// Helpers
// Intersection between a plane and a ray
public bool Intersect( Ray _Ray, ref float3 _intersection )
{
float fGradient = n.Dot( _Ray.Aim );
if ( (float) System.Math.Abs( fGradient ) < float.Epsilon )
return false; // It cannot hit! (or very far away at least!)
_Ray.Length = (-d - _Ray.Pos.Dot(n)) / fGradient;
_intersection = _Ray.GetHitPos();
return true;
}
public AngleAxis( Quat _q )
{
Angle = (float) System.Math.Acos( _q.qs );
float fSine = (float) System.Math.Sin( Angle );
Angle *= 2.0f;
Quat Temp = new Quat( _q );
Temp.Normalize();
if ( System.Math.Abs( fSine ) > float.Epsilon )
Axis = Temp.qv / fSine;
else
Axis.Set( 0, 0, 0 );
}
// Here, we choose the convention that the vertical axis defining THETA is the Y axis
// and the axes defining PHI are X and Z where PHI = 0 when the vector is aligned to the positive Z axis
//
// NOTE ==> The '_Direction' vector must be normalized!!
//
public static double ComputeZH( int l, float3 _Direction )
{
// Convert from cartesian to polar coords
double θ = 0.0;
double ϕ = 0.0f;
CartesianToSpherical( _Direction, out θ, out ϕ );
return ComputeZH( l, θ );
}
/// <summary>
/// Encodes a function evaluated by the provided delegate into a series of ZH coefficients
/// </summary>
/// <param name="_Coefficients">The coefficients supposed to best fit the provided function (the length of the vector must be _Order²)</param>
/// <param name="_SamplesCount">The amount of samples to use to fit the function</param>
/// <param name="_RandomSeed">The random seed to initialize the RNG with when drawing random sample position</param>
/// <param name="_Order">The order of the SH vector to encode</param>
/// <param name="_Delegate">The delegate that will be called to evaluate the function to encode</param>
public static void EncodeIntoSH( float3[] _Coefficients, int _SamplesCountTheta, int _SamplesCountPhi, int _RandomSeed, int _Order, EvaluateFunctionSHVector3 _Delegate )
{
Random RNG = new Random( _RandomSeed );
// Reset coefficients
for ( int CoefficientIndex=0; CoefficientIndex < _Coefficients.Length; CoefficientIndex++ ) {
_Coefficients[CoefficientIndex] = float3.Zero;
}
float3 Value = new float3();
for ( int PhiIndex=0; PhiIndex < _SamplesCountPhi; PhiIndex++ )
for ( int ThetaIndex=0; ThetaIndex < _SamplesCountTheta; ThetaIndex++ ) {
// Draw uniformly sampled θ and ϕ angles
double θ = 2.0 * Math.Acos( Math.Sqrt( 1.0 - (ThetaIndex + RNG.NextDouble()) / _SamplesCountTheta ) );
double ϕ = 2.0 * Math.PI * (PhiIndex + RNG.NextDouble()) / _SamplesCountPhi;
// Accumulate coefficients
_Delegate( θ, ϕ, Value );
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= +l; m++ )
_Coefficients[l*(l+1)+m] += (float) Ylm( l, m, θ, ϕ ) * Value;
}
// Final normalizing
float Normalizer = 4.0f * (float) Math.PI / (_SamplesCountTheta * _SamplesCountPhi);
for ( int CoefficientIndex=0; CoefficientIndex < _Order*_Order; CoefficientIndex++ )
_Coefficients[CoefficientIndex] *= Normalizer;
}
// Modulate all coefficients of degree l by scalar a.
