fix description

This commit is contained in:
Sébastien Loriot 2023-11-29 13:17:10 +01:00
parent 5879bb72c6
commit 4bed66e82f
1 changed files with 4 additions and 4 deletions

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