mirror of https://github.com/CGAL/cgal
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@ -937,11 +937,11 @@ namespace CommonKernelFunctors {
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// (abac points inside the tetra abcd if its orientation is positive and outside otherwise)
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// (abac points inside the tetra abcd if its orientation is positive and outside otherwise)
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// In order to increase the numerical precision of the computation, we consider the
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// In order to increase the numerical precision of the computation, we consider the
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// vector abad in the basis defined by (ab, abac, ab^abac).
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// vector abad in the basis defined by (ab, abac, ab^abac).
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// In this basis, adab=(ab * abad, abac * abad, [ab^abac] * abad), as all basis vector are orthogonal.
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// In this basis, adab=(ab * abad, abac * abad, [ab^abac] * abad), as all basis vectors are orthogonal.
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// We have ab * abad = 0, so in the plane (zy) of the new basis
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// We have ab * abad = 0, so in the plane (yz) of the new basis
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// the dihedral angle is the angle between the z axis and abad
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// the dihedral angle is the angle between the y axis and abad
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// which is the arctan of y/z (up to normalization)
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// which is the arctan of y/z (up to normalization)
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// (Note that ab^abac is in the plane abc, pointing inside the tetra if its orientation is positive and outside otherwise).
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// (Note that ab^abac is in the plane abc, pointing outside the tetra if its orientation is positive and inside otherwise).
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// For the normalization, abad appears in both scalar products
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// For the normalization, abad appears in both scalar products
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// in the quotient so we can ignore its norm. For the second
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// in the quotient so we can ignore its norm. For the second
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// terms of the scalar products, we are left with ab^abac and abac.
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// terms of the scalar products, we are left with ab^abac and abac.
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