modified the chebyshev12 routine to put out readily normalized circular harmonics and added

[mtx_circular_harmonics] to the file mtx_spherical_harmonics, as well as a corresponding helpfile.
why: useful for circular (1D) ambisonics, e.g. ...


svn path=/trunk/externals/iem/iemmatrix/; revision=11792

3 files changed, 16 insertions, 5 deletions

diff --git a/src/mtx_spherical_harmonics/chebyshev12.c b/src/mtx_spherical_harmonics/chebyshev12.c
index 462341b..64af232 100644
--- a/src/mtx_spherical_harmonics/chebyshev12.c
+++ b/src/mtx_spherical_harmonics/chebyshev12.c
@@ -1,5 +1,5 @@
 /* 
- Evaluates all circular harmonics 
+ Evaluates all fully normalized circular harmonics 
  at the angles phi up to the order nmax. 
  using the recurrence for the Chebyshev
  polynomials of the first and second kind
@@ -42,6 +42,8 @@ void chebyshev12(double *phi, Cheby12WorkSpace *wc) {
    const int incr=2*wc->nmax+1;
    double *cosphi;
    double *sinphi;
+   const double oneoversqrt2pi=1.0/sqrt(2.0*M_PI);
+   const double oneoversqrtpi=1.0/sqrt(M_PI);
    // memory allocation
    if ((wc!=0)&&(phi!=0)) {
       if ((cosphi=(double*)calloc(wc->l,sizeof(double)))==0) {
@@ -56,9 +58,9 @@ void chebyshev12(double *phi, Cheby12WorkSpace *wc) {
          cosphi[l]=cos(phi[l]);
          sinphi[l]=sin(phi[l]);
          // initial value T_0=1
-         wc->t[l0]=1;
-         wc->t[l0+1]=cosphi[l];
-         wc->t[l0-1]=sinphi[l];
+         wc->t[l0]=oneoversqrt2pi;
+         wc->t[l0+1]=cosphi[l]*oneoversqrtpi;
+         wc->t[l0-1]=sinphi[l]*oneoversqrtpi;
       }
       // recurrence for n>1
       for (n=2; n<=wc->nmax; n++) {
diff --git a/src/mtx_spherical_harmonics/sharmonics.c b/src/mtx_spherical_harmonics/sharmonics.c
index 5d6f853..dbfcb18 100644
--- a/src/mtx_spherical_harmonics/sharmonics.c
+++ b/src/mtx_spherical_harmonics/sharmonics.c
@@ -43,7 +43,7 @@ static void sharmonics_initlegendrenormlzd(SHWorkSpace *ws) {
    }
 }
 
-// multiplying Chebyshev sin/cos to the preliminary result
+// multiplying normalized Chebyshev sin/cos to the preliminary result
 // Y_n^m(phi,theta) = Y_n^m(theta) * T_m(phi)
 // ny0 and nt0 denote where the position (n,m)=(n,0) or m=0 is in the arrays
 // ly0 and lt0 denote the starting position for one vertex in the arrays
diff --git a/src/mtx_spherical_harmonics/sharmonics_normalization.c b/src/mtx_spherical_harmonics/sharmonics_normalization.c
index ca97292..d7fe00a 100644
--- a/src/mtx_spherical_harmonics/sharmonics_normalization.c
+++ b/src/mtx_spherical_harmonics/sharmonics_normalization.c
@@ -27,8 +27,14 @@ SHNorml *sharmonics_normalization_new (const size_t nmax) {
          wn=0;
       }
       else {
+	 /*
+         deprecated:
          // computing N_n^m for m=0, wrongly normalized
          wn->n[0]=sqrt(1/(2*M_PI));
+	 */
+
+         // computing N_n^m for m=0,
+         wn->n[0]=oneoversqrt2;
          for (n=1,n0=1; n<=nmax; n++) {
             wn->n[n0]=wn->n[0] * sqrt(2*n+1);
             n0+=n+1;
@@ -40,11 +46,14 @@ SHNorml *sharmonics_normalization_new (const size_t nmax) {
             }
             n0+=n+1;
          }
+	 /*
+	 deprecated:
          // correcting normalization of N_n^0
          for (n=0,n0=0; n<=nmax; n++) {
             wn->n[n0]*=oneoversqrt2;
             n0+=n+1;
          }
+	 */
       }
    }
    return wn;