GCC Code Coverage Report

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1			/**
2			* @file
3			* @brief Affine transformation classes
4			*//*
5			* Authors:
6			* ? <?@?.?>
7			* Krzysztof Kosiński <tweenk.pl@gmail.com>
8			* Johan Engelen
9			*
10			* Copyright ?-2012 Authors
11			*
12			* This library is free software; you can redistribute it and/or
13			* modify it either under the terms of the GNU Lesser General Public
14			* License version 2.1 as published by the Free Software Foundation
15			* (the "LGPL") or, at your option, under the terms of the Mozilla
16			* Public License Version 1.1 (the "MPL"). If you do not alter this
17			* notice, a recipient may use your version of this file under either
18			* the MPL or the LGPL.
19			*
20			* You should have received a copy of the LGPL along with this library
21			* in the file COPYING-LGPL-2.1; if not, write to the Free Software
22			* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23			* You should have received a copy of the MPL along with this library
24			* in the file COPYING-MPL-1.1
25			*
26			* The contents of this file are subject to the Mozilla Public License
27			* Version 1.1 (the "License"); you may not use this file except in
28			* compliance with the License. You may obtain a copy of the License at
29			* http://www.mozilla.org/MPL/
30			*
31			* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
32			* OF ANY KIND, either express or implied. See the LGPL or the MPL for
33			* the specific language governing rights and limitations.
34			*/
35
36			#ifndef LIB2GEOM_SEEN_TRANSFORMS_H
37			#define LIB2GEOM_SEEN_TRANSFORMS_H
38
39			#include <cmath>
40			#include <2geom/forward.h>
41			#include <2geom/affine.h>
42			#include <2geom/angle.h>
43			#include <boost/concept/assert.hpp>
44
45			namespace Geom {
46
47			/** @brief Type requirements for transforms.
48			* @ingroup Concepts */
49			template <typename T>
50			struct TransformConcept {
51			T t, t2;
52			Affine m;
53			Point p;
54			bool bool_;
55			Coord epsilon;
56			void constraints() {
57			m = t; //implicit conversion
58			m *= t;
59			m = m * t;
60			m = t * m;
61			p *= t;
62			p = p * t;
63			t *= t;
64			t = t * t;
65			t = pow(t, 3);
66			bool_ = (t == t);
67			bool_ = (t != t);
68			t = T::identity();
69			t = t.inverse();
70			bool_ = are_near(t, t2);
71			bool_ = are_near(t, t2, epsilon);
72			}
73			};
74
75			/** @brief Base template for transforms.
76			* This class is an implementation detail and should not be used directly. */
77			template <typename T>
78			class TransformOperations
79			: boost::equality_comparable< T
80			, boost::multipliable< T
81			> >
82			{
83			public:
84			template <typename T2>
85		803786	Affine operator*(T2 const &t) const {
86		803786	Affine ret(*static_cast<T const*>(this)); ret *= t; return ret;
87			}
88			};
89
90			/** @brief Integer exponentiation for transforms.
91			* Negative exponents will yield the corresponding power of the inverse. This function
92			* can also be applied to matrices.
93			* @param t Affine or transform to exponantiate
94			* @param n Exponent
95			* @return \f$A^n\f$ if @a n is positive, \f$(A^{-1})^n\f$ if negative, identity if zero.
96			* @ingroup Transforms */
97			template <typename T>
98			T pow(T const &t, int n) {
99			BOOST_CONCEPT_ASSERT((TransformConcept<T>));
100			if (n == 0) return T::identity();
101			T result(T::identity());
102			T x(n < 0 ? t.inverse() : t);
103			if (n < 0) n = -n;
104			while ( n ) { // binary exponentiation - fast
105			if ( n & 1 ) { result *= x; --n; }
106			x *= x; n /= 2;
107			}
108			return result;
109			}
110
111			/** @brief Translation by a vector.
112			* @ingroup Transforms */
113			class Translate
114			: public TransformOperations< Translate >
115			{
116			Point vec;
117			public:
118			/// Create a translation that doesn't do anything.
119		✗	Translate() = default;
120			/// Construct a translation from its vector.
121		80637	explicit Translate(Point const &p) : vec(p) {}
122			/// Construct a translation from its coordinates.
123		✗	Translate(Coord x, Coord y) : vec(x, y) {}
124
125		71634	operator Affine() const { return Affine(1, 0, 0, 1, vec[X], vec[Y]); }
126		4356054	Coord operator[](Dim2 dim) const { return vec[dim]; }
127			Coord operator[](unsigned dim) const { return vec[dim]; }
128		✗	Translate &operator*=(Translate const &o) { vec += o.vec; return *this; }
129		✗	bool operator==(Translate const &o) const { return vec == o.vec; }
130
131		1	Point vector() const { return vec; }
132			/// Get the inverse translation.
133		✗	Translate inverse() const { return Translate(-vec); }
134			/// Get a translation that doesn't do anything.
