Chris@101: // Boost.Polygon library transform.hpp header file
Chris@16: 
Chris@16: // Copyright (c) Intel Corporation 2008.
Chris@16: // Copyright (c) 2008-2012 Simonson Lucanus.
Chris@16: // Copyright (c) 2012-2012 Andrii Sydorchuk.
Chris@16: 
Chris@16: // See http://www.boost.org for updates, documentation, and revision history.
Chris@16: // Use, modification and distribution is subject to the Boost Software License,
Chris@16: // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_POLYGON_TRANSFORM_HPP
Chris@16: #define BOOST_POLYGON_TRANSFORM_HPP
Chris@16: 
Chris@16: #include "isotropy.hpp"
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace polygon {
Chris@16: // Transformation of Coordinate System.
Chris@16: // Enum meaning:
Chris@16: // Select which direction_2d to change the positive direction of each
Chris@16: // axis in the old coordinate system to map it to the new coordiante system.
Chris@16: // The first direction_2d listed for each enum is the direction to map the
Chris@16: // positive horizontal direction to.
Chris@16: // The second direction_2d listed for each enum is the direction to map the
Chris@16: // positive vertical direction to.
Chris@16: // The zero position bit (LSB) indicates whether the horizontal axis flips
Chris@16: // when transformed.
Chris@16: // The 1st postion bit indicates whether the vertical axis flips when
Chris@16: // transformed.
Chris@16: // The 2nd position bit indicates whether the horizontal and vertical axis
Chris@16: // swap positions when transformed.
Chris@16: // Enum Values:
Chris@16: //   000 EAST NORTH
Chris@16: //   001 WEST NORTH
Chris@16: //   010 EAST SOUTH
Chris@16: //   011 WEST SOUTH
Chris@16: //   100 NORTH EAST
Chris@16: //   101 SOUTH EAST
Chris@16: //   110 NORTH WEST
Chris@16: //   111 SOUTH WEST
Chris@16: class axis_transformation {
Chris@16:  public:
Chris@16:   enum ATR {
Chris@101: #ifdef BOOST_POLYGON_ENABLE_DEPRECATED
Chris@101:     EN = 0,
Chris@101:     WN = 1,
Chris@101:     ES = 2,
Chris@101:     WS = 3,
Chris@101:     NE = 4,
Chris@101:     SE = 5,
Chris@101:     NW = 6,
Chris@101:     SW = 7,
Chris@101: #endif
Chris@16:     NULL_TRANSFORM = 0,
Chris@16:     BEGIN_TRANSFORM = 0,
Chris@101:     EAST_NORTH = 0,
Chris@101:     WEST_NORTH = 1, FLIP_X       = 1,
Chris@101:     EAST_SOUTH = 2, FLIP_Y       = 2,
Chris@101:     WEST_SOUTH = 3, FLIP_XY      = 3,
Chris@101:     NORTH_EAST = 4, SWAP_XY      = 4,
Chris@101:     SOUTH_EAST = 5, ROTATE_LEFT  = 5,
Chris@101:     NORTH_WEST = 6, ROTATE_RIGHT = 6,
Chris@101:     SOUTH_WEST = 7, FLIP_SWAP_XY = 7,
Chris@16:     END_TRANSFORM = 7
Chris@16:   };
Chris@16: 
Chris@16:   // Individual axis enum values indicate which axis an implicit individual
Chris@16:   // axis will be mapped to.
Chris@16:   // The value of the enum paired with an axis provides the information
Chris@16:   // about what the axis will transform to.
Chris@16:   // Three individual axis values, one for each axis, are equivalent to one
Chris@16:   // ATR enum value, but easier to work with because they are independent.
Chris@16:   // Converting to and from the individual axis values from the ATR value
Chris@16:   // is a convenient way to implement tranformation related functionality.
