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/*
* Moebius_transformations.c
*/
#include "kernel.h"
CONST MoebiusTransformation Moebius_identity =
{
{
{{1.0, 0.0}, {0.0, 0.0}},
{{0.0, 0.0}, {1.0, 0.0}}
},
orientation_preserving
};
void Moebius_copy(
MoebiusTransformation *dest,
MoebiusTransformation *source)
{
sl2c_copy(dest->matrix, source->matrix);
dest->parity = source->parity;
}
void Moebius_invert(
MoebiusTransformation *mt,
MoebiusTransformation *mt_inverse)
{
sl2c_invert(mt->matrix, mt_inverse->matrix);
if (mt->parity == orientation_reversing)
sl2c_complex_conjugate(mt_inverse->matrix, mt_inverse->matrix);
mt_inverse->parity = mt->parity;
}
void Moebius_product(
MoebiusTransformation *a,
MoebiusTransformation *b,
MoebiusTransformation *product)
{
SL2CMatrix factor1,
factor2;
sl2c_copy(factor1, a->matrix);
sl2c_copy(factor2, b->matrix);
if (a->parity == orientation_reversing)
sl2c_complex_conjugate(factor2, factor2);
sl2c_product(factor1, factor2, product->matrix);
product->parity = (a->parity == b->parity) ?
orientation_preserving:
orientation_reversing;
}
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