private static void Filter( float3[] _SH, int l, float a )
{
for ( int m=-l; m <= l; m++ )
_SH[l*(l+1)+m] *= a;
}
/// <summary>
/// Converts a cartesian UNIT vector into spherical coordinates (θ,ϕ)
/// </summary>
/// <param name="_Direction">The cartesian unit vector to convert</param>
/// <param name="_θ">The polar elevation</param>
/// <param name="_ϕ">The azimuth</param>
public static void CartesianToSpherical( float3 _Direction, out double _θ, out double _ϕ )
{
_θ = Math.Acos( Math.Max( -1.0f, Math.Min( +1.0f, _Direction.z ) ) );
_ϕ = Math.Atan2( _Direction.y, _Direction.x );
}
/// <summary>
/// Applies a simple fast rotation about the Y axis
/// </summary>
/// <param name="_Vector">The vector to rotate</param>
/// <param name="_ϕ">The rotation angle</param>
/// <param name="_RotatedVector">The rotated vector</param>
/// <param name="_Order">The order of the vectors (i.e. vectors must have a length of Order²)</param>
public static void RotateY( float3[] _Vector, double _ϕ, float3[] _RotatedVector, int _Order )
{
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= l; m++ )
if ( m != 0 )
{
float fCos = (float) Math.Cos( Math.Abs( m ) * _ϕ );
float fSin = (float) Math.Sin( Math.Abs( m ) * _ϕ );
int CoeffIndex0 = l*(l+1) + m;
int CoeffIndex1 = l*(l+1) - m;
_RotatedVector[CoeffIndex0] = _Vector[CoeffIndex0] * fCos - Math.Sign( m ) * _Vector[CoeffIndex1] * fSin;
}
else
_RotatedVector[l*(l+1)] = _Vector[l*(l+1)]; // <= Don't rotate zonal harmonics
}
/// <summary>
/// Converts spherical coordinates (θ,ϕ) into a cartesian UNIT vector
/// </summary>
/// <param name="_θ">The polar elevation</param>
/// <param name="_ϕ">The azimuth</param>
/// <param name="_Direction">The unit vector in cartesian coordinates</param>
public static void SphericalToCartesian( double _θ, double _ϕ, float3 _Direction )
{
_Direction.x = (float) (Math.Sin( _θ ) * Math.Cos( _ϕ ));
_Direction.y = (float) (Math.Sin( _θ ) * Math.Sin( _ϕ ));
_Direction.z = (float) Math.Cos( _θ );
}
/// <summary>
/// Initializes the provided vector with the SH coefficients corresponding to the specified direction
/// </summary>
/// <param name="_Order">The order of the SH vector</param>
/// <param name="_Direction">The direction of the SH sampling</param>
/// <param name="_Coefficients">The array of coefficients to fill up</param>
public static void InitializeSHCoefficients( int _Order, float3 _Direction, float3[] _Coefficients )
{
int Index = 0;
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= +l; m++ )
{
float fCoeff = (float) Ylm( l, m, _Direction );
_Coefficients[Index++].Set( fCoeff, fCoeff, fCoeff );
}
}
/// <summary>
/// Applies a simple mirroring on the Y axis
/// </summary>
/// <param name="_Vector">The vector to mirror</param>
/// <param name="_MirroredVector">The mirrored vector</param>
/// <param name="_Order">The order of the vectors (i.e. vectors must have a length of Order²)</param>
public static void MirrorY( float3[] _Vector, float3[] _MirroredVector, int _Order )
{
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= l; m++ )
{
int k = l*(l+1) + m;
_MirroredVector[k] = (((l+m) & 1) == 0 ? +1 : -1) * _Vector[k];
}
}
// Assignment operators
public void Set ( Ray _r ) { m_Pos = _r.m_Pos; m_Aim = _r.m_Aim; m_Length = _r.m_Length; m_MarchedLength = _r.m_MarchedLength; m_Datum = _r.m_Datum; }
// Apply a Gaussian window of width w (usually the SH order).