Chris@16:   // Enum meanings:
Chris@16:   // PX: map to positive x axis
Chris@16:   // NX: map to negative x axis
Chris@16:   // PY: map to positive y axis
Chris@16:   // NY: map to negative y axis
Chris@16:   enum INDIVIDUAL_AXIS {
Chris@16:     PX = 0,
Chris@16:     NX = 1,
Chris@16:     PY = 2,
Chris@16:     NY = 3
Chris@16:   };
Chris@16: 
Chris@16:   axis_transformation() : atr_(NULL_TRANSFORM) {}
Chris@16:   explicit axis_transformation(ATR atr) : atr_(atr) {}
Chris@16:   axis_transformation(const axis_transformation& atr) : atr_(atr.atr_) {}
Chris@16: 
Chris@16:   explicit axis_transformation(const orientation_2d& orient) {
Chris@16:     const ATR tmp[2] = {
Chris@16:       NORTH_EAST,  // sort x, then y
Chris@16:       EAST_NORTH   // sort y, then x
Chris@16:     };
Chris@16:     atr_ = tmp[orient.to_int()];
Chris@16:   }
Chris@16: 
Chris@16:   explicit axis_transformation(const direction_2d& dir) {
Chris@16:     const ATR tmp[4] = {
Chris@16:       SOUTH_EAST,  // sort x, then y
Chris@16:       NORTH_EAST,  // sort x, then y
Chris@16:       EAST_SOUTH,  // sort y, then x
Chris@16:       EAST_NORTH   // sort y, then x
Chris@16:     };
Chris@16:     atr_ = tmp[dir.to_int()];
Chris@16:   }
Chris@16: 
Chris@16:   // assignment operator
Chris@16:   axis_transformation& operator=(const axis_transformation& a) {
Chris@16:     atr_ = a.atr_;
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // assignment operator
Chris@16:   axis_transformation& operator=(const ATR& atr) {
Chris@16:     atr_ = atr;
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // equivalence operator
Chris@16:   bool operator==(const axis_transformation& a) const {
Chris@16:     return atr_ == a.atr_;
Chris@16:   }
Chris@16: 
Chris@16:   // inequivalence operator
Chris@16:   bool operator!=(const axis_transformation& a) const {
Chris@16:     return !(*this == a);
Chris@16:   }
Chris@16: 
Chris@16:   // ordering
Chris@16:   bool operator<(const axis_transformation& a) const {
Chris@16:     return atr_ < a.atr_;
Chris@16:   }
Chris@16: 
Chris@16:   // concatenate this with that
Chris@16:   axis_transformation& operator+=(const axis_transformation& a) {
Chris@16:     bool abit2 = (a.atr_ & 4) != 0;
Chris@16:     bool abit1 = (a.atr_ & 2) != 0;
Chris@16:     bool abit0 = (a.atr_ & 1) != 0;
Chris@16:     bool bit2 = (atr_ & 4) != 0;
Chris@16:     bool bit1 = (atr_ & 2) != 0;
Chris@16:     bool bit0 = (atr_ & 1) != 0;
Chris@16:     int indexes[2][2] = {
Chris@16:       { (int)bit2, (int)(!bit2) },
Chris@16:       { (int)abit2, (int)(!abit2) }
Chris@16:     };
Chris@16:     int zero_bits[2][2] = {
Chris@16:       {bit0, bit1}, {abit0, abit1}
Chris@16:     };
Chris@16:     int nbit1 = zero_bits[0][1] ^ zero_bits[1][indexes[0][1]];
Chris@16:     int nbit0 = zero_bits[0][0] ^ zero_bits[1][indexes[0][0]];
Chris@16:     indexes[0][0] = indexes[1][indexes[0][0]];
Chris@16:     indexes[0][1] = indexes[1][indexes[0][1]];
Chris@16:     int nbit2 = indexes[0][0] & 1;  // swap xy
Chris@16:     atr_ = (ATR)((nbit2 << 2) + (nbit1 << 1) + nbit0);
