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diff --git a/include/2geom/transforms.h b/include/2geom/transforms.h new file mode 100644 index 0000000..cc55e29 --- /dev/null +++ b/include/2geom/transforms.h @@ -0,0 +1,370 @@ +/** + * @file + * @brief Affine transformation classes + *//* + * Authors: + * ? <?@?.?> + * Krzysztof Kosiński <tweenk.pl@gmail.com> + * Johan Engelen + * + * Copyright ?-2012 Authors + * + * This library is free software; you can redistribute it and/or + * modify it either under the terms of the GNU Lesser General Public + * License version 2.1 as published by the Free Software Foundation + * (the "LGPL") or, at your option, under the terms of the Mozilla + * Public License Version 1.1 (the "MPL"). If you do not alter this + * notice, a recipient may use your version of this file under either + * the MPL or the LGPL. + * + * You should have received a copy of the LGPL along with this library + * in the file COPYING-LGPL-2.1; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * You should have received a copy of the MPL along with this library + * in the file COPYING-MPL-1.1 + * + * The contents of this file are subject to the Mozilla Public License + * Version 1.1 (the "License"); you may not use this file except in + * compliance with the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY + * OF ANY KIND, either express or implied. See the LGPL or the MPL for + * the specific language governing rights and limitations. + */ + +#ifndef LIB2GEOM_SEEN_TRANSFORMS_H +#define LIB2GEOM_SEEN_TRANSFORMS_H + +#include <cmath> +#include <2geom/forward.h> +#include <2geom/affine.h> +#include <2geom/angle.h> +#include <boost/concept/assert.hpp> + +namespace Geom { + +/** @brief Type requirements for transforms. + * @ingroup Concepts */ +template <typename T> +struct TransformConcept { + T t, t2; + Affine m; + Point p; + bool bool_; + Coord epsilon; + void constraints() { + m = t; //implicit conversion + m *= t; + m = m * t; + m = t * m; + p *= t; + p = p * t; + t *= t; + t = t * t; + t = pow(t, 3); + bool_ = (t == t); + bool_ = (t != t); + t = T::identity(); + t = t.inverse(); + bool_ = are_near(t, t2); + bool_ = are_near(t, t2, epsilon); + } +}; + +/** @brief Base template for transforms. + * This class is an implementation detail and should not be used directly. */ +template <typename T> +class TransformOperations + : boost::equality_comparable< T + , boost::multipliable< T + > > +{ +public: + template <typename T2> + Affine operator*(T2 const &t) const { + Affine ret(*static_cast<T const*>(this)); ret *= t; return ret; + } +}; + +/** @brief Integer exponentiation for transforms. + * Negative exponents will yield the corresponding power of the inverse. This function + * can also be applied to matrices. + * @param t Affine or transform to exponantiate + * @param n Exponent + * @return \f$A^n\f$ if @a n is positive, \f$(A^{-1})^n\f$ if negative, identity if zero. + * @ingroup Transforms */ +template <typename T> +T pow(T const &t, int n) { + BOOST_CONCEPT_ASSERT((TransformConcept<T>)); + if (n == 0) return T::identity(); + T result(T::identity()); + T x(n < 0 ? t.inverse() : t); + if (n < 0) n = -n; + while ( n ) { // binary exponentiation - fast + if ( n & 1 ) { result *= x; --n; } + x *= x; n /= 2; + } + return result; +} + +/** @brief Translation by a vector. + * @ingroup Transforms */ +class Translate + : public TransformOperations< Translate > +{ + Point vec; +public: + /// Create a translation that doesn't do anything. + Translate() : vec(0, 0) {} + /// Construct a translation from its vector. + Translate(Point const &p) : vec(p) {} + /// Construct a translation from its coordinates. + Translate(Coord x, Coord y) : vec(x, y) {} + + operator Affine() const { Affine ret(1, 0, 0, 1, vec[X], vec[Y]); return ret; } + Coord operator[](Dim2 dim) const { return vec[dim]; } + Coord operator[](unsigned dim) const { return vec[dim]; } + Translate &operator*=(Translate const &o) { vec += o.vec; return *this; } + bool operator==(Translate const &o) const { return vec == o.vec; } + + Point vector() const { return vec; } + /// Get the inverse translation. + Translate inverse() const { return