public static void FilterGaussian( float3[] _SH, int w )
{
for ( int l = 0; l < 3; l++ )
Filter( _SH, l, (float) Math.Exp( -(Math.PI * l / w) * (Math.PI * l / w) / 2.0 ) );
}
public Ray Bend ( float3 _Axis, float _fBendFactor ) { m_Aim += _fBendFactor * m_Aim.Dot(_Axis) * _Axis; m_Aim.Normalize(); return this; }
// Helpers
public Ray March ( float _fDelta ) { m_Pos += _fDelta * m_Aim; m_Length -= _fDelta; m_MarchedLength += _fDelta; return this; }
public Ray ( float3 _Pos, float3 _Aim, float _fLength, float _fMarchedLength ) : this( _Pos, _Aim, _fLength ) { m_MarchedLength = _fMarchedLength; }
public Ray ( float3 _Pos, float3 _Aim, float _fLength ): this( _Pos, _Aim ) { m_Length = _fLength; }
public Ray ( float3 _Pos, float3 _Aim ) { m_Pos = _Pos; m_Aim = _Aim; }
// Apply a Lanczos window of width w (usually the SH order).
public static void FilterLanczos( float3[] _SH, int w )
{
for (int l = 0; l < 3; l++)
if ( l == 0 )
Filter( _SH, l, 1 );
else
Filter( _SH, l, (float) (Math.Sin(Math.PI * l / w) / (Math.PI * l / w)) );
}
// Constructors/Destructor
public BoundingSphere()
{
m_Center = new float3(); m_Radius = 0.0f;
}
public void Set(float3 _Source)
{
x = _Source.x; y = _Source.y;
}
public BoundingSphere(float _X, float _Y, float _Z, float _Radius)
{
m_Center = new float3(_X, _Y, _Z); m_Radius = _Radius;
}
/// <summary>
/// Applies rotation to the specified 3-vector using the specified rotation matrix returned by the "BuildRotationMatrix()" method
/// </summary>
/// <param name="_Vector">The 3-vector to rotate</param>
/// <param name="_RotationMatrix">The SH rotation matrix</param>
/// <param name="_RotatedVector">The rotated vector</param>
/// <param name="_Order">The order of the vectors (i.e. vectors must have a length of Order²)</param>
public static void Rotate( float3[] _Vector, double[,] _RotationMatrix, float3[] _RotatedVector, int _Order )
{
int MatrixSize = 1;
int SourceCoefficientIndex = 0;
int DestCoefficientIndex = 0;
for ( int l=0; l < _Order; l++, MatrixSize+=2 )
{
int BandOffset = l * l;
for ( int n=0; n < MatrixSize; n++ )
{
_RotatedVector[DestCoefficientIndex] = new float3( 0.0f, 0.0f, 0.0f );
for ( int m=0; m < MatrixSize; m++ )
_RotatedVector[DestCoefficientIndex] += _Vector[SourceCoefficientIndex+m] * (float) _RotationMatrix[BandOffset + m,BandOffset + n];
DestCoefficientIndex++;
}
SourceCoefficientIndex += MatrixSize;
}
}
public BoundingSphere(float3 _Center, float _Radius)
{
m_Center = _Center; m_Radius = _Radius;
}
/// <summary>
/// Converts spherical coordinates (θ,ϕ) into a cartesian UNIT vector
/// </summary>
/// <param name="_θ">The polar elevation</param>
/// <param name="_ϕ">The azimuth</param>
/// <returns>The unit vector in cartesian coordinates</returns>
public static float3 SphericalToCartesian( double _θ, double _ϕ )
{
float3 Result = new float3();
SphericalToCartesian( _θ, _ϕ, Result );
return Result;
}
public float Distance( float3 _p )
{
return _p.Dot(n) + d;
}
// Here, we choose the convention that the vertical axis defining THETA is the Y axis
// and the axes defining PHI are X and Z where PHI = 0 when the vector is aligned to the positive Z axis
//
// NOTE ==> The '_Direction' vector must be normalized!!
//
public static double Ylm( int l, int m, float3 _Direction )
{
// Convert from cartesian to polar coords
double θ = 0.0;
double ϕ = 0.0f;
CartesianToSpherical( _Direction, out θ, out ϕ );
return Ylm( l, m, θ, ϕ );
}
// Intersection between 2 planes
public bool Intersect( Plane _p, Ray _ray )
{
// Check if both planes are coplanar
if ( (float) System.Math.Abs( 1.0f - _p.n.Dot(n) ) < float.Epsilon )
return false;
// Let's have fun!
float3 I = new float3();
_ray.Pos.Set( 0, 0, 0 );
_ray.Aim = n;
if ( !_p.Intersect( _ray, ref I ) )
return false;
_ray.Aim = _p.n;
if ( !_p.Intersect( _ray, ref I ) )
return false;
_ray.Pos = I;
_ray.Aim = I - _ray.Pos;
if ( !Intersect( _ray, ref I ) )
return false;
_ray.Pos = I;
// We have at least one point belonging to both planes!
