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eez-flow-template-stm32f746.../Middlewares/eez/libs/agg/agg_trans_perspective.h

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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
//----------------------------------------------------------------------------
//
// Perspective 2D transformations
//
//----------------------------------------------------------------------------
#ifndef AGG_TRANS_PERSPECTIVE_INCLUDED
#define AGG_TRANS_PERSPECTIVE_INCLUDED
#include <cmath>
#include "agg_trans_affine.h"
namespace agg
{
//=======================================================trans_perspective
struct trans_perspective
{
double sx, shy, w0, shx, sy, w1, tx, ty, w2;
//------------------------------------------------------- Construction
// Identity matrix
trans_perspective() :
sx (1), shy(0), w0(0),
shx(0), sy (1), w1(0),
tx (0), ty (0), w2(1) {}
// Custom matrix
trans_perspective(double v0, double v1, double v2,
double v3, double v4, double v5,
double v6, double v7, double v8) :
sx (v0), shy(v1), w0(v2),
shx(v3), sy (v4), w1(v5),
tx (v6), ty (v7), w2(v8) {}
// Custom matrix from m[9]
explicit trans_perspective(const double* m) :
sx (m[0]), shy(m[1]), w0(m[2]),
shx(m[3]), sy (m[4]), w1(m[5]),
tx (m[6]), ty (m[7]), w2(m[8]) {}
// From affine
explicit trans_perspective(const trans_affine& a) :
sx (a.sx ), shy(a.shy), w0(0),
shx(a.shx), sy (a.sy ), w1(0),
tx (a.tx ), ty (a.ty ), w2(1) {}
// Rectangle to quadrilateral
trans_perspective(double x1, double y1, double x2, double y2,
const double* quad);
// Quadrilateral to rectangle
trans_perspective(const double* quad,
double x1, double y1, double x2, double y2);
// Arbitrary quadrilateral transformations
trans_perspective(const double* src, const double* dst);
//-------------------------------------- Quadrilateral transformations
// The arguments are double[8] that are mapped to quadrilaterals:
// x1,y1, x2,y2, x3,y3, x4,y4
bool quad_to_quad(const double* qs, const double* qd);
bool rect_to_quad(double x1, double y1,
double x2, double y2,
const double* q);
bool quad_to_rect(const double* q,
double x1, double y1,
double x2, double y2);
// Map square (0,0,1,1) to the quadrilateral and vice versa
bool square_to_quad(const double* q);
bool quad_to_square(const double* q);
//--------------------------------------------------------- Operations
// Reset - load an identity matrix
const trans_perspective& reset();
// Invert matrix. Returns false in degenerate case
bool invert();
// Direct transformations operations
const trans_perspective& translate(double x, double y);
const trans_perspective& rotate(double a);
const trans_perspective& scale(double s);
const trans_perspective& scale(double x, double y);
// Multiply the matrix by another one
const trans_perspective& multiply(const trans_perspective& m);
// Multiply "m" by "this" and assign the result to "this"
const trans_perspective& premultiply(const trans_perspective& m);
// Multiply matrix to inverse of another one
const trans_perspective& multiply_inv(const trans_perspective& m);
// Multiply inverse of "m" by "this" and assign the result to "this"
const trans_perspective& premultiply_inv(const trans_perspective& m);
// Multiply the matrix by another one
const trans_perspective& multiply(const trans_affine& m);
// Multiply "m" by "this" and assign the result to "this"
const trans_perspective& premultiply(const trans_affine& m);
// Multiply the matrix by inverse of another one
const trans_perspective& multiply_inv(const trans_affine& m);
// Multiply inverse of "m" by "this" and assign the result to "this"
const trans_perspective& premultiply_inv(const trans_affine& m);
//--------------------------------------------------------- Load/Store
void store_to(double* m) const;
const trans_perspective& load_from(const double* m);
//---------------------------------------------------------- Operators
// Multiply the matrix by another one
const trans_perspective& operator *= (const trans_perspective& m)
{
return multiply(m);
}
const trans_perspective& operator *= (const trans_affine& m)
{
return multiply(m);
}
// Multiply the matrix by inverse of another one
const trans_perspective& operator /= (const trans_perspective& m)
{
return multiply_inv(m);
}
const trans_perspective& operator /= (const trans_affine& m)
{
return multiply_inv(m);
}
// Multiply the matrix by another one and return
// the result in a separete matrix.