135		✗	static Translate identity() { return {}; }
136
137			friend class Point;
138			};
139
140			inline bool are_near(Translate const &a, Translate const &b, Coord eps = EPSILON) {
141			return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps);
142			}
143
144			/** @brief Scaling from the origin.
145			* During scaling, the point (0,0) will not move. To obtain a scale with a different
146			* invariant point, combine with translation to the origin and back.
147			* @ingroup Transforms */
148			class Scale
149			: public TransformOperations< Scale >
150			{
151			Point vec = { 1, 1 };
152			public:
153			/// Create a scaling that doesn't do anything.
154		✗	Scale() = default;
155			/// Create a scaling from two scaling factors given as coordinates of a point.
156		✗	explicit Scale(Point const &p) : vec(p) {}
157			/// Create a scaling from two scaling factors.
158		80079	Scale(Coord x, Coord y) : vec(x, y) {}
159			/// Create an uniform scaling from a single scaling factor.
160		100	explicit Scale(Coord s) : vec(s, s) {}
161		104385	inline operator Affine() const { return Affine(vec[X], 0, 0, vec[Y], 0, 0); }
162
163		61866	Coord operator[](Dim2 d) const { return vec[d]; }
164			Coord operator[](unsigned d) const { return vec[d]; }
165			//TODO: should we keep these mutators? add them to the other transforms?
166		✗	Coord &operator[](Dim2 d) { return vec[d]; }
167			Coord &operator[](unsigned d) { return vec[d]; }
168		✗	Scale &operator*=(Scale const &b) { vec[X] *= b[X]; vec[Y] *= b[Y]; return *this; }
169		✗	bool operator==(Scale const &o) const { return vec == o.vec; }
170
171			Point vector() const { return vec; }
172		✗	Scale inverse() const { return Scale(1./vec[0], 1./vec[1]); }
173		✗	static Scale identity() { return {}; }
174
175			friend class Point;
176			};
177
178			inline bool are_near(Scale const &a, Scale const &b, Coord eps=EPSILON) {
179			return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps);
180			}
181
182			/** @brief Rotation around the origin.
183			* Combine with translations to the origin and back to get a rotation around a different point.
184			* @ingroup Transforms */
185			class Rotate
186			: public TransformOperations< Rotate >
187			{
188			Point vec = { 1, 0 };
189			public:
190			/// Construct a zero-degree rotation.
191		2	Rotate() = default;
192			/** @brief Construct a rotation from its angle in radians.
193			* Positive arguments correspond to counter-clockwise rotations (if Y grows upwards). */
194		322	explicit Rotate(Coord theta) : vec(Point::polar(theta)) {}
195			/// Construct a rotation from its characteristic vector.
196		20124	explicit Rotate(Point const &p) : vec(p.normalized()) {}
197			/// Construct a rotation from the coordinates of its characteristic vector.
198			explicit Rotate(Coord x, Coord y) : Rotate(Point(x, y)) {}
199		271447	operator Affine() const { return Affine(vec[X], vec[Y], -vec[Y], vec[X], 0, 0); }
200
201			/** @brief Get the characteristic vector of the rotation.
202			* @return A vector that would be obtained by applying this transform to the X versor. */
203			Point const &vector() const { return vec; }
204		10000	Coord angle() const { return atan2(vec); }
205			Coord operator[](Dim2 dim) const { return vec[dim]; }
206			Coord operator[](unsigned dim) const { return vec[dim]; }
207		✗	Rotate &operator*=(Rotate const &o) { vec *= o; return *this; }
208		✗	bool operator==(Rotate const &o) const { return vec == o.vec; }
209		10483	Rotate inverse() const {
210		10483	Rotate r;
211		10483	r.vec = Point(vec[X], -vec[Y]);
212		10483	return r;
213			}
214			/// @brief Get a zero-degree rotation.
215		✗	static Rotate identity() { return {}; }
216			/** @brief Construct a rotation from its angle in degrees.
217			* Positive arguments correspond to clockwise rotations if Y grows downwards. */
218		✗	static Rotate from_degrees(Coord deg) { return Rotate(rad_from_deg(deg)); }
219			static Affine around(Point const &p, Coord angle);
220
221			friend class Point;
222			};
223
224			inline bool are_near(Rotate const &a, Rotate const &b, Coord eps = EPSILON) {
225			return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps);
226			}
227
228			/** @brief Common base for shearing transforms.
229			* This class is an implementation detail and should not be used directly.
230			* @ingroup Transforms */
231			template <typename S>
232			class ShearBase
233			: public TransformOperations<S>
234			{
235			protected:
236			Coord f = 0;
237		✗	ShearBase() = default;
238			explicit ShearBase(Coord _f) : f(_f) {}
239			public:
240			Coord factor() const { return f; }
241			void setFactor(Coord nf) { f = nf; }
242		✗	S &operator*=(S const &s) { f += s.f; return static_cast<S &>(*this); }
243			bool operator==(ShearBase<S> const &s) const { return f == s.f; }
244			S inverse() const { return S(-f); }
245		✗	static S identity() { return {}; }
246
247			friend class Point;
248			friend class Affine;
249			};
250
251			/** @brief Horizontal shearing.