_ray.Aim = n.Cross(_p.n).Normalized;
return true;
}
/// <summary>
/// Computes the 9 Ylm coefficients for order 2 SH evaluated in the requested direction
/// </summary>
/// <param name="_direction"></param>
/// <param name="_SH"></param>
static void Ylm( float3 _direction, double[] _SH )
{
const double c0 = 0.28209479177387814347403972578039; // 1/2 sqrt(1/pi)
const double c1 = 0.48860251190291992158638462283835; // 1/2 sqrt(3/pi)
const double c2 = 1.09254843059207907054338570580270; // 1/2 sqrt(15/pi)
const double c3 = 0.31539156525252000603089369029571; // 1/4 sqrt(5/pi)
float x = _direction.x;
float y = _direction.y;
float z = _direction.z;
_SH[0] = c0;
_SH[1] = c1*y;
_SH[2] = c1*z;
_SH[3] = c1*x;
_SH[4] = c2*x*y;
_SH[5] = c2*y*z;
_SH[6] = c3*(3.0*z*z - 1.0);
_SH[7] = c2*x*z;
_SH[8] = 0.5*c2*(x*x - y*y);
}
/// <summary>
/// Computes the ambient occlusion of the specified coordinate by shooting N rays in a lobe oriented in the specified light direction
/// </summary>
/// <param name="_Light"></param>
/// <param name="_X"></param>
/// <param name="_Y"></param>
/// <param name="_Z2HeightScale">Scale factor to apply to world Z coordinate to be remapped into the heights' [0,1] range</param>
/// <param name="_LobeExponent">1 is a simple cosine lobe</param>
/// <returns></returns>
///
private float ComputeAO( int _LightIndex, uint _X, uint _Y, float _Z2HeightScale, float3[,] _rays )
{
int RaysCount = _rays.GetLength( 1 );
int maxStepsCount = integerTrackbarControlMaxStepsCount.Value;
float Z0 = m_imageSourceHeightMap[_X,_Y].y;
double AO = 0.0f;
int samplesCount = 0;
for ( int rayIndex=0; rayIndex < RaysCount; rayIndex++ ) {
float3 wsRay = _rays[_LightIndex,rayIndex];
if ( wsRay.z < 0.0f ) {
// AO += 1.0;
// SamplesCount++;
continue; // Pointing to the ground so don't account for it...
}
// Make sure the ray has a unit step so we always travel at least one pixel
// m_RayWorld.z *= _Z2HeightScale;
// float Normalizer = 1.0f / Math.Max( Math.Abs( m_RayWorld.x ), Math.Abs( m_RayWorld.y ) );
// float Normalizer = 1.0f;
// Normalizer = Math.Max( Normalizer, (1.0f - Z) / (128.0f * m_RayWorld.z) ); // This makes sure we can't use more than 128 steps to escape the heightfield
//
// float Normalizer = (1.0f - Z) / (128.0f * m_RayWorld.z);
//
// m_RayWorld.x *= Normalizer;
// m_RayWorld.y *= Normalizer;
// m_RayWorld.z *= Normalizer;
// Start from the provided coordinates
float X = _X;
float Y = _Y;
float Z = Z0;
// Compute intersection with the height field
int stepIndex = 0;
while ( stepIndex < maxStepsCount && Z < 1.0f && X > 0.0f && Y > 0.0f && X < W && Y < H ) {
X += wsRay.x;
Y += wsRay.y;
Z += wsRay.z;
float height = SampleHeightField( X, Y );
if ( height > Z ) {
// Hit!