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // concatenation operator
Chris@16:   axis_transformation operator+(const axis_transformation& a) const {
Chris@16:     axis_transformation retval(*this);
Chris@16:     return retval+=a;
Chris@16:   }
Chris@16: 
Chris@16:   // populate_axis_array writes the three INDIVIDUAL_AXIS values that the
Chris@16:   // ATR enum value of 'this' represent into axis_array
Chris@16:   void populate_axis_array(INDIVIDUAL_AXIS axis_array[]) const {
Chris@16:     bool bit2 = (atr_ & 4) != 0;
Chris@16:     bool bit1 = (atr_ & 2) != 0;
Chris@16:     bool bit0 = (atr_ & 1) != 0;
Chris@16:     axis_array[1] = (INDIVIDUAL_AXIS)(((int)(!bit2) << 1) + bit1);
Chris@16:     axis_array[0] = (INDIVIDUAL_AXIS)(((int)(bit2) << 1) + bit0);
Chris@16:   }
Chris@16: 
Chris@16:   // it is recommended that the directions stored in an array
Chris@16:   // in the caller code for easier isotropic access by orientation value
Chris@16:   void get_directions(direction_2d& horizontal_dir,
Chris@16:                       direction_2d& vertical_dir) const {
Chris@16:     bool bit2 = (atr_ & 4) != 0;
Chris@16:     bool bit1 = (atr_ & 2) != 0;
Chris@16:     bool bit0 = (atr_ & 1) != 0;
Chris@16:     vertical_dir = direction_2d((direction_2d_enum)(((int)(!bit2) << 1) + !bit1));
Chris@16:     horizontal_dir = direction_2d((direction_2d_enum)(((int)(bit2) << 1) + !bit0));
Chris@16:   }
Chris@16: 
Chris@16:   // combine_axis_arrays concatenates this_array and that_array overwriting
Chris@16:   // the result into this_array
Chris@16:   static void combine_axis_arrays(INDIVIDUAL_AXIS this_array[],
Chris@16:                                   const INDIVIDUAL_AXIS that_array[]) {
Chris@16:     int indexes[2] = { this_array[0] >> 1, this_array[1] >> 1 };
Chris@16:     int zero_bits[2][2] = {
Chris@16:       { this_array[0] & 1, this_array[1] & 1 },
Chris@16:       { that_array[0] & 1, that_array[1] & 1 }
Chris@16:     };
Chris@16:     this_array[0] = (INDIVIDUAL_AXIS)((int)this_array[0] |
Chris@16:                                       ((int)zero_bits[0][0] ^
Chris@16:                                        (int)zero_bits[1][indexes[0]]));
Chris@16:     this_array[1] = (INDIVIDUAL_AXIS)((int)this_array[1] |
Chris@16:                                       ((int)zero_bits[0][1] ^
Chris@16:                                        (int)zero_bits[1][indexes[1]]));
Chris@16:   }
Chris@16: 
Chris@16:   // write_back_axis_array converts an array of three INDIVIDUAL_AXIS values
Chris@16:   // to the ATR enum value and sets 'this' to that value
Chris@16:   void write_back_axis_array(const INDIVIDUAL_AXIS this_array[]) {
Chris@16:     int bit2 = ((int)this_array[0] & 2) != 0;  // swap xy
Chris@16:     int bit1 = ((int)this_array[1] & 1);
Chris@16:     int bit0 = ((int)this_array[0] & 1);
Chris@16:     atr_ = ATR((bit2 << 2) + (bit1 << 1) + bit0);
Chris@16:   }
Chris@16: 
Chris@16:   // behavior is deterministic but undefined in the case where illegal
Chris@16:   // combinations of directions are passed in.
