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/* ----------------------------------------------------------------------- *

 * This file is part of GEL, http://www.imm.dtu.dk/GEL

 * Copyright (C) the authors and DTU Informatics

 * For license and list of authors, see ../../doc/intro.pdf

 * @brief Abstract 4x4 floating point matrix class

 * ----------------------------------------------------------------------- */

/** @file ArithSqMat4x4Float.h

 * @brief Abstract 4x4 floating point matrix class

 */

#ifndef __CGLA_ARITHSQMAT4X4FLOAT_H

#define __CGLA_ARITHSQMAT4X4FLOAT_H

#include "ExceptionStandard.h"

#include "CGLA.h"

#include "Vec3f.h"

#include "Vec3Hf.h"

#include "Vec4f.h"

#include "ArithSqMatFloat.h"

namespace CGLA 

{

  CGLA_DERIVEEXCEPTION(Mat4x4fException)

  CGLA_DERIVEEXCEPTION(Mat4x4fNotAffine)

  CGLA_DERIVEEXCEPTION(Mat4x4fSingular)

  /** \brief 4 by 4 float matrix template.

      this class template is useful for transformations such as perspective 

      projections or translation where 3x3 matrices do not suffice. */

  template<class VT, class M>

  class ArithSqMat4x4Float: public ArithSqMatFloat<VT, M, 4>

  {

  public:

    /// Vector type

    typedef VT VectorType;

    /// The type of a matrix element

    typedef typename VT::ScalarType ScalarType;

  public:

    /// Construct a Mat4x4f from four V vectors

    ArithSqMat4x4Float(VT a, VT b, VT c, VT d): 

      ArithSqMatFloat<VT, M, 4> (a,b,c,d) {}

    /// Construct the NAN matrix

    ArithSqMat4x4Float() {}

    /// Construct matrix where all values are equal to constructor argument.

    explicit ArithSqMat4x4Float(ScalarType  _a):

      ArithSqMatFloat<VT,M,4>(_a) {}

    /** Multiply vector onto matrix. Here the fourth coordinate 

	is se to 0. This removes any translation from the matrix.

	Useful if one wants to transform a vector which does not

	represent a point but a direction. Note that this is not

	correct for transforming normal vectors if the matric 

	contains anisotropic scaling. */

    template<class T, class VecT>

    const VecT mul_3D_vector(const ArithVec3Float<T,VecT>& v_in) const

    {

      VT v_out  = (*this) * VT(v_in[0],v_in[1],v_in[2],0);

      return VecT(v_out[0],v_out[1],v_out[2]);

    }

    /** Multiply 3D point onto matrix. Here the fourth coordinate 

	becomes 1 to ensure that the point is translated. Note that

	the vector is converted back into a Vec3f without any 

	division by w. This is deliberate: Typically, w=1 except

	for projections. If we are doing projection, we can use

	project_3D_point instead */

    template<class T, class VecT>

    const VecT mul_3D_point(const ArithVec3Float<T,VecT> & v_in) const

    {

      VT v_out  = (*this) * VT(v_in[0],v_in[1],v_in[2],1);

      return VecT(v_out[0],v_out[1],v_out[2]);

    }

    /** Multiply 3D point onto matrix. We set w=1 before 

	multiplication and divide by w after multiplication. */

    template<class T, class VecT>

    const VecT project_3D_point(const ArithVec3Float<T,VecT>& v_in) const

    {

      VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],1);

      v_out.de_homogenize();

      return VecT(v_out[0],v_out[1],v_out[2]);

    }

  };

  /** Compute the adjoint of a matrix. This is the matrix where each

      entry is the subdeterminant of 'in' where the row and column of 

      the element is removed. Use mostly to compute the inverse */

  template<class VT, class M>

  M adjoint(const ArithSqMat4x4Float<VT,M>&);

	/** Compute the determinant of a 4x4 matrix. The code below is what

			I found to be most robust. The original implementation used direct

			computation of the 3x3 sub-determinants and I also tried a direct

			computation based on enumerating all permutations. The code below

			is better. */

	template<class V, class M>

			inline double determinant(const ArithSqMat4x4Float<V,M>& m)

			{

/* 					return m[0][0] * (m[1][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */

/* 														m[2][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])+ */

/* 														m[3][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])) */

/* 							- m[1][0] * (m[0][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */

/* 													 m[2][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */

/* 													 m[3][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])) */

/* 							+ m[2][0] * (m[0][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])- */

/* 													 m[1][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */

/* 													 m[3][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])) */

/* 							- m[3][0] * (m[0][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])- */

/* 													 m[1][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])+ */

/* 													 m[2][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])); */

		typedef typename M::ScalarType ScalarType;

    ScalarType a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;

    /* assign to individual variable names to aid selecting */

		/*  correct elements */

		a1 = m[0][0]; b1 = m[1][0]; c1 = m[2][0]; d1 = m[3][0];

		a2 = m[0][1]; b2 = m[1][1]; c2 = m[2][1]; d2 = m[3][1];

		a3 = m[0][2]; b3 = m[1][2]; c3 = m[2][2]; d3 = m[3][2];

		a4 = m[0][3]; b4 = m[1][3]; c4 = m[2][3]; d4 = m[3][3];

					return 

							a1 * (b2*(c3*d4-d3*c4)-c2*(b3*d4-d3*b4)+d2*(b3*c4-c3*b4))

							- b1 * (a2*(c3*d4-d3*c4)-c2*(a3*d4-d3*a4)+d2*(a3*c4-c3*a4))

							+ c1 * (a2*(b3*d4-d3*b4)-b2*(a3*d4-d3*a4)+d2*(a3*b4-b3*a4))

							- d1 * (a2*(b3*c4-c3*b4)-b2*(a3*c4-c3*a4)+c2*(a3*b4-b3*a4));

			}

  /// Compute the inverse matrix of a Mat4x4f.

  template<class VT, class M>

  M invert(const ArithSqMat4x4Float<VT,M>&);

  /// Compute the inverse matrix of a Mat4x4f that is affine

  template<class VT, class M>

  M invert_affine(const ArithSqMat4x4Float<VT,M>&);

}

#endif