mirror of
https://github.com/alliedmodders/hl2sdk.git
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125 lines
3.2 KiB
C++
125 lines
3.2 KiB
C++
//========= Copyright Valve Corporation, All rights reserved. ============//
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//
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// Purpose: spherical math routines
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//
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//=====================================================================================//
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#include <math.h>
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#include <float.h> // Needed for FLT_EPSILON
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#include "basetypes.h"
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#include <memory.h>
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#include "tier0/dbg.h"
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#include "mathlib/mathlib.h"
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#include "mathlib/vector.h"
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#include "mathlib/spherical_geometry.h"
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// memdbgon must be the last include file in a .cpp file!!!
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#include "tier0/memdbgon.h"
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float s_flFactorials[]={
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1.,
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1.,
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2.,
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6.,
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24.,
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120.,
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720.,
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5040.,
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40320.,
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362880.,
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3628800.,
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39916800.,
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479001600.,
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6227020800.,
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87178291200.,
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1307674368000.,
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20922789888000.,
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355687428096000.,
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6402373705728000.,
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121645100408832000.,
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2432902008176640000.,
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51090942171709440000.,
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1124000727777607680000.,
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25852016738884976640000.,
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620448401733239439360000.,
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15511210043330985984000000.,
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403291461126605635584000000.,
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10888869450418352160768000000.,
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304888344611713860501504000000.,
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8841761993739701954543616000000.,
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265252859812191058636308480000000.,
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8222838654177922817725562880000000.,
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263130836933693530167218012160000000.,
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8683317618811886495518194401280000000.
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};
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float AssociatedLegendrePolynomial( int nL, int nM, float flX )
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{
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// evaluate associated legendre polynomial at flX, using recurrence relation
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float flPmm = 1.;
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if ( nM > 0 )
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{
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float flSomX2 = sqrt( ( 1 - flX ) * ( 1 + flX ) );
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float flFact = 1.;
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for( int i = 0 ; i < nM; i++ )
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{
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flPmm *= -flFact * flSomX2;
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flFact += 2.0;
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}
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}
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if ( nL == nM )
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return flPmm;
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float flPmmp1 = flX * ( 2.0 * nM + 1.0 ) * flPmm;
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if ( nL == nM + 1 )
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return flPmmp1;
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float flPll = 0.;
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for( int nLL = nM + 2 ; nLL <= nL; nLL++ )
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{
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flPll = ( ( 2.0 * nLL - 1.0 ) * flX * flPmmp1 - ( nLL + nM - 1.0 ) * flPmm ) * ( 1.0 / ( nLL - nM ) );
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flPmm = flPmmp1;
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flPmmp1 = flPll;
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}
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return flPll;
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}
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static float SHNormalizationFactor( int nL, int nM )
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{
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double flTemp = ( ( 2. * nL + 1.0 ) * s_flFactorials[ nL - nM ] )/ ( 4. * M_PI * s_flFactorials[ nL + nM ] );
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return sqrt( flTemp );
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}
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#define SQRT_2 1.414213562373095
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FORCEINLINE float SphericalHarmonic( int nL, int nM, float flTheta, float flPhi, float flCosTheta )
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{
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if ( nM == 0 )
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return SHNormalizationFactor( nL, 0 ) * AssociatedLegendrePolynomial( nL, nM, flCosTheta );
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if ( nM > 0 )
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return SQRT_2 * SHNormalizationFactor( nL, nM ) * cos ( nM * flPhi ) *
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AssociatedLegendrePolynomial( nL, nM, flCosTheta );
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return
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SQRT_2 * SHNormalizationFactor( nL, -nM ) * sin( -nM * flPhi ) * AssociatedLegendrePolynomial( nL, -nM, flCosTheta );
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}
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float SphericalHarmonic( int nL, int nM, float flTheta, float flPhi )
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{
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return SphericalHarmonic( nL, nM, flTheta, flPhi, cos( flTheta ) );
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}
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float SphericalHarmonic( int nL, int nM, Vector const &vecDirection )
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{
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Assert( fabs( VectorLength( vecDirection ) - 1.0 ) < 0.0001 );
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float flPhi = acos( vecDirection.z );
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float flTheta = 0;
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float S = Square( vecDirection.x ) + Square( vecDirection.y );
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if ( S > 0 )
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{
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flTheta = atan2( vecDirection.y, vecDirection.x );
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}
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return SphericalHarmonic( nL, nM, flTheta, flPhi, cos( flTheta ) );
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}
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