trans_perspective operator * (const trans_perspective& m) const
{
return trans_perspective(*this).multiply(m);
}
trans_perspective operator * (const trans_affine& m) const
{
return trans_perspective(*this).multiply(m);
}
// Multiply the matrix by inverse of another one
// and return the result in a separete matrix.
trans_perspective operator / (const trans_perspective& m) const
{
return trans_perspective(*this).multiply_inv(m);
}
trans_perspective operator / (const trans_affine& m) const
{
return trans_perspective(*this).multiply_inv(m);
}
// Calculate and return the inverse matrix
trans_perspective operator ~ () const
{
trans_perspective ret = *this;
ret.invert();
return ret;
}
// Equal operator with default epsilon
bool operator == (const trans_perspective& m) const
{
return is_equal(m, affine_epsilon);
}
// Not Equal operator with default epsilon
bool operator != (const trans_perspective& 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, affine part only
void transform_affine(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 slow because
// it explicitly inverts the matrix on every call. For massive
// operations it's better to invert() the matrix and then use
// direct transformations.
void inverse_transform(double* x, double* y) const;
//---------------------------------------------------------- Auxiliary
const trans_perspective& from_affine(const trans_affine& a);
double determinant() const;
double determinant_reciprocal() const;
bool is_valid(double epsilon = affine_epsilon) const;
bool is_identity(double epsilon = affine_epsilon) const;
bool is_equal(const trans_perspective& m,
double epsilon = affine_epsilon) const;
// Determine the major affine parameters. Use with caution
// considering possible degenerate cases.
double scale() const;
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;
//--------------------------------------------------------------------
class iterator_x
{
double den;
double den_step;
double nom_x;
double nom_x_step;
double nom_y;
double nom_y_step;
public:
double x;
double y;
iterator_x() {}
iterator_x(double px, double py, double step, const trans_perspective& m) :
den(px * m.w0 + py * m.w1 + m.w2),
den_step(m.w0 * step),
nom_x(px * m.sx + py * m.shx + m.tx),
nom_x_step(step * m.sx),
nom_y(px * m.shy + py * m.sy + m.ty),
nom_y_step(step * m.shy),
x(nom_x / den),
y(nom_y / den)
{}
void operator ++ ()
{
den += den_step;
nom_x += nom_x_step;
nom_y += nom_y_step;
double d = 1.0 / den;
x = nom_x * d;
y = nom_y * d;
}
};
//--------------------------------------------------------------------
iterator_x begin(double x, double y, double step) const
{
return iterator_x(x, y, step, *this);
}
};
//------------------------------------------------------------------------
inline bool trans_perspective::square_to_quad(const double* q)
{
double dx = q[0] - q[2] + q[4] - q[6];
double dy = q[1] - q[3] + q[5] - q[7];
if(dx == 0.0 && dy == 0.0)
{
// Affine case (parallelogram)
//---------------
sx = q[2] - q[0];
shy = q[3] - q[1];
w0 = 0.0;
shx = q[4] - q[2];
sy = q[5] - q[3];
w1 = 0.0;
tx = q[0];
ty = q[1];
w2 = 1.0;
}
else
{
double dx1 = q[2] - q[4];
double dy1 = q[3] - q[5];
double dx2 = q[6] - q[4];
double dy2 = q[7] - q[5];
double den = dx1 * dy2 - dx2 * dy1;
if(den == 0.0)
{
// Singular case
//---------------
sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0;
return false;
}
// General case
//---------------
double u = (dx * dy2 - dy * dx2) / den;
double v = (dy * dx1 - dx * dy1) / den;
sx = q[2] - q[0] + u * q[2];
shy = q[3] - q[1] + u * q[3];
w0 = u;
