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74 lines
2.7 KiB
74 lines
2.7 KiB
5 years ago
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//========= Copyright Valve Corporation, All rights reserved. ============//
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// Purpose: Functions for spherical geometry.
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//
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// $NoKeywords: $
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//
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//=============================================================================//
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#ifndef SPHERICAL_GEOMETRY_H
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#define SPHERICAL_GEOMETRY_H
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#ifdef _WIN32
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#pragma once
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#endif
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#include <math.h>
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#include <float.h>
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// see http://mathworld.wolfram.com/SphericalTrigonometry.html
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// return the spherical distance, in radians, between 2 points on the unit sphere.
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FORCEINLINE float UnitSphereLineSegmentLength( Vector const &a, Vector const &b )
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{
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// check unit length
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Assert( fabs( VectorLength( a ) - 1.0 ) < 1.0e-3 );
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Assert( fabs( VectorLength( b ) - 1.0 ) < 1.0e-3 );
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return acos( DotProduct( a, b ) );
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}
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// given 3 points on the unit sphere, return the spherical area (in radians) of the triangle they form.
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// valid for "small" triangles.
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FORCEINLINE float UnitSphereTriangleArea( Vector const &a, Vector const &b , Vector const &c )
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{
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float flLengthA = UnitSphereLineSegmentLength( b, c );
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float flLengthB = UnitSphereLineSegmentLength( c, a );
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float flLengthC = UnitSphereLineSegmentLength( a, b );
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if ( ( flLengthA == 0. ) || ( flLengthB == 0. ) || ( flLengthC == 0. ) )
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return 0.; // zero area triangle
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// now, find the 3 incribed angles for the triangle
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float flHalfSumLens = 0.5 * ( flLengthA + flLengthB + flLengthC );
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float flSinSums = sin( flHalfSumLens );
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float flSinSMinusA= sin( flHalfSumLens - flLengthA );
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float flSinSMinusB= sin( flHalfSumLens - flLengthB );
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float flSinSMinusC= sin( flHalfSumLens - flLengthC );
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float flTanAOver2 = sqrt ( ( flSinSMinusB * flSinSMinusC ) / ( flSinSums * flSinSMinusA ) );
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float flTanBOver2 = sqrt ( ( flSinSMinusA * flSinSMinusC ) / ( flSinSums * flSinSMinusB ) );
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float flTanCOver2 = sqrt ( ( flSinSMinusA * flSinSMinusB ) / ( flSinSums * flSinSMinusC ) );
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// Girards formula : area = sum of angles - pi.
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return 2.0 * ( atan( flTanAOver2 ) + atan( flTanBOver2 ) + atan( flTanCOver2 ) ) - M_PI;
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}
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// spherical harmonics-related functions. Best explanation at http://www.research.scea.com/gdc2003/spherical-harmonic-lighting.pdf
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// Evaluate associated legendre polynomial P( l, m ) at flX, using recurrence relation
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float AssociatedLegendrePolynomial( int nL, int nM, float flX );
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// Evaluate order N spherical harmonic with spherical coordinates
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// nL = band, 0..N
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// nM = -nL .. nL
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// theta = 0..M_PI
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// phi = 0.. 2 * M_PHI
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float SphericalHarmonic( int nL, int nM, float flTheta, float flPhi );
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// evaluate spherical harmonic with normalized vector direction
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float SphericalHarmonic( int nL, int nM, Vector const &vecDirection );
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#endif // SPHERICAL_GEOMETRY_H
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