Translate(-vec); } + /// Get a translation that doesn't do anything. + static Translate identity() { Translate ret; return ret; } + + friend class Point; +}; + +inline bool are_near(Translate const &a, Translate const &b, Coord eps=EPSILON) { + return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps); +} + +/** @brief Scaling from the origin. + * During scaling, the point (0,0) will not move. To obtain a scale with a different + * invariant point, combine with translation to the origin and back. + * @ingroup Transforms */ +class Scale + : public TransformOperations< Scale > +{ + Point vec; +public: + /// Create a scaling that doesn't do anything. + Scale() : vec(1, 1) {} + /// Create a scaling from two scaling factors given as coordinates of a point. + explicit Scale(Point const &p) : vec(p) {} + /// Create a scaling from two scaling factors. + Scale(Coord x, Coord y) : vec(x, y) {} + /// Create an uniform scaling from a single scaling factor. + explicit Scale(Coord s) : vec(s, s) {} + inline operator Affine() const { Affine ret(vec[X], 0, 0, vec[Y], 0, 0); return ret; } + + Coord operator[](Dim2 d) const { return vec[d]; } + Coord operator[](unsigned d) const { return vec[d]; } + //TODO: should we keep these mutators? add them to the other transforms? + Coord &operator[](Dim2 d) { return vec[d]; } + Coord &operator[](unsigned d) { return vec[d]; } + Scale &operator*=(Scale const &b) { vec[X] *= b[X]; vec[Y] *= b[Y]; return *this; } + bool operator==(Scale const &o) const { return vec == o.vec; } + + Point vector() const { return vec; } + Scale inverse() const { return Scale(1./vec[0], 1./vec[1]); } + static Scale identity() { Scale ret; return ret; } + + friend class Point; +}; + +inline bool are_near(Scale const &a, Scale const &b, Coord eps=EPSILON) { + return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps); +} + +/** @brief Rotation around the origin. + * Combine with translations to the origin and back to get a rotation around a different point. + * @ingroup Transforms */ +class Rotate + : public TransformOperations< Rotate > +{ + Point vec; ///< @todo Convert to storing the angle, as it's more space-efficient. +public: + /// Construct a zero-degree rotation. + Rotate() : vec(1, 0) {} + /** @brief Construct a rotation from its angle in radians. + * Positive arguments correspond to counter-clockwise rotations (if Y grows upwards). */ + explicit Rotate(Coord theta) : vec(Point::polar(theta)) {} + /// Construct a rotation from its characteristic vector. + explicit Rotate(Point const &p) : vec(unit_vector(p)) {} + /// Construct a rotation from the coordinates of its characteristic vector. + explicit Rotate(Coord x, Coord y) { Rotate(Point(x, y)); } + operator Affine() const { Affine ret(vec[X], vec[Y], -vec[Y], vec[X], 0, 0); return ret; } + + /** @brief Get the characteristic vector of the rotation. + * @return A vector that would be obtained by applying this transform to the X versor. */ + Point vector() const { return vec; } + Coord angle() const { return atan2(vec); } + Coord operator[](Dim2 dim) const { return vec[dim]; } + Coord operator[](unsigned dim) const { return vec[dim]; } + Rotate &operator*=(Rotate const &o) { vec *= o; return *this; } + bool operator==(Rotate const &o) const { return vec == o.vec; } + Rotate inverse() const { + Rotate r; + r.vec = Point(vec[X], -vec[Y]); + return r; + } + /// @brief Get a zero-degree rotation. + static Rotate identity() { Rotate ret; return ret; } + /** @brief Construct a rotation from its angle in degrees. + * Positive arguments correspond to clockwise rotations if Y grows downwards. */ + static Rotate from_degrees(Coord deg) { + Coord rad = (deg / 180.0) * M_PI; + return Rotate(rad); + } + static Affine around(Point const &p, Coord angle); + + friend class Point; +}; + +inline bool are_near(Rotate const &a, Rotate const &b, Coord eps=EPSILON) { + return are_near(a[X], b[X], eps) && are_near(a[Y], b[Y], eps); +} + +/** @brief Common base for shearing transforms. + * This class is an implementation detail and should not be used directly. + * @ingroup Transforms */ +template <typename S> +class ShearBase + : public TransformOperations< S > +{ +protected: + Coord f; + ShearBase(Coord _f) : f(_f) {} +public: + Coord factor() const { return f; } + void setFactor(Coord nf) { f = nf; } + S &operator*=(S const &s) { f += s.f; return static_cast<S &>(*this); } + bool operator==(S const &s) const { return f == s.f; } + S inverse() const { S ret(-f); return ret; } + static S identity() { S ret(0); return ret; } + + friend class Point; + friend class Affine; +}; + +/** @brief Horizontal shearing. + * Points on the X axis will not move. Combine with translations to get a shear + * with a different invariant line. + * @ingroup Transforms */ +class HShear + : public ShearBase<HShear> +{ +public: + explicit HShear(Coord h) : ShearBase<HShear>(h) {} + operator Affine() const { Affine ret(1, 0, f, 1, 0, 0); return ret; } +}; + +inline bool are_near(HShear const &a, HShear const &b, Coord eps=EPSILON) { + return are_near(a.factor(), b.factor(), eps); +} + +/** @brief Vertical shearing. + * Points on the Y axis will not move. Combine with translations to get a shear + * with a different invariant line. + * @ingroup Transforms */ +class VShear + : public ShearBase<VShear> +{ +public: + explicit VShear(Coord h) : ShearBase<VShear>(h) {} + operator Affine() const { Affine ret(1, f, 0, 1, 0, 0); return ret; } +}; + +inline bool are_near(VShear const &a, VShear const &b, Coord eps=EPSILON) { + return are_near(a.factor(), b.factor(), eps); +} + +/** @brief Combination of a translation and uniform scale. + * The translation part is applied first, then the result is scaled from the new origin. + * This way when the class is used to accumulate a zoom transform, trans always points + * to the new origin in original coordinates. + * @ingroup Transforms */ +class Zoom + : public TransformOperations< Zoom > +{ + Coord _scale; + Point _trans; + Zoom() : _scale(1), _trans() {} +public: + /// Construct a zoom from a scaling factor. + explicit Zoom(Coord s) : _scale(s), _trans() {} + /// Construct a zoom from a translation. + explicit Zoom(Translate const &t) : _scale(1), _trans(t.vector()) {} + /// Construct a zoom from a scaling factor and a translation. + Zoom(Coord s, Translate const &t) : _scale(s), _trans(t.vector()) {} + + operator Affine() const { + Affine ret(_scale, 0, 0, _scale, _trans[X] * _scale, _trans[Y] * _scale); + return ret; + } + Zoom &operator*=(Zoom const &z) { + _trans += z._trans / _scale; + _scale *= z._scale; + return *this; + } + bool operator==(Zoom const &z) const { return _scale == z._scale && _trans == z._trans; } + + Coord scale() const { return _scale; } + void setScale(Coord s) { _scale = s; } + Point translation() const { return _trans; } + void setTranslation(Point const &p) { _trans = p; } + Zoom inverse() const { Zoom ret(1/_scale, Translate(-_trans*_scale)); return ret; } + static Zoom identity() { Zoom ret(1.0); return ret; } + static Zoom map_rect(Rect const &old_r, Rect const &new_r); + + friend class Point; + friend class Affine; +}; + +inline bool are_near(Zoom const &a, Zoom const &b, Coord eps=EPSILON) { + return are_near(a.scale(), b.scale(), eps) && + are_near(a.translation(), b.translation(), eps); +} + +/** @brief Specialization of exponentiation for Scale. + * @relates Scale */ +template<> +inline Scale pow(Scale const &s, int n) { + Scale ret(::pow(s[X], n), ::pow(s[Y], n)); + return ret; +} +/** @brief Specialization of exponentiation for Translate. + * @relates Translate */ +template<> +inline Translate pow(Translate const &t, int n) { + Translate ret(t[X] * n, t[Y] * n); + return ret; +} + + +/** @brief Reflects objects about line. + * The line, defined by a vector along the line and a point on it, acts as a mirror. + * @ingroup Transforms + * @see Line::reflection() + */ +Affine reflection(Point const & vector, Point const & origin); + +//TODO: decomposition of Affine into some finite combination of the above classes + +} // end namespace Geom + +#endif // LIB2GEOM_SEEN_TRANSFORMS_H + +/* + Local Variables: + mode:c++ + c-file-style:"stroustrup" + c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) + indent-tabs-mode:nil + fill-column:99 + End: +*/ +// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : |