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// Anti-Grain Geometry - Version 2.4
// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
//
// Permission to copy, use, modify, sell and distribute this software
// is granted provided this copyright notice appears in all copies.
// This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
//
//----------------------------------------------------------------------------
// Contact: mcseem@antigrain.com
// mcseemagg@yahoo.com
// http://www.antigrain.com
//----------------------------------------------------------------------------
//
// Affine transformation classes.
//
//----------------------------------------------------------------------------
#ifndef AGG_TRANS_AFFINE_INCLUDED
#define AGG_TRANS_AFFINE_INCLUDED
#include <cmath>
#include "agg_basics.h"
namespace agg
{
const double affine_epsilon = 1e-14;
//============================================================trans_affine
//
// See Implementation agg_trans_affine.cpp
//
// Affine transformation are linear transformations in Cartesian coordinates
// (strictly speaking not only in Cartesian, but for the beginning we will
// think so). They are rotation, scaling, translation and skewing.
// After any affine transformation a line segment remains a line segment
// and it will never become a curve.
//
// There will be no math about matrix calculations, since it has been
// described many times. Ask yourself a very simple question:
// "why do we need to understand and use some matrix stuff instead of just
// rotating, scaling and so on". The answers are:
//
// 1. Any combination of transformations can be done by only 4 multiplications
// and 4 additions in floating point.
// 2. One matrix transformation is equivalent to the number of consecutive
// discrete transformations, i.e. the matrix "accumulates" all transformations
// in the order of their settings. Suppose we have 4 transformations:
// * rotate by 30 degrees,
// * scale X to 2.0,
// * scale Y to 1.5,
// * move to (100, 100).
// The result will depend on the order of these transformations,
// and the advantage of matrix is that the sequence of discret calls:
// rotate(30), scaleX(2.0), scaleY(1.5), move(100,100)
// will have exactly the same result as the following matrix transformations:
//
// affine_matrix m;
// m *= rotate_matrix(30);
// m *= scaleX_matrix(2.0);
// m *= scaleY_matrix(1.5);
// m *= move_matrix(100,100);
//
// m.transform_my_point_at_last(x, y);
//
// What is the good of it? In real life we will set-up the matrix only once
// and then transform many points, let alone the convenience to set any
// combination of transformations.
//
// So, how to use it? Very easy - literally as it's shown above. Not quite,
// let us write a correct example:
//
// agg::trans_affine m;
// m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0);
// m *= agg::trans_affine_scaling(2.0, 1.5);
// m *= agg::trans_affine_translation(100.0, 100.0);
// m.transform(&x, &y);
//
// The affine matrix is all you need to perform any linear transformation,
// but all transformations have origin point (0,0). It means that we need to
// use 2 translations if we want to rotate someting around (100,100):
//
// m *= agg::trans_affine_translation(-100.0, -100.0); // move to (0,0)
// m *= agg::trans_affine_rotation(30.0 * 3.1415926 / 180.0); // rotate
// m *= agg::trans_affine_translation(100.0, 100.0); // move back to (100,100)
//----------------------------------------------------------------------
struct trans_affine
{
static const trans_affine identity;
double sx, shy, shx, sy, tx, ty;
//------------------------------------------ Construction
// Identity matrix
trans_affine() :
sx(1.0), shy(0.0), shx(0.0), sy(1.0), tx(0.0), ty(0.0)
{}
// Custom matrix. Usually used in derived classes
trans_affine(double v0, double v1, double v2,
double v3, double v4, double v5) :
sx(v0), shy(v1), shx(v2), sy(v3), tx(v4), ty(v5)
{}
// Custom matrix from m[6]
explicit trans_affine(const double* m) :
sx(m[0]), shy(m[1]), shx(m[2]), sy(m[3]), tx(m[4]), ty(m[5])
{}
// Rectangle to a parallelogram.
trans_affine(double x1, double y1, double x2, double y2,
const double* parl)
{
rect_to_parl(x1, y1, x2, y2, parl);
}
// Parallelogram to a rectangle.
trans_affine(const double* parl,
double x1, double y1, double x2, double y2)
{
parl_to_rect(parl, x1, y1, x2, y2);
}
// Arbitrary parallelogram transformation.