shx = q[6] - q[0] + v * q[6];
sy = q[7] - q[1] + v * q[7];
w1 = v;
tx = q[0];
ty = q[1];
w2 = 1.0;
}
return true;
}
//------------------------------------------------------------------------
inline bool trans_perspective::invert()
{
double d0 = sy * w2 - w1 * ty;
double d1 = w0 * ty - shy * w2;
double d2 = shy * w1 - w0 * sy;
double d = sx * d0 + shx * d1 + tx * d2;
if(d == 0.0)
{
sx = shy = w0 = shx = sy = w1 = tx = ty = w2 = 0.0;
return false;
}
d = 1.0 / d;
trans_perspective a = *this;
sx = d * d0;
shy = d * d1;
w0 = d * d2;
shx = d * (a.w1 *a.tx - a.shx*a.w2);
sy = d * (a.sx *a.w2 - a.w0 *a.tx);
w1 = d * (a.w0 *a.shx - a.sx *a.w1);
tx = d * (a.shx*a.ty - a.sy *a.tx);
ty = d * (a.shy*a.tx - a.sx *a.ty);
w2 = d * (a.sx *a.sy - a.shy*a.shx);
return true;
}
//------------------------------------------------------------------------
inline bool trans_perspective::quad_to_square(const double* q)
{
if(!square_to_quad(q)) return false;
invert();
return true;
}
//------------------------------------------------------------------------
inline bool trans_perspective::quad_to_quad(const double* qs,
const double* qd)
{
trans_perspective p;
if(! quad_to_square(qs)) return false;
if(!p.square_to_quad(qd)) return false;
multiply(p);
return true;
}
//------------------------------------------------------------------------
inline bool trans_perspective::rect_to_quad(double x1, double y1,
double x2, double y2,
const double* q)
{
double r[8];
r[0] = r[6] = x1;
r[2] = r[4] = x2;
r[1] = r[3] = y1;
r[5] = r[7] = y2;
return quad_to_quad(r, q);
}
//------------------------------------------------------------------------
inline bool trans_perspective::quad_to_rect(const double* q,
double x1, double y1,
double x2, double y2)
{
double r[8];
r[0] = r[6] = x1;
r[2] = r[4] = x2;
r[1] = r[3] = y1;
r[5] = r[7] = y2;
return quad_to_quad(q, r);
}
//------------------------------------------------------------------------
inline trans_perspective::trans_perspective(double x1, double y1,
double x2, double y2,
const double* quad)
{
rect_to_quad(x1, y1, x2, y2, quad);
}
//------------------------------------------------------------------------
inline trans_perspective::trans_perspective(const double* quad,
double x1, double y1,
double x2, double y2)
{
quad_to_rect(quad, x1, y1, x2, y2);
}
//------------------------------------------------------------------------
inline trans_perspective::trans_perspective(const double* src,
const double* dst)
{
quad_to_quad(src, dst);
}
//------------------------------------------------------------------------
inline const trans_perspective& trans_perspective::reset()
{
sx = 1; shy = 0; w0 = 0;
shx = 0; sy = 1; w1 = 0;
tx = 0; ty = 0; w2 = 1;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::multiply(const trans_perspective& a)
{
trans_perspective b = *this;
sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0;
shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1;
tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2;
shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0;
sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1;
ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2;
w0 = a.w0 *b.sx + a.w1 *b.shy + a.w2*b.w0;
w1 = a.w0 *b.shx + a.w1 *b.sy + a.w2*b.w1;
w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2*b.w2;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::multiply(const trans_affine& a)
{
trans_perspective b = *this;
sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0;
shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1;
tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2;
shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0;
sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1;
ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::premultiply(const trans_perspective& b)
{
trans_perspective a = *this;
sx = a.sx *b.sx + a.shx*b.shy + a.tx*b.w0;
shx = a.sx *b.shx + a.shx*b.sy + a.tx*b.w1;
tx = a.sx *b.tx + a.shx*b.ty + a.tx*b.w2;
shy = a.shy*b.sx + a.sy *b.shy + a.ty*b.w0;
sy = a.shy*b.shx + a.sy *b.sy + a.ty*b.w1;
ty = a.shy*b.tx + a.sy *b.ty + a.ty*b.w2;
w0 = a.w0 *b.sx + a.w1 *b.shy + a.w2*b.w0;
w1 = a.w0 *b.shx + a.w1 *b.sy + a.w2*b.w1;
w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2*b.w2;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::premultiply(const trans_affine& b)
{
trans_perspective a = *this;
sx = a.sx *b.sx + a.shx*b.shy;
shx = a.sx *b.shx + a.shx*b.sy;
tx = a.sx *b.tx + a.shx*b.ty + a.tx;
shy = a.shy*b.sx + a.sy *b.shy;
sy = a.shy*b.shx + a.sy *b.sy;
ty = a.shy*b.tx + a.sy *b.ty + a.ty;
w0 = a.w0 *b.sx + a.w1 *b.shy;
w1 = a.w0 *b.shx + a.w1 *b.sy;
w2 = a.w0 *b.tx + a.w1 *b.ty + a.w2;
return *this;
}
//------------------------------------------------------------------------
const trans_perspective&
trans_perspective::multiply_inv(const trans_perspective& m)
{
trans_perspective t = m;
t.invert();
return multiply(t);
}
//------------------------------------------------------------------------
const trans_perspective&
trans_perspective::multiply_inv(const trans_affine& m)
{
trans_affine t = m;
t.invert();
return multiply(t);
}
//------------------------------------------------------------------------
const trans_perspective&
trans_perspective::premultiply_inv(const trans_perspective& m)
{
trans_perspective t = m;
t.invert();
return *this = t.multiply(*this);
}
//------------------------------------------------------------------------
const trans_perspective&
trans_perspective::premultiply_inv(const trans_affine& m)
{
trans_perspective t(m);
t.invert();
return *this = t.multiply(*this);
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::translate(double x, double y)
{
tx += x;
ty += y;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective& trans_perspective::rotate(double a)
{
multiply(trans_affine_rotation(a));
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective& trans_perspective::scale(double s)
{
multiply(trans_affine_scaling(s));
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective& trans_perspective::scale(double x, double y)
{
multiply(trans_affine_scaling(x, y));
return *this;
}
//------------------------------------------------------------------------
inline void trans_perspective::transform(double* px, double* py) const
{
double x = *px;
double y = *py;
double m = 1.0 / (x*w0 + y*w1 + w2);
*px = m * (x*sx + y*shx + tx);
*py = m * (x*shy + y*sy + ty);
}
//------------------------------------------------------------------------
inline void trans_perspective::transform_affine(double* x, double* y) const
{
double tmp = *x;
*x = tmp * sx + *y * shx + tx;
*y = tmp * shy + *y * sy + ty;
}
//------------------------------------------------------------------------
inline void trans_perspective::transform_2x2(double* x, double* y) const
{
double tmp = *x;
*x = tmp * sx + *y * shx;
*y = tmp * shy + *y * sy;
}
//------------------------------------------------------------------------
inline void trans_perspective::inverse_transform(double* x, double* y) const
{
trans_perspective t(*this);
if(t.invert()) t.transform(x, y);
}
//------------------------------------------------------------------------
