1 |
#include <stdio.h> |
2 |
#include <cmath> |
3 |
|
4 |
#include "math/RealSphericalHarmonic.hpp" |
5 |
|
6 |
using namespace oopse; |
7 |
|
8 |
RealSphericalHarmonic::RealSphericalHarmonic() { |
9 |
} |
10 |
|
11 |
double RealSphericalHarmonic::getValueAt(double costheta, double phi) { |
12 |
|
13 |
double p, phase; |
14 |
|
15 |
// associated Legendre polynomial |
16 |
p = LegendreP(L,M,costheta); |
17 |
|
18 |
if (functionType == SH_SIN) { |
19 |
phase = sin((double)M * phi); |
20 |
} else { |
21 |
phase = cos((double)M * phi); |
22 |
} |
23 |
|
24 |
return coefficient*p*phase; |
25 |
|
26 |
} |
27 |
|
28 |
//---------------------------------------------------------------------------// |
29 |
// |
30 |
// double LegendreP (int l, int m, double x); |
31 |
// |
32 |
// Computes the value of the associated Legendre polynomial P_lm (x) |
33 |
// of order l at a given point. |
34 |
// |
35 |
// Input: |
36 |
// l = degree of the polynomial >= 0 |
37 |
// m = parameter satisfying 0 <= m <= l, |
38 |
// x = point in which the computation is performed, range -1 <= x <= 1. |
39 |
// Returns: |
40 |
// value of the polynomial in x |
41 |
// |
42 |
//---------------------------------------------------------------------------// |
43 |
double RealSphericalHarmonic::LegendreP (int l, int m, double x) { |
44 |
// check parameters |
45 |
if (m < 0 || m > l || fabs(x) > 1.0) { |
46 |
printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x); |
47 |
return NAN; |
48 |
} |
49 |
|
50 |
double pmm = 1.0; |
51 |
if (m > 0) { |
52 |
double h = sqrt((1.0-x)*(1.0+x)), |
53 |
f = 1.0; |
54 |
for (int i = 1; i <= m; i++) { |
55 |
pmm *= -f * h; |
56 |
f += 2.0; |
57 |
} |
58 |
} |
59 |
if (l == m) |
60 |
return pmm; |
61 |
else { |
62 |
double pmmp1 = x * (2 * m + 1) * pmm; |
63 |
if (l == (m+1)) |
64 |
return pmmp1; |
65 |
else { |
66 |
double pll = 0.0; |
67 |
for (int ll = m+2; ll <= l; ll++) { |
68 |
pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m); |
69 |
pmm = pmmp1; |
70 |
pmmp1 = pll; |
71 |
} |
72 |
return pll; |
73 |
} |
74 |
} |
75 |
} |
76 |
|