trans_affine(const double* src, const double* dst)
{
parl_to_parl(src, dst);
}
//---------------------------------- Parellelogram transformations
// transform a parallelogram to another one. Src and dst are
// pointers to arrays of three points (double[6], x1,y1,...) that
// identify three corners of the parallelograms assuming implicit
// fourth point. The arguments are arrays of double[6] mapped
// to x1,y1, x2,y2, x3,y3 where the coordinates are:
// *-----------------*
// / (x3,y3)/
// / /
// /(x1,y1) (x2,y2)/
// *-----------------*
const trans_affine& parl_to_parl(const double* src,
const double* dst);
const trans_affine& rect_to_parl(double x1, double y1,
double x2, double y2,
const double* parl);
const trans_affine& parl_to_rect(const double* parl,
double x1, double y1,
double x2, double y2);
//------------------------------------------ Operations
// Reset - load an identity matrix
const trans_affine& reset();
// Direct transformations operations
const trans_affine& translate(double x, double y);
const trans_affine& rotate(double a);
const trans_affine& scale(double s);
const trans_affine& scale(double x, double y);
// Multiply matrix to another one
const trans_affine& multiply(const trans_affine& m);
// Multiply "m" to "this" and assign the result to "this"
const trans_affine& premultiply(const trans_affine& m);
// Multiply matrix to inverse of another one
const trans_affine& multiply_inv(const trans_affine& m);
// Multiply inverse of "m" to "this" and assign the result to "this"
const trans_affine& premultiply_inv(const trans_affine& m);
// Invert matrix. Do not try to invert degenerate matrices,
// there's no check for validity. If you set scale to 0 and
// then try to invert matrix, expect unpredictable result.
const trans_affine& invert();
// Mirroring around X
const trans_affine& flip_x();
// Mirroring around Y
const trans_affine& flip_y();
//------------------------------------------- Load/Store
// Store matrix to an array [6] of double
void store_to(double* m) const
{
*m++ = sx; *m++ = shy; *m++ = shx; *m++ = sy; *m++ = tx; *m++ = ty;
}
// Load matrix from an array [6] of double
const trans_affine& load_from(const double* m)
{
sx = *m++; shy = *m++; shx = *m++; sy = *m++; tx = *m++; ty = *m++;
return *this;
}
//------------------------------------------- Operators
// Multiply the matrix by another one
const trans_affine& operator *= (const trans_affine& m)
{
return multiply(m);
}
// Multiply the matrix by inverse of another one
const trans_affine& operator /= (const trans_affine& m)
{
return multiply_inv(m);
}
// Multiply the matrix by another one and return
// the result in a separate matrix.
trans_affine operator * (const trans_affine& m) const
{
return trans_affine(*this).multiply(m);
}
// Multiply the matrix by inverse of another one
// and return the result in a separate matrix.
trans_affine operator / (const trans_affine& m) const
{
return trans_affine(*this).multiply_inv(m);
}
// Calculate and return the inverse matrix
trans_affine operator ~ () const
{
trans_affine ret = *this;
return ret.invert();
}
// Equal operator with default epsilon
bool operator == (const trans_affine& m) const
{
return is_equal(m, affine_epsilon);
}
// Not Equal operator with default epsilon
bool operator != (const trans_affine& m) const
{
return !is_equal(m, affine_epsilon);
}
//-------------------------------------------- Transformations
// Direct transformation of x and y
void transform(double* x, double* y) const;
// Direct transformation of x and y, 2x2 matrix only, no translation
void transform_2x2(double* x, double* y) const;
// Inverse transformation of x and y. It works slower than the
// direct transformation. For massive operations it's better to
// invert() the matrix and then use direct transformations.
void inverse_transform(double* x, double* y) const;
//-------------------------------------------- Auxiliary
// Calculate the determinant of matrix
double determinant() const
{
return sx * sy - shy * shx;
}
// Calculate the reciprocal of the determinant
double determinant_reciprocal() const
{
return 1.0 / (sx * sy - shy * shx);
}
// Get the average scale (by X and Y).
// Basically used to calculate the approximation_scale when
// decomposinting curves into line segments.
double scale() const;
// Check to see if the matrix is not degenerate
bool is_valid(double epsilon = affine_epsilon) const;
// Check to see if it's an identity matrix
bool is_identity(double epsilon = affine_epsilon) const;
// Check to see if two matrices are equal
bool is_equal(const trans_affine& m, double epsilon = affine_epsilon) const;
// Determine the major parameters. Use with caution considering
// possible degenerate cases.