AO += 1.0;
break;
}
stepIndex++;
}
samplesCount++;
}
AO /= samplesCount;
return (float) (1.0 - AO);
}
/// <summary>
/// Computes the SH coefficients of originaly Y-aligned Zonal Harmonics coefficients rotated to match the provided axis
/// </summary>
/// <param name="_ZHCoefficients">The ZH coefficients to rotate</param>
/// <param name="_TargetAxis">The target axis to match (the original axis being positive Y)</param>
/// <param name="_RotatedSHCoefficients">The rotated SH coefficients</param>
/// <remarks>Be careful the returned coefficients are SH coefficients, hence the _RotatedSHCoefficients vector should be N² if rotating an order N Zonal Harmonics vector</remarks>
public static void ComputeRotatedZHCoefficients( double[] _ZHCoefficients, float3 _TargetAxis, double[] _RotatedSHCoefficients )
{
// Compute the convolution coefficients from input ZH coeffs
double[] ConvolutionCoefficients = new double[_ZHCoefficients.Length];
for ( int ConvolutionCoefficientIndex=0; ConvolutionCoefficientIndex < _ZHCoefficients.Length; ConvolutionCoefficientIndex++ )
ConvolutionCoefficients[ConvolutionCoefficientIndex] = Math.Sqrt( 4.0 * Math.PI / (2 * ConvolutionCoefficientIndex + 1) ) * _ZHCoefficients[ConvolutionCoefficientIndex];
// Perform rotation
for ( int l=0; l < _ZHCoefficients.Length; l++ )
for ( int m=-l; m <= +l; m++ )
_RotatedSHCoefficients[l*(l+1)+m] = Ylm( l, m, _TargetAxis ) * ConvolutionCoefficients[l];
}
private void GenerateRays( int _raysCount, StructuredBuffer<float3> _target )
{
_raysCount = Math.Min( MAX_THREADS, _raysCount );
// Half-Life 2 basis
float3[] HL2Basis = new float3[] {
new float3( (float) Math.Sqrt( 2.0 / 3.0 ), 0.0f, (float) Math.Sqrt( 1.0 / 3.0 ) ),
new float3( -(float) Math.Sqrt( 1.0 / 6.0 ), (float) Math.Sqrt( 1.0 / 2.0 ), (float) Math.Sqrt( 1.0 / 3.0 ) ),
new float3( -(float) Math.Sqrt( 1.0 / 6.0 ), -(float) Math.Sqrt( 1.0 / 2.0 ), (float) Math.Sqrt( 1.0 / 3.0 ) )
};
float centerTheta = (float) Math.Acos( HL2Basis[0].z );
float[] centerPhi = new float[] {
(float) Math.Atan2( HL2Basis[0].y, HL2Basis[0].x ),
(float) Math.Atan2( HL2Basis[1].y, HL2Basis[1].x ),
(float) Math.Atan2( HL2Basis[2].y, HL2Basis[2].x ),
};
for ( int rayIndex=0; rayIndex < _raysCount; rayIndex++ ) {
double phi = (Math.PI / 3.0) * (2.0 * SimpleRNG.GetUniform() - 1.0);
// Stratified version
double theta = (Math.Acos( Math.Sqrt( (rayIndex + SimpleRNG.GetUniform()) / _raysCount ) ));
// // Don't give a shit version (a.k.a. melonhead version)
// // double Theta = Math.Acos( Math.Sqrt(WMath.SimpleRNG.GetUniform() ) );
// double Theta = 0.5 * Math.PI * WMath.SimpleRNG.GetUniform();
theta = Math.Min( 0.499f * Math.PI, theta );
double cosTheta = Math.Cos( theta );
double sinTheta = Math.Sin( theta );
double lengthFactor = 1.0 / sinTheta; // The ray is scaled so we ensure we always walk at least a texel in the texture
cosTheta *= lengthFactor;
sinTheta *= lengthFactor; // Yeah, yields 1... :)
_target.m[0*MAX_THREADS+rayIndex].Set( (float) (Math.Cos( centerPhi[0] + phi ) * sinTheta),