Chris@16:   axis_transformation& set_directions(const direction_2d& horizontal_dir,
Chris@16:                                       const direction_2d& vertical_dir) {
Chris@16:     int bit2 = (static_cast<orientation_2d>(horizontal_dir).to_int()) != 0;
Chris@16:     int bit1 = !(vertical_dir.to_int() & 1);
Chris@16:     int bit0 = !(horizontal_dir.to_int() & 1);
Chris@16:     atr_ = ATR((bit2 << 2) + (bit1 << 1) + bit0);
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // transform the three coordinates by reference
Chris@16:   template <typename coordinate_type>
Chris@16:   void transform(coordinate_type& x, coordinate_type& y) const {
Chris@16:     int bit2 = (atr_ & 4) != 0;
Chris@16:     int bit1 = (atr_ & 2) != 0;
Chris@16:     int bit0 = (atr_ & 1) != 0;
Chris@16:     x *= -((bit0 << 1) - 1);
Chris@16:     y *= -((bit1 << 1) - 1);
Chris@16:     predicated_swap(bit2 != 0, x, y);
Chris@16:   }
Chris@16: 
Chris@16:   // invert this axis_transformation
Chris@16:   axis_transformation& invert() {
Chris@16:     int bit2 = ((atr_ & 4) != 0);
Chris@16:     int bit1 = ((atr_ & 2) != 0);
Chris@16:     int bit0 = ((atr_ & 1) != 0);
Chris@16:     // swap bit 0 and bit 1 if bit2 is 1
Chris@16:     predicated_swap(bit2 != 0, bit0, bit1);
Chris@16:     bit1 = bit1 << 1;
Chris@16:     atr_ = (ATR)(atr_ & (32+16+8+4));  // mask away bit0 and bit1
Chris@16:     atr_ = (ATR)(atr_ | bit0 | bit1);
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // get the inverse axis_transformation of this
Chris@16:   axis_transformation inverse() const {
Chris@16:     axis_transformation retval(*this);
Chris@16:     return retval.invert();
Chris@16:   }
Chris@16: 
Chris@16:  private:
Chris@16:   ATR atr_;
Chris@16: };
Chris@16: 
Chris@16: // Scaling object to be used to store the scale factor for each axis.
Chris@16: // For use by the transformation object, in that context the scale factor
Chris@16: // is the amount that each axis scales by when transformed.
Chris@16: template <typename scale_factor_type>
Chris@16: class anisotropic_scale_factor {
Chris@16:  public:
Chris@16:   anisotropic_scale_factor() {
Chris@16:     scale_[0] = 1;
Chris@16:     scale_[1] = 1;
Chris@16:   }
Chris@16:   anisotropic_scale_factor(scale_factor_type xscale,
Chris@16:                            scale_factor_type yscale) {
Chris@16:     scale_[0] = xscale;
Chris@16:     scale_[1] = yscale;
Chris@16:   }
Chris@16: 
Chris@16:   // get a component of the anisotropic_scale_factor by orientation
Chris@16:   scale_factor_type get(orientation_2d orient) const {
Chris@16:     return scale_[orient.to_int()];
Chris@16:   }
Chris@16: 
Chris@16:   // set a component of the anisotropic_scale_factor by orientation
Chris@16:   void set(orientation_2d orient, scale_factor_type value) {
Chris@16:     scale_[orient.to_int()] = value;
Chris@16:   }
Chris@16: 
Chris@16:   scale_factor_type x() const {
Chris@16:     return scale_[HORIZONTAL];
Chris@16:   }
Chris@16: 
Chris@16:   scale_factor_type y() const {
Chris@16:     return scale_[VERTICAL];
Chris@16:   }
Chris@16: 
Chris@16:   void x(scale_factor_type value) {
Chris@16:     scale_[HORIZONTAL] = value;
Chris@16:   }
Chris@16: 
Chris@16:   void y(scale_factor_type value) {
Chris@16:     scale_[VERTICAL] = value;
Chris@16:   }
Chris@16: 
Chris@16:   // concatination operator (convolve scale factors)
Chris@16:   anisotropic_scale_factor operator+(const anisotropic_scale_factor& s) const {
