Modified source engine (2017) developed by valve and leaked in 2020. Not for commercial purporses
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 
 
 
 

73 lines
2.7 KiB

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