | } |
2175 | |
2176 | QDataStream & operator>>(QDataStream &s, QTransform::Affine &m) |
2177 | { |
2178 | if (s.version() == 1) { |
2179 | float m11, m12, m21, m22, dx, dy; |
2180 | s >> m11; s >> m12; s >> m21; s >> m22; s >> dx; s >> dy; |
2181 | |
2182 | m.m_matrix[0][0] = m11; |
2183 | m.m_matrix[0][1] = m12; |
2184 | m.m_matrix[1][0] = m21; |
2185 | m.m_matrix[1][1] = m22; |
2186 | m.m_matrix[2][0] = dx; |
2187 | m.m_matrix[2][1] = dy; |
2188 | } else { |
2189 | s >> m.m_matrix[0][0]; |
2190 | s >> m.m_matrix[0][1]; |
2191 | s >> m.m_matrix[1][0]; |
2192 | s >> m.m_matrix[1][1]; |
2193 | s >> m.m_matrix[2][0]; |
2194 | s >> m.m_matrix[2][1]; |
2195 | } |
2196 | m.m_matrix[0][2] = 0; |
2197 | m.m_matrix[1][2] = 0; |
2198 | m.m_matrix[2][2] = 1; |
2199 | return s; |
2200 | } |
2201 | |
2202 | QDataStream &operator<<(QDataStream &s, const QTransform::Affine &m) |
2203 | { |
2204 | if (s.version() == 1) { |
2205 | s << (float)m.m_matrix[0][0] |
2206 | << (float)m.m_matrix[0][1] |
2207 | << (float)m.m_matrix[1][0] |
2208 | << (float)m.m_matrix[1][1] |
2209 | << (float)m.m_matrix[2][0] |
2210 | << (float)m.m_matrix[2][1]; |
2211 | } else { |
2212 | s << m.m_matrix[0][0] |
2213 | << m.m_matrix[0][1] |
2214 | << m.m_matrix[1][0] |
2215 | << m.m_matrix[1][1] |
2216 | << m.m_matrix[2][0] |
2217 | << m.m_matrix[2][1]; |
2218 | } |
2219 | return s; |
2220 | } |
2221 | |
2222 | QT_END_NAMESPACE |
2223 |
Definitions
- nanWarning
- do_map
- adjoint
- transposed
- inverted
- translate
- fromTranslate
- scale
- fromScale
- shear
- rotate
- rotate
- rotateRadians
- rotateRadians
- operator==
- qHash
- operator!=
- operator*=
- operator*
- reset
- operator<<
- operator>>
- operator<<
- map
- map
- map
- map
- map
- map
- map
- QHomogeneousCoordinate
- QHomogeneousCoordinate
- QHomogeneousCoordinate
- toPoint
- mapHomogeneous
- lineTo_clipped
- cubicTo_clipped
- mapProjective
- map
- mapToPolygon
- squareToQuad
- quadToSquare
- quadToQuad
- setMatrix
- mapRect
- mapRect
- map
- map
- type
- operator QVariant
- qt_scaleForTransform
- operator>>
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