Chris@16:     anisotropic_scale_factor<scale_factor_type> retval(*this);
Chris@16:     return retval += s;
Chris@16:   }
Chris@16: 
Chris@16:   // concatinate this with that
Chris@16:   const anisotropic_scale_factor& operator+=(
Chris@16:       const anisotropic_scale_factor& s) {
Chris@16:     scale_[0] *= s.scale_[0];
Chris@16:     scale_[1] *= s.scale_[1];
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // transform this scale with an axis_transform
Chris@16:   anisotropic_scale_factor& transform(axis_transformation atr) {
Chris@16:     direction_2d dirs[2];
Chris@16:     atr.get_directions(dirs[0], dirs[1]);
Chris@16:     scale_factor_type tmp[2] = {scale_[0], scale_[1]};
Chris@16:     for (int i = 0; i < 2; ++i) {
Chris@16:       scale_[orientation_2d(dirs[i]).to_int()] = tmp[i];
Chris@16:     }
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // scale the two coordinates
Chris@16:   template <typename coordinate_type>
Chris@16:   void scale(coordinate_type& x, coordinate_type& y) const {
Chris@16:     x = scaling_policy<coordinate_type>::round(
Chris@16:         (scale_factor_type)x * get(HORIZONTAL));
Chris@16:     y = scaling_policy<coordinate_type>::round(
Chris@16:         (scale_factor_type)y * get(HORIZONTAL));
Chris@16:   }
Chris@16: 
Chris@16:   // invert this scale factor to give the reverse scale factor
Chris@16:   anisotropic_scale_factor& invert() {
Chris@16:     x(1/x());
Chris@16:     y(1/y());
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:  private:
Chris@16:   scale_factor_type scale_[2];
Chris@16: };
Chris@16: 
Chris@16: // Transformation object, stores and provides services for transformations.
Chris@16: // Consits of axis transformation, scale factor and translation.
Chris@16: // The tranlation is the position of the origin of the new coordinate system of
Chris@16: // in the old system. Coordinates are scaled before they are transformed.
Chris@16: template <typename coordinate_type>
Chris@16: class transformation {
Chris@16:  public:
Chris@16:   transformation() : atr_(), p_(0, 0) {}
Chris@16:   explicit transformation(axis_transformation atr) : atr_(atr), p_(0, 0) {}
Chris@16:   explicit transformation(axis_transformation::ATR atr) : atr_(atr), p_(0, 0) {}
Chris@16:   transformation(const transformation& tr) : atr_(tr.atr_), p_(tr.p_) {}
Chris@16: 
Chris@16:   template <typename point_type>
Chris@16:   explicit transformation(const point_type& p) : atr_(), p_(0, 0) {
Chris@16:     set_translation(p);
Chris@16:   }
Chris@16: 
Chris@16:   template <typename point_type>
Chris@16:   transformation(axis_transformation atr,
Chris@16:                  const point_type& p) : atr_(atr), p_(0, 0) {
Chris@16:     set_translation(p);
Chris@16:   }
Chris@16: 
Chris@16:   template <typename point_type>
Chris@16:   transformation(axis_transformation atr,
Chris@16:                  const point_type& referencePt,
Chris@16:                  const point_type& destinationPt) : atr_(), p_(0, 0) {
Chris@16:     transformation<coordinate_type> tmp(referencePt);
Chris@16:     transformation<coordinate_type> rotRef(atr);
Chris@16:     transformation<coordinate_type> tmpInverse = tmp.inverse();
Chris@16:     point_type decon(referencePt);
Chris@16:     deconvolve(decon, destinationPt);
Chris@16:     transformation<coordinate_type> displacement(decon);
Chris@16:     tmp += rotRef;
Chris@16:     tmp += tmpInverse;