double rotation() const;
void translation(double* dx, double* dy) const;
void scaling(double* x, double* y) const;
void scaling_abs(double* x, double* y) const;
};
//------------------------------------------------------------------------
inline void trans_affine::transform(double* x, double* y) const
{
register double tmp = *x;
*x = tmp * sx + *y * shx + tx;
*y = tmp * shy + *y * sy + ty;
}
//------------------------------------------------------------------------
inline void trans_affine::transform_2x2(double* x, double* y) const
{
register double tmp = *x;
*x = tmp * sx + *y * shx;
*y = tmp * shy + *y * sy;
}
//------------------------------------------------------------------------
inline void trans_affine::inverse_transform(double* x, double* y) const
{
register double d = determinant_reciprocal();
register double a = (*x - tx) * d;
register double b = (*y - ty) * d;
*x = a * sy - b * shx;
*y = b * sx - a * shy;
}
//------------------------------------------------------------------------
inline double trans_affine::scale() const
{
double x = 0.707106781 * sx + 0.707106781 * shx;
double y = 0.707106781 * shy + 0.707106781 * sy;
return sqrt(x*x + y*y);
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::translate(double x, double y)
{
tx += x;
ty += y;
return *this;
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::rotate(double a)
{
double ca = cos(a);
double sa = sin(a);
double t0 = sx * ca - shy * sa;
double t2 = shx * ca - sy * sa;
double t4 = tx * ca - ty * sa;
shy = sx * sa + shy * ca;
sy = shx * sa + sy * ca;
ty = tx * sa + ty * ca;
sx = t0;
shx = t2;
tx = t4;
return *this;
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::scale(double x, double y)
{
double mm0 = x; // Possible hint for the optimizer
double mm3 = y;
sx *= mm0;
shx *= mm0;
tx *= mm0;
shy *= mm3;
sy *= mm3;
ty *= mm3;
return *this;
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::scale(double s)
{
double m = s; // Possible hint for the optimizer
sx *= m;
shx *= m;
tx *= m;
shy *= m;
sy *= m;
ty *= m;
return *this;
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::premultiply(const trans_affine& m)
{
trans_affine t = m;
return *this = t.multiply(*this);
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::multiply_inv(const trans_affine& m)
{
trans_affine t = m;
t.invert();
return multiply(t);
}
//------------------------------------------------------------------------
inline const trans_affine& trans_affine::premultiply_inv(const trans_affine& m)
{
trans_affine t = m;
t.invert();
return *this = t.multiply(*this);
}
//------------------------------------------------------------------------
inline void trans_affine::scaling_abs(double* x, double* y) const
{
// Used to calculate scaling coefficients in image resampling.
// When there is considerable shear this method gives us much
// better estimation than just sx, sy.
*x = sqrt(sx * sx + shx * shx);
*y = sqrt(shy * shy + sy * sy);
}
//====================================================trans_affine_rotation
// Rotation matrix. sin() and cos() are calculated twice for the same angle.
// There's no harm because the performance of sin()/cos() is very good on all
// modern processors. Besides, this operation is not going to be invoked too
// often.
class trans_affine_rotation : public trans_affine
{
public:
trans_affine_rotation(double a) :
trans_affine(cos(a), sin(a), -sin(a), cos(a), 0.0, 0.0)
{}
};
//====================================================trans_affine_scaling
// Scaling matrix. x, y - scale coefficients by X and Y respectively
class trans_affine_scaling : public trans_affine
{
public:
trans_affine_scaling(double x, double y) :
trans_affine(x, 0.0, 0.0, y, 0.0, 0.0)
{}
trans_affine_scaling(double s) :
trans_affine(s, 0.0, 0.0, s, 0.0, 0.0)
{}
};
//================================================trans_affine_translation
// Translation matrix
class trans_affine_translation : public trans_affine
{
public:
trans_affine_translation(double x, double y) :
trans_affine(1.0, 0.0, 0.0, 1.0, x, y)
{}
};
//====================================================trans_affine_skewing
// Sckewing (shear) matrix
class trans_affine_skewing : public trans_affine
{
public:
trans_affine_skewing(double x, double y) :
trans_affine(1.0, tan(y), tan(x), 1.0, 0.0, 0.0)
{}
};
//===============================================trans_affine_line_segment
// Rotate, Scale and Translate, associating 0...dist with line segment
// x1,y1,x2,y2
class trans_affine_line_segment : public trans_affine
{
public:
trans_affine_line_segment(double x1, double y1, double x2, double y2,
double dist)
{
double dx = x2 - x1;
double dy = y2 - y1;
if(dist > 0.0)
{
multiply(trans_affine_scaling(sqrt(dx * dx + dy * dy) / dist));
}
multiply(trans_affine_rotation(atan2(dy, dx)));
multiply(trans_affine_translation(x1, y1));
}
};
//============================================trans_affine_reflection_unit
// Reflection matrix. Reflect coordinates across the line through
// the origin containing the unit vector (ux, uy).
// Contributed by John Horigan
class trans_affine_reflection_unit : public trans_affine
{
public:
trans_affine_reflection_unit(double ux, double uy) :
trans_affine(2.0 * ux * ux - 1.0,
2.0 * ux * uy,
2.0 * ux * uy,
2.0 * uy * uy - 1.0,
0.0, 0.0)
{}
};
//=================================================trans_affine_reflection
// Reflection matrix. Reflect coordinates across the line through
// the origin at the angle a or containing the non-unit vector (x, y).
// Contributed by John Horigan
class trans_affine_reflection : public trans_affine_reflection_unit
{
public:
trans_affine_reflection(double a) :
trans_affine_reflection_unit(cos(a), sin(a))
{}
trans_affine_reflection(double x, double y) :
trans_affine_reflection_unit(x / sqrt(x * x + y * y), y / sqrt(x * x + y * y))
{}
};
}
#endif
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