inline void trans_perspective::store_to(double* m) const
{
*m++ = sx; *m++ = shy; *m++ = w0;
*m++ = shx; *m++ = sy; *m++ = w1;
*m++ = tx; *m++ = ty; *m++ = w2;
}
//------------------------------------------------------------------------
inline const trans_perspective& trans_perspective::load_from(const double* m)
{
sx = *m++; shy = *m++; w0 = *m++;
shx = *m++; sy = *m++; w1 = *m++;
tx = *m++; ty = *m++; w2 = *m++;
return *this;
}
//------------------------------------------------------------------------
inline const trans_perspective&
trans_perspective::from_affine(const trans_affine& a)
{
sx = a.sx; shy = a.shy; w0 = 0;
shx = a.shx; sy = a.sy; w1 = 0;
tx = a.tx; ty = a.ty; w2 = 1;
return *this;
}
//------------------------------------------------------------------------
inline double trans_perspective::determinant() const
{
return sx * (sy * w2 - ty * w1) +
shx * (ty * w0 - shy * w2) +
tx * (shy * w1 - sy * w0);
}
//------------------------------------------------------------------------
inline double trans_perspective::determinant_reciprocal() const
{
return 1.0 / determinant();
}
//------------------------------------------------------------------------
inline bool trans_perspective::is_valid(double epsilon) const
{
return std::fabs(sx) > epsilon && std::fabs(sy) > epsilon && std::fabs(w2) > epsilon;
}
//------------------------------------------------------------------------
inline bool trans_perspective::is_identity(double epsilon) const
{
return is_equal_eps(sx, 1.0, epsilon) &&
is_equal_eps(shy, 0.0, epsilon) &&
is_equal_eps(w0, 0.0, epsilon) &&
is_equal_eps(shx, 0.0, epsilon) &&
is_equal_eps(sy, 1.0, epsilon) &&
is_equal_eps(w1, 0.0, epsilon) &&
is_equal_eps(tx, 0.0, epsilon) &&
is_equal_eps(ty, 0.0, epsilon) &&
is_equal_eps(w2, 1.0, epsilon);
}
//------------------------------------------------------------------------
inline bool trans_perspective::is_equal(const trans_perspective& m,
double epsilon) const
{
return is_equal_eps(sx, m.sx, epsilon) &&
is_equal_eps(shy, m.shy, epsilon) &&
is_equal_eps(w0, m.w0, epsilon) &&
is_equal_eps(shx, m.shx, epsilon) &&
is_equal_eps(sy, m.sy, epsilon) &&
is_equal_eps(w1, m.w1, epsilon) &&
is_equal_eps(tx, m.tx, epsilon) &&
is_equal_eps(ty, m.ty, epsilon) &&
is_equal_eps(w2, m.w2, epsilon);
}
//------------------------------------------------------------------------
inline double trans_perspective::scale() const
{
double x = 0.707106781 * sx + 0.707106781 * shx;
double y = 0.707106781 * shy + 0.707106781 * sy;
return std::sqrt(x*x + y*y);
}
//------------------------------------------------------------------------
inline double trans_perspective::rotation() const
{
double x1 = 0.0;
double y1 = 0.0;
double x2 = 1.0;
double y2 = 0.0;
transform(&x1, &y1);
transform(&x2, &y2);
return std::atan2(y2-y1, x2-x1);
}
//------------------------------------------------------------------------
void trans_perspective::translation(double* dx, double* dy) const
{
*dx = tx;
*dy = ty;
}
//------------------------------------------------------------------------
void trans_perspective::scaling(double* x, double* y) const
{
double x1 = 0.0;
double y1 = 0.0;
double x2 = 1.0;
double y2 = 1.0;
trans_perspective t(*this);
t *= trans_affine_rotation(-rotation());
t.transform(&x1, &y1);
t.transform(&x2, &y2);
*x = x2 - x1;
*y = y2 - y1;
}
//------------------------------------------------------------------------
void trans_perspective::scaling_abs(double* x, double* y) const
{
*x = std::sqrt(sx * sx + shx * shx);
*y = std::sqrt(shy * shy + sy * sy);
}
}
#endif