Chris@16:     tmp += displacement;
Chris@16:     (*this) = tmp;
Chris@16:   }
Chris@16: 
Chris@16:   // equivalence operator
Chris@16:   bool operator==(const transformation& tr) const {
Chris@16:     return (atr_ == tr.atr_) && (p_ == tr.p_);
Chris@16:   }
Chris@16: 
Chris@16:   // inequivalence operator
Chris@16:   bool operator!=(const transformation& tr) const {
Chris@16:     return !(*this == tr);
Chris@16:   }
Chris@16: 
Chris@16:   // ordering
Chris@16:   bool operator<(const transformation& tr) const {
Chris@16:     return (atr_ < tr.atr_) || ((atr_ == tr.atr_) && (p_ < tr.p_));
Chris@16:   }
Chris@16: 
Chris@16:   // concatenation operator
Chris@16:   transformation operator+(const transformation& tr) const {
Chris@16:     transformation<coordinate_type> retval(*this);
Chris@16:     return retval+=tr;
Chris@16:   }
Chris@16: 
Chris@16:   // concatenate this with that
Chris@16:   const transformation& operator+=(const transformation& tr) {
Chris@16:     coordinate_type x, y;
Chris@16:     transformation<coordinate_type> inv = inverse();
Chris@16:     inv.transform(x, y);
Chris@16:     p_.set(HORIZONTAL, p_.get(HORIZONTAL) + x);
Chris@16:     p_.set(VERTICAL, p_.get(VERTICAL) + y);
Chris@16:     // concatenate axis transforms
Chris@16:     atr_ += tr.atr_;
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // get the axis_transformation portion of this
Chris@16:   axis_transformation get_axis_transformation() const {
Chris@16:     return atr_;
Chris@16:   }
Chris@16: 
Chris@16:   // set the axis_transformation portion of this
Chris@16:   void set_axis_transformation(const axis_transformation& atr) {
Chris@16:     atr_ = atr;
Chris@16:   }
Chris@16: 
Chris@16:   // get the translation
Chris@16:   template <typename point_type>
Chris@16:   void get_translation(point_type& p) const {
Chris@16:     assign(p, p_);
Chris@16:   }
Chris@16: 
Chris@16:   // set the translation
Chris@16:   template <typename point_type>
Chris@16:   void set_translation(const point_type& p) {
Chris@16:     assign(p_, p);
Chris@16:   }
Chris@16: 
Chris@16:   // apply the 2D portion of this transformation to the two coordinates given
Chris@16:   void transform(coordinate_type& x, coordinate_type& y) const {
Chris@16:     y -= p_.get(VERTICAL);
Chris@16:     x -= p_.get(HORIZONTAL);
Chris@16:     atr_.transform(x, y);
Chris@16:   }
Chris@16: 
Chris@16:   // invert this transformation
Chris@16:   transformation& invert() {
Chris@16:     coordinate_type x = p_.get(HORIZONTAL), y = p_.get(VERTICAL);
Chris@16:     atr_.transform(x, y);
Chris@16:     x *= -1;
Chris@16:     y *= -1;
Chris@16:     p_ = point_data<coordinate_type>(x, y);
Chris@16:     atr_.invert();
Chris@16:     return *this;
Chris@16:   }
Chris@16: 
Chris@16:   // get the inverse of this transformation
Chris@16:   transformation inverse() const {
Chris@16:     transformation<coordinate_type> ret_val(*this);
Chris@16:     return ret_val.invert();
Chris@16:   }
Chris@16: 
Chris@16:   void get_directions(direction_2d& horizontal_dir,
Chris@16:                       direction_2d& vertical_dir) const {
Chris@16:     return atr_.get_directions(horizontal_dir, vertical_dir);
Chris@16:   }
Chris@16: 
Chris@16:  private:
Chris@16:   axis_transformation atr_;
Chris@16:   point_data<coordinate_type> p_;
Chris@16: };
Chris@16: }  // polygon
Chris@16: }  // boost
Chris@16: 
Chris@16: #endif  // BOOST_POLYGON_TRANSFORM_HPP