text: 
  
  #include "tgeometry.h"
  #ifdef LINUX
  #include <values.h>
  #endif
  
  using namespace std;
  
  const T3DPointD TConsts::nap3d((numeric_limits<double>::max)(),
  							   (numeric_limits<double>::max)(),
  							   (numeric_limits<double>::max)());
  
  const TThickPoint TConsts::natp((numeric_limits<double>::max)(),
  								(numeric_limits<double>::max)(),
  								(numeric_limits<double>::max)());
  
  const TPointD TConsts::napd((numeric_limits<double>::max)(),
  							(numeric_limits<double>::max)());
  
  const TPointI TConsts::nap((numeric_limits<int>::max)(),
  						   (numeric_limits<int>::max)());
  
  const TRectD TConsts::infiniteRectD(-(numeric_limits<double>::max)(),
  									-(numeric_limits<double>::max)(),
  									(numeric_limits<double>::max)(),
  									(numeric_limits<double>::max)());
  
  const TRectI TConsts::infiniteRectI(-(numeric_limits<int>::max)(),
  									-(numeric_limits<int>::max)(),
  									(numeric_limits<int>::max)(),
  									(numeric_limits<int>::max)());
  
  //==================================================================================================
  
  // operazioni fra affini
  TAffine &TAffine::operator=(const TAffine &a)
  {
  	a11 = a.a11;
  	a12 = a.a12;
  	a13 = a.a13;
  	a21 = a.a21;
  	a22 = a.a22;
  	a23 = a.a23;
  	return *this;
  }
  //--------------------------------------------------------------------------------------------------
  TAffine TAffine::operator*(const TAffine &b) const
  {
  	return TAffine(
  		a11 * b.a11 + a12 * b.a21,
  		a11 * b.a12 + a12 * b.a22,
  		a11 * b.a13 + a12 * b.a23 + a13,
  
  		a21 * b.a11 + a22 * b.a21,
  		a21 * b.a12 + a22 * b.a22,
  		a21 * b.a13 + a22 * b.a23 + a23);
  }
  //--------------------------------------------------------------------------------------------------
  TAffine TAffine::operator*=(const TAffine &b)
  {
  	return *this = *this * b;
  }
  //--------------------------------------------------------------------------------------------------
  TAffine TAffine::inv() const
  {
  	if (a12 == 0.0 && a21 == 0.0) {
  		assert(a11 != 0.0);
  		assert(a22 != 0.0);
  		double inv_a11 = 1.0 / a11;
  		double inv_a22 = 1.0 / a22;
  		return TAffine(inv_a11, 0, -a13 * inv_a11,
  					   0, inv_a22, -a23 * inv_a22);
  	} else if (a11 == 0.0 && a22 == 0.0) {
  		assert(a12 != 0.0);
  		assert(a21 != 0.0);
  		double inv_a21 = 1.0 / a21;
  		double inv_a12 = 1.0 / a12;
  		return TAffine(0, inv_a21, -a23 * inv_a21,
  					   inv_a12, 0, -a13 * inv_a12);
  	} else {
  		double d = 1. / det();
  		return TAffine(a22 * d, -a12 * d, (a12 * a23 - a22 * a13) * d,
  					   -a21 * d, a11 * d, (a21 * a13 - a11 * a23) * d);
  	}
  }
  //--------------------------------------------------------------------------------------------------
  double TAffine::det() const
  {
  	return a11 * a22 - a12 * a21;
  }
  
  //--------------------------------------------------------------------------------------------------
  
  //Confronti tra affini
  bool TAffine::operator==(const TAffine &a) const
  {
  	return a11 == a.a11 && a12 == a.a12 && a13 == a.a13 &&
  		   a21 == a.a21 && a22 == a.a22 && a23 == a.a23;
  }
  //--------------------------------------------------------------------------------------------------
  bool TAffine::operator!=(const TAffine &a) const
  {
  	return a11 != a.a11 || a12 != a.a12 || a13 != a.a13 ||
  		   a21 != a.a21 || a22 != a.a22 || a23 != a.a23;
  }
  //--------------------------------------------------------------------------------------------------
  bool TAffine::isIdentity(double err) const
  {
  	return ((a11 - 1.0) * (a11 - 1.0) + (a22 - 1.0) * (a22 - 1.0) +
  			a12 * a12 + a13 * a13 + a21 * a21 + a23 * a23) < err;
  }
  //--------------------------------------------------------------------------------------------------
  bool TAffine::isTranslation(double err) const
  {
  	return ((a11 - 1.0) * (a11 - 1.0) + (a22 - 1.0) * (a22 - 1.0) +
  			a12 * a12 + a21 * a21) < err;
  }
  //--------------------------------------------------------------------------------------------------
  bool TAffine::isIsotropic(double err) const
  {
  	return areAlmostEqual(a11, a22, err) && areAlmostEqual(a12, -a21, err);
  }
  
  //--------------------------------------------------------------------------------------------------
  
  // applicazione
  TPointD TAffine::operator*(const TPointD &p) const
  {
  	return TPointD(p.x * a11 + p.y * a12 + a13, p.x * a21 + p.y * a22 + a23);
  }
  
  //--------------------------------------------------------------------------------------------------
  
  TRectD TAffine::operator*(const TRectD &rect) const
  {
  	if (rect != TConsts::infiniteRectD) {
  		TPointD p1 = *this * rect.getP00(),
  				p2 = *this * rect.getP01(),
  				p3 = *this * rect.getP10(),
  				p4 = *this * rect.getP11();
  		return TRectD(tmin(p1.x, p2.x, p3.x, p4.x), tmin(p1.y, p2.y, p3.y, p4.y),
  					  tmax(p1.x, p2.x, p3.x, p4.x), tmax(p1.y, p2.y, p3.y, p4.y));
  	} else
  		return TConsts::infiniteRectD;
  }
  
  //--------------------------------------------------------------------------------------------------
  
  TAffine TAffine::place(double u, double v, double x, double y) const
  {
  	return TAffine(a11, a12, x - (a11 * u + a12 * v),
  				   a21, a22, y - (a21 * u + a22 * v));
  }
  
  //--------------------------------------------------------------------------------------------------
  
  TAffine TAffine::place(const TPointD &pIn, const TPointD &pOut) const
  {
  	return TAffine(a11, a12, pOut.x - (a11 * pIn.x + a12 * pIn.y),
  				   a21, a22, pOut.y - (a21 * pIn.x + a22 * pIn.y));
  }
  
  //==================================================================================================
  
  TRotation::TRotation(double degrees)
  {
  	double rad, sn, cs;
  	int idegrees = (int)degrees;
  	if ((double)idegrees == degrees && idegrees % 90 == 0) {
  		switch ((idegrees / 90) & 3) {
  		case 0:
  			sn = 0;
  			cs = 1;
  			break;
  		case 1:
  			sn = 1;
  			cs = 0;
  			break;
  		case 2:
  			sn = 0;
  			cs = -1;
  			break;
  		case 3:
  			sn = -1;
  			cs = 0;
  			break;
  		default:
  			sn = 0;
  			cs = 0;
  			break;
  		}
  	} else {
  		rad = degrees * (TConsts::pi_180);
  		sn = sin(rad);
  		cs = cos(rad);
  		if (sn == 1 || sn == -1)
  			cs = 0;
  		if (cs == 1 || cs == -1)
  			sn = 0;
  	}
  	a11 = cs;
  	a12 = -sn;
  	a21 = -a12;
  	a22 = a11;
  }
  //--------------------------------------------------------------------------------------------------
  TRotation::TRotation(const TPointD &center, double degrees)
  {
  	TAffine a = TTranslation(center) * TRotation(degrees) * TTranslation(-center);
  	a11 = a.a11;
  	a12 = a.a12;
  	a13 = a.a13;
  	a21 = a.a21;
  	a22 = a.a22;
  	a23 = a.a23;
  }
  
  //==================================================================================================
  
  TScale::TScale(const TPointD &center, double sx, double sy)
  {
  	TAffine a = TTranslation(center) * TScale(sx, sy) * TTranslation(-center);
  	a11 = a.a11;
  	a12 = a.a12;
  	a13 = a.a13;
  	a21 = a.a21;
  	a22 = a.a22;
  	a23 = a.a23;
  }
  //--------------------------------------------------------------------------------------------------
  TScale::TScale(const TPointD &center, double s)
  {
  	TAffine a = TTranslation(center) * TScale(s) * TTranslation(-center);
  	a11 = a.a11;
  	a12 = a.a12;
  	a13 = a.a13;
  	a21 = a.a21;
  	a22 = a.a22;
  	a23 = a.a23;
  }
  