(float) (Math.Sin( centerPhi[0] + phi ) * sinTheta),
(float) cosTheta );
_target.m[1*MAX_THREADS+rayIndex].Set( (float) (Math.Cos( centerPhi[1] + phi ) * sinTheta),
(float) (Math.Sin( centerPhi[1] + phi ) * sinTheta),
(float) cosTheta );
_target.m[2*MAX_THREADS+rayIndex].Set( (float) (Math.Cos( centerPhi[2] + phi ) * sinTheta),
(float) (Math.Sin( centerPhi[2] + phi ) * sinTheta),
(float) cosTheta );
}
_target.Write();
}
/// <summary>
/// Computes the convolution of 2 3-vectors of SH coefficients of the specified order using Clebsch-Gordan coefficients
/// </summary>
/// <param name="_Vector0">First 3-vector</param>
/// <param name="_Vector1">Second 3-vector</param>
/// <param name="_Order">The order of the vectors (i.e. vectors must have a length of Order²)</param>
/// <returns>The convolution of the 2 vectors</returns>
/// <remarks>This method is quite time-consuming as the convolution is computed using 5 loops but, as an optimisation, we can notice that most Clebsh-Gordan are 0
/// and a vector of non-null coefficients could be precomputed as only the vectors' coefficients change</remarks>
public static float3[] Convolve( float3[] _Vector0, float3[] _Vector1, int _Order )
{
if ( _Vector0 == null || _Vector1 == null )
throw new Exception( "Invalid coefficients!" );
if ( _Vector0.Length != _Vector1.Length )
throw new Exception( "Coefficient vectors length mismatch!" );
if ( _Order * _Order != _Vector0.Length )
throw new Exception( "Coefficient vectors are not of the specified order!" );
float3[] ConvolvedCoeffs = new float3[_Vector0.Length];
// Compute convolution
int TotalCoeffIndex = 0;
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= +l; m++, TotalCoeffIndex++ )
{
ConvolvedCoeffs[TotalCoeffIndex] = new float3( 0.0f, 0.0f, 0.0f );
int InnerTotalCoeffIndex = 0;
for ( int l1=0; l1 < _Order; l1++ )
for ( int m1=-l1; m1 <= +l1; m1++, InnerTotalCoeffIndex++ )
for ( int l2=0; l2 < _Order; l2++ )
{
int Bl2m1mIndex = l2*(l2+1) + m1 - m;
if ( Bl2m1mIndex < 0 || Bl2m1mIndex >= _Order * _Order )
continue;
double Sign = ((m1 - m) & 1) == 0 ? +1 : -1;
double Sqrt = Math.Sqrt( (2.0 * l1 + 1) * (2.0 * l2 + 1) / (4.0 * Math.PI * (2.0 * l + 1)) );
double CGC0 = ComputeClebschGordan( l1, l2, 0, 0, l, 0 );
if ( Math.Abs( CGC0 ) < 1e-4 )
continue;
double CGC1 = ComputeClebschGordan( l1, l2, m1, m - m1, l, m );
if ( Math.Abs( CGC1 ) < 1e-4 )
continue;
float3 A = _Vector0[InnerTotalCoeffIndex];
float3 B = _Vector1[Bl2m1mIndex];
double FinalCoeff = Sqrt * CGC0 * CGC1;
ConvolvedCoeffs[TotalCoeffIndex] += (float) (Sign * FinalCoeff) * A * B;
}
}
return ConvolvedCoeffs;
}
private void Generate_CPU( int _RaysCount )
{
try {
tabControlGenerators.Enabled = false;
// Half-life basis (Z points outside of the surface, as in normal maps)
float3[] basis = new float3[] {
new float3( (float) Math.Sqrt( 2.0 / 3.0 ), 0.0f, (float) Math.Sqrt( 1.0 / 3.0 ) ),
new float3( (float) -Math.Sqrt( 1.0 / 6.0 ), (float) Math.Sqrt( 1.0 / 2.0 ), (float) Math.Sqrt( 1.0 / 3.0 ) ),
