transforms.h revision b980eb7f577389245ccf42ab7fa9e19801fecbd2
/**
* @file
* @brief Affine transformation classes
*//*
* Authors:
* ? <?@?.?>
* Krzysztof Kosiński <tweenk.pl@gmail.com>
*
* Copyright ?-2009 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 SEEN_Geom_TRANSFORMS_H
#define SEEN_Geom_TRANSFORMS_H
#include <2geom/forward.h>
#include <2geom/affine.h>
#include <cmath>
namespace Geom {
/** @brief Type requirements for transforms.
* @ingroup Concepts */
template <typename T>
struct TransformConcept {
T t;
Affine m;
Point p;
bool bool_;
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();
}
};
/** @brief Base template for transforms. */
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 >
{
Translate() : vec(0, 0) {}
Point vec;
public:
/** @brief Construct a translation from its vector. */
explicit Translate(Point const &p) : vec(p) {}
/** @brief Construct a translation from its coordinates. */
explicit 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; }
/** @brief Get the inverse translation. */
Translate inverse() const { return Translate(-vec); }
/** @brief Get a translation that doesn't do anything. */
static Translate identity() { Translate ret; return ret; }
friend class Point;
};
/** @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;
Scale() : vec(1, 1) {}
public:
explicit Scale(Point const &p) : vec(p) {}
Scale(Coord x, Coord y) : vec(x, y) {}
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; }
Scale inverse() const { return Scale(1./vec[0], 1./vec[1]); }
static Scale identity() { Scale ret; return ret; }
friend class Point;
};
/** @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 >
{
Rotate() : vec(1, 0) {}
Point vec;
public:
/** @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)) {}
/** @brief Construct a rotation from its characteristic vector. */
explicit Rotate(Point const &p) : vec(unit_vector(p)) {}
/** @brief 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 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 0-degree rotation. */
static Rotate identity() { Rotate ret; return ret; }
/** @brief Construct a rotation from its angle in degrees.
* Positive arguments correspond to counter-clockwise rotations (if Y grows upwards). */
static Rotate from_degrees(Coord deg) {
Coord rad = (deg / 180.0) * M_PI;
return Rotate(rad);
}
friend class Point;
};
/** @brief Common base for shearing transforms.
* @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 const*>(this); }
bool operator==(S const &s) const { return f == s.f; }
S inverse() const { return S(-f); }
static S identity() { return S(0); }
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; }
};
/** @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; }
};
/** @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;
}
//TODO: matrix to trans/scale/rotate
} /* namespace Geom */
#endif /* !SEEN_Geom_TRANSFORMS_H */
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