252			* Points on the X axis will not move. Combine with translations to get a shear
253			* with a different invariant line.
254			* @ingroup Transforms */
255			class HShear
256			: public ShearBase<HShear>
257			{
258			public:
259		✗	HShear() = default;
260			explicit HShear(Coord h) : ShearBase<HShear>(h) {}
261		✗	operator Affine() const { return Affine(1, 0, f, 1, 0, 0); }
262			};
263
264			inline bool are_near(HShear const &a, HShear const &b, Coord eps=EPSILON) {
265			return are_near(a.factor(), b.factor(), eps);
266			}
267
268			/** @brief Vertical shearing.
269			* Points on the Y axis will not move. Combine with translations to get a shear
270			* with a different invariant line.
271			* @ingroup Transforms */
272			class VShear
273			: public ShearBase<VShear>
274			{
275			public:
276		✗	VShear() = default;
277			explicit VShear(Coord h) : ShearBase<VShear>(h) {}
278		✗	operator Affine() const { return Affine(1, f, 0, 1, 0, 0); }
279			};
280
281			inline bool are_near(VShear const &a, VShear const &b, Coord eps = EPSILON) {
282			return are_near(a.factor(), b.factor(), eps);
283			}
284
285			/** @brief Combination of a translation and uniform scale.
286			* The translation part is applied first, then the result is scaled from the new origin.
287			* This way when the class is used to accumulate a zoom transform, trans always points
288			* to the new origin in original coordinates.
289			* @ingroup Transforms */
290			class Zoom
291			: public TransformOperations< Zoom >
292			{
293			Coord _scale = 1;
294			Point _trans;
295			public:
296		✗	Zoom() = default;
297			/// Construct a zoom from a scaling factor.
298			explicit Zoom(Coord s) : _scale(s) {}
299			/// Construct a zoom from a translation.
300			explicit Zoom(Point const &t) : _trans(t) {}
301			explicit Zoom(Translate const &t) : Zoom(t.vector()) {}
302			/// Construct a zoom from a scaling factor and a translation.
303		2	Zoom(Coord s, Point const &t) : _scale(s), _trans(t) {}
304		1	Zoom(Coord s, Translate const &t) : Zoom(s, t.vector()) {}
305
306		✗	operator Affine() const {
307		✗	return Affine(_scale, 0, 0, _scale, _trans[X] * _scale, _trans[Y] * _scale);
308			}
309		✗	Zoom &operator*=(Zoom const &z) {
310		✗	_trans += z._trans / _scale;
311		✗	_scale *= z._scale;
312		✗	return *this;
313			}
314			bool operator==(Zoom const &z) const { return _scale == z._scale && _trans == z._trans; }
315
316		✗	Coord scale() const { return _scale; }
317			void setScale(Coord s) { _scale = s; }
318			Point translation() const { return _trans; }
319			void setTranslation(Point const &p) { _trans = p; }
320			Zoom inverse() const { return Zoom(1 / _scale, Translate(-_trans * _scale)); }
321		✗	static Zoom identity() { return {}; }
322			static Zoom map_rect(Rect const &old_r, Rect const &new_r);
323
324			friend class Point;
325			friend class Affine;
326			};
327
328			inline bool are_near(Zoom const &a, Zoom const &b, Coord eps = EPSILON) {
329			return are_near(a.scale(), b.scale(), eps) &&
330			are_near(a.translation(), b.translation(), eps);
331			}
332
333			/** @brief Specialization of exponentiation for Scale.
334			* @relates Scale */
335			template<>
336			inline Scale pow(Scale const &s, int n) {
337			return Scale(::pow(s[X], n), ::pow(s[Y], n));
338			}
339			/** @brief Specialization of exponentiation for Translate.
340			* @relates Translate */
341			template<>
342			inline Translate pow(Translate const &t, int n) {
343			return Translate(t[X] * n, t[Y] * n);
344			}
345
346			/** @brief Reflects objects about line.
347			* The line, defined by a vector along the line and a point on it, acts as a mirror.
348			* @ingroup Transforms
349			* @see Line::reflection()
350			*/
351			Affine reflection(Point const & vector, Point const & origin);
352
353			//TODO: decomposition of Affine into some finite combination of the above classes
354
355			} // namespace Geom
356
357			#endif // LIB2GEOM_SEEN_TRANSFORMS_H
358
359			/*
360			Local Variables:
361			mode:c++
362			c-file-style:"stroustrup"
363			c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
364			indent-tabs-mode:nil
365			fill-column:99
366			End:
367			*/
368			// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
369