new float3( (float) -Math.Sqrt( 1.0 / 6.0 ), (float) -Math.Sqrt( 1.0 / 2.0 ), (float) Math.Sqrt( 1.0 / 3.0 ) ),
};
// // 1] Compute normal map
// float3 dX = new float3();
// float3 dY = new float3();
// float3 N;
// float ddX = floatTrackbarControlPixelSize.Value;
// float ddH = floatTrackbarControlHeight.Value;
// for ( int Y=0; Y < H; Y++ )
// {
// int Y0 = Math.Max( 0, Y-1 );
// int Y1 = Math.Min( H-1, Y+1 );
// for ( int X=0; X < W; X++ )
// {
// int X0 = Math.Max( 0, X-1 );
// int X1 = Math.Min( W-1, X+1 );
//
// float Hx0 = m_BitmapSource.ContentXYZ[X0,Y].y;
// float Hx1 = m_BitmapSource.ContentXYZ[X1,Y].y;
// float Hy0 = m_BitmapSource.ContentXYZ[X,Y0].y;
// float Hy1 = m_BitmapSource.ContentXYZ[X,Y1].y;
//
// dX.Set( 2.0f * ddX, 0.0f, ddH * (Hx1 - Hx0) );
// dY.Set( 0.0f, 2.0f * ddX, ddH * (Hy1 - Hy0) );
//
// N = dX.Cross( dY ).Normalized;
//
// m_Normal[X,Y] = new float3(
// N.Dot( Basis[0] ),
// N.Dot( Basis[1] ),
// N.Dot( Basis[2] ) );
// }
//
// // Update and show progress
// UpdateProgress( m_Normal, Y, true );
// }
// UpdateProgress( m_Normal, H, true );
float LobeExponent = 4.0f;//floatTrackbarControlLobeExponent.Value;
float PixelSize_mm = 1000.0f / floatTrackbarControlPixelDensity.Value;
float scale = 0.1f * PixelSize_mm / floatTrackbarControlHeight.Value; // Scale factor to apply to pixel distances so they're renormalized in [0,1], our "heights space"...
// Scale *= floatTrackbarControlZFactor.Value; // Cheat Z velocity so AO is amplified!
// 2] Build local rays only once
int raysCount = integerTrackbarControlRaysCount.Value;
float3[,] rays = new float3[3,raysCount];
// Create orthonormal bases to orient the lobe
float3 Xr = basis[0].Cross( float3.UnitZ ).Normalized; // We can safely use (0,0,1) as the "up" direction since the HL2 basis doesn't have any vertical direction
float3 Yr = Xr.Cross( basis[0] );
float3 Xg = basis[1].Cross( float3.UnitZ ).Normalized; // We can safely use (0,0,1) as the "up" direction since the HL2 basis doesn't have any vertical direction
float3 Yg = Xg.Cross( basis[1] );
float3 Xb = basis[2].Cross( float3.UnitZ ).Normalized; // We can safely use (0,0,1) as the "up" direction since the HL2 basis doesn't have any vertical direction
float3 Yb = Xb.Cross( basis[2] );
double Exponent = 1.0 / (1.0 + LobeExponent);
for ( int RayIndex=0; RayIndex < raysCount; RayIndex++ )
{
// if ( false ) {
// double Phi = 2.0 * Math.PI * WMath.SimpleRNG.GetUniform();
// // double Theta = Math.Acos( Math.Pow( WMath.SimpleRNG.GetUniform(), Exponent ) );
// double Theta = Math.PI / 3.0 * WMath.SimpleRNG.GetUniform();
//
// float3 RayLocal = new float3(
// (float) (Math.Cos( Phi ) * Math.Sin( Theta )),
// (float) (Math.Sin( Phi ) * Math.Sin( Theta )),
// (float) Math.Cos( Theta ) );
//
// Rays[0,RayIndex] = RayLocal.x * Xr + RayLocal.y * Yr + RayLocal.z * Basis[0];
// Rays[1,RayIndex] = RayLocal.x * Xg + RayLocal.y * Yg + RayLocal.z * Basis[1];
// Rays[2,RayIndex] = RayLocal.x * Xb + RayLocal.y * Yb + RayLocal.z * Basis[2];
