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Simplify calculating the ambisonic rotator coefficients

master
Chris Robinson 2022-08-26 00:26:29 -07:00
parent 1ee81ab3f0
commit 1a99ac48f6
1 changed files with 32 additions and 33 deletions
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65
alc/alu.cpp
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@ -559,49 +559,48 @@ inline float WrapRadians(float r)
* precomputed since they're constant. The second-order coefficients are
* followed by the third-order coefficients, etc.
*/
template<size_t L>
constexpr size_t CalcRotatorSize()
{ return (L*2 + 1)*(L*2 + 1) + CalcRotatorSize<L-1>(); }
template<> constexpr size_t CalcRotatorSize<0>() = delete;
template<> constexpr size_t CalcRotatorSize<1>() = delete;
template<> constexpr size_t CalcRotatorSize<2>() { return 5*5; }
struct RotatorCoeffs {
float u, v, w;
struct CoeffValues {
float u, v, w;
};
std::array<CoeffValues,CalcRotatorSize<MaxAmbiOrder>()> mCoeffs{};
template<size_t N0, size_t N1>
static std::array<RotatorCoeffs,N0+N1> ConcatArrays(const std::array<RotatorCoeffs,N0> &lhs,
const std::array<RotatorCoeffs,N1> &rhs)
constexpr RotatorCoeffs()
{
std::array<RotatorCoeffs,N0+N1> ret;
auto iter = std::copy(lhs.cbegin(), lhs.cend(), ret.begin());
std::copy(rhs.cbegin(), rhs.cend(), iter);
return ret;
}
auto coeffs = mCoeffs.begin();
template<int l, int num_elems=l*2+1>
static std::array<RotatorCoeffs,num_elems*num_elems> GenCoeffs()
{
std::array<RotatorCoeffs,num_elems*num_elems> ret{};
auto coeffs = ret.begin();
for(int m{-l};m <= l;++m)
for(int l=2;l <= MaxAmbiOrder;++l)
{
for(int n{-l};n <= l;++n)
for(int m{-l};m <= l;++m)
{
// compute u,v,w terms of Eq.8.1 (Table I)
const bool d{m == 0}; // the delta function d_m0
const float denom{static_cast<float>((std::abs(n) == l) ?
(2*l) * (2*l - 1) : (l*l - n*n))};
for(int n{-l};n <= l;++n)
{
// compute u,v,w terms of Eq.8.1 (Table I)
const bool d{m == 0}; // the delta function d_m0
const float denom{static_cast<float>((std::abs(n) == l) ?
(2*l) * (2*l - 1) : (l*l - n*n))};
const int abs_m{std::abs(m)};
coeffs->u = std::sqrt(static_cast<float>(l*l - m*m)/denom);
coeffs->v = std::sqrt(static_cast<float>(l+abs_m-1) * static_cast<float>(l+abs_m) /
denom) * (1.0f+d) * (1.0f - 2.0f*d) * 0.5f;
coeffs->w = std::sqrt(static_cast<float>(l-abs_m-1) * static_cast<float>(l-abs_m) /
denom) * (1.0f-d) * -0.5f;
++coeffs;
const int abs_m{std::abs(m)};
coeffs->u = std::sqrt(static_cast<float>(l*l - m*m)/denom);
coeffs->v = std::sqrt(static_cast<float>(l+abs_m-1) *
static_cast<float>(l+abs_m) / denom) * (1.0f+d) * (1.0f - 2.0f*d) * 0.5f;
coeffs->w = std::sqrt(static_cast<float>(l-abs_m-1) *
static_cast<float>(l-abs_m) / denom) * (1.0f-d) * -0.5f;
++coeffs;
}
}
}
return ret;
}
};
const auto RotatorCoeffArray = RotatorCoeffs::ConcatArrays(RotatorCoeffs::GenCoeffs<2>(),
RotatorCoeffs::GenCoeffs<3>());
const RotatorCoeffs RotatorCoeffArray{};
/**
* Given the matrix, pre-filled with the (zeroth- and) first-order rotation
@ -665,7 +664,7 @@ void AmbiRotator(AmbiRotateMatrix &matrix, const int order)
};
// compute rotation matrix of each subsequent band recursively
auto coeffs = RotatorCoeffArray.cbegin();
auto coeffs = RotatorCoeffArray.mCoeffs.cbegin();
size_t band_idx{4}, last_band{1};
for(int l{2};l <= order;++l)
{