transforms.h revision 00f9ca0b3aa57e09f3c3f3632c5427fc03499df5
/**
* @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>
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) {
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
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