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			a0*b2*c1 -
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			a0*b2*c1 -
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			a1*b0*c2 ;
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			a1*b0*c2 ;
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	}
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	}
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}
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}
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		/** Compute the determinant of a 4x4 matrix. The code below is what
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				I found to be most robust. The original implementation used direct
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				computation of the 3x3 sub-determinants and I also tried a direct
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				computation based on enumerating all permutations. The code below
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				is better. */
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	template<class V, class M>
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	double
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	determinant(const ArithSqMat4x4Float<V,M>& m)
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	{
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		typedef typename M::ScalarType ScalarType;
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    ScalarType ans;
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    ScalarType a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;
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    /* assign to individual variable names to aid selecting */
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		/*  correct elements */
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		a1 = m[0][0]; b1 = m[1][0]; c1 = m[2][0]; d1 = m[3][0];
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		a2 = m[0][1]; b2 = m[1][1]; c2 = m[2][1]; d2 = m[3][1];
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		a3 = m[0][2]; b3 = m[1][2]; c3 = m[2][2]; d3 = m[3][2];
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		a4 = m[0][3]; b4 = m[1][3]; c4 = m[2][3]; d4 = m[3][3];
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		ans =
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				a1 * (b2*(c3*d4-d3*c4)-c2*(b3*d4-d3*b4)+d2*(b3*c4-c3*b4))
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				- b1 * (a2*(c3*d4-d3*c4)-c2*(a3*d4-d3*a4)+d2*(a3*c4-c3*a4))
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				+ c1 * (a2*(b3*d4-d3*b4)-b2*(a3*d4-d3*a4)+d2*(a3*b4-b3*a4))
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				- d1 * (a2*(b3*c4-c3*b4)-b2*(a3*c4-c3*a4)+c2*(a3*b4-b3*a4));
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		return ans;
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	}
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	template<class V, class M>
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	template<class V, class M>
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	M invert_affine(const ArithSqMat4x4Float<V,M>& this_mat)
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	M invert_affine(const ArithSqMat4x4Float<V,M>& this_mat)
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	{
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	{
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		//   The following code has been copied from a gem in Graphics Gems II by
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		//   The following com[3]e has been copied from a gem in Graphics Gems II by
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		//   Kevin Wu.
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		//   Kevin Wu.
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		//   The function is very fast, but it can only invert affine matrices. An
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		//   The function is very fast, but it can only invert affine matrices. An
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		//   exception NotAffine is thrown if the matrix is not affine, and another
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		//   exception NotAffine is thrown if the matrix is not affine, and another
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		//   exception Singular is thrown if the matrix is singular.
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		//   exception Singular is thrown if the matrix is singular.
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	}
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	}
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	template class ArithSqMat4x4Float<Vec4f, Mat4x4f>;
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	template class ArithSqMat4x4Float<Vec4f, Mat4x4f>;
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	template Mat4x4f adjoint(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template Mat4x4f adjoint(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template double determinant(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template Mat4x4f invert(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template Mat4x4f invert(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template Mat4x4f invert_affine(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template Mat4x4f invert_affine(const ArithSqMat4x4Float<Vec4f,Mat4x4f>&);
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	template class ArithSqMat4x4Float<Vec4d, Mat4x4d>;
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	template class ArithSqMat4x4Float<Vec4d, Mat4x4d>;
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	template Mat4x4d adjoint(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template Mat4x4d adjoint(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template double determinant(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template Mat4x4d invert(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template Mat4x4d invert(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template Mat4x4d invert_affine(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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	template Mat4x4d invert_affine(const ArithSqMat4x4Float<Vec4d,Mat4x4d>&);
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}
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}