// } else
{
double Phi = Math.PI / 3.0 * (2.0 * SimpleRNG.GetUniform() - 1.0);
double Theta = 0.49 * Math.PI * SimpleRNG.GetUniform();
rays[0,RayIndex] = new float3(
(float) (Math.Cos( Phi ) * Math.Sin( Theta )),
(float) (Math.Sin( Phi ) * Math.Sin( Theta )),
(float) Math.Cos( Theta ) );
Phi = Math.PI / 3.0 * (2.0 * SimpleRNG.GetUniform() - 1.0 + 2.0);
Theta = 0.49 * Math.PI * SimpleRNG.GetUniform();
rays[1,RayIndex] = new float3(
(float) (Math.Cos( Phi ) * Math.Sin( Theta )),
(float) (Math.Sin( Phi ) * Math.Sin( Theta )),
(float) Math.Cos( Theta ) );
Phi = Math.PI / 3.0 * (2.0 * SimpleRNG.GetUniform() - 1.0 + 4.0);
Theta = 0.49 * Math.PI * SimpleRNG.GetUniform();
rays[2,RayIndex] = new float3(
(float) (Math.Cos( Phi ) * Math.Sin( Theta )),
(float) (Math.Sin( Phi ) * Math.Sin( Theta )),
(float) Math.Cos( Theta ) );
}
rays[0,RayIndex].z *= scale;
rays[1,RayIndex].z *= scale;
rays[2,RayIndex].z *= scale;
}
// 3] Compute directional occlusion
float4[] scanline = new float4[W];
float4 gammaRGB = float4.Zero;
for ( uint Y=0; Y < H; Y++ ) {
for ( uint X=0; X < W; X++ ) {
gammaRGB.x = ComputeAO( 0, X, Y, scale, rays );
gammaRGB.y = ComputeAO( 1, X, Y, scale, rays );
gammaRGB.z = ComputeAO( 2, X, Y, scale, rays );
gammaRGB.w = (gammaRGB.x+gammaRGB.y+gammaRGB.z) / 3.0f;
m_sRGBProfile.GammaRGB2LinearRGB( gammaRGB, ref scanline[X] );
}
m_imageResult.WriteScanline( Y, scanline );
// Update and show progress
UpdateProgress( m_imageResult, Y, true );
}
UpdateProgress( m_imageResult, H, true );
// m_BitmapResult.Save( "eye_generic_01_disp_hl2.png", ImageFormat.Png );
}
catch ( Exception _e )
{
MessageBox( "An error occurred during generation:\r\n" + _e.Message, MessageBoxButtons.OK, MessageBoxIcon.Error );
}
finally
{
tabControlGenerators.Enabled = true;
}
}
/// <summary>
/// Evaluates the amplitude encoded by the Y-aligned ZH coefficients in the provided direction
/// </summary>
/// <param name="_Coefficients">The SH coefficients encoding an amplitude in various directions</param>
/// <param name="_Direction">The direction where to evalute the ZH</param>
/// <returns>The ZH evaluation in the provided direction</returns>
public static double EvaluateZH( double[] _Coefficients, float3 _Direction )
{
// Convert from cartesian to polar coords
double θ = 0.0;
double ϕ = 0.0f;
CartesianToSpherical( _Direction, out θ, out ϕ );
return EvaluateZH( _Coefficients, θ );
}
float4x4 ComputeCameraProjection()
{
float t = (float) (DateTime.Now - m_startTime).TotalSeconds;
// Make a camera orbiting around the cube
float T = t;
float3 cameraPosition = 3.0f * new float3( (float) Math.Cos( T ), (float) Math.Cos( 3 * T ), (float) Math.Sin( T ) );
float3 cameraTarget = new float3( 0, 0, 0 );
float4x4 camera2World = new float4x4();
camera2World.BuildRotLeftHanded( cameraPosition, cameraTarget, float3.UnitY );
// Build the perspective projection matrix
float4x4 camera2Proj = new float4x4();
camera2Proj.BuildProjectionPerspective( 80.0f * (float) Math.PI / 180.0f, (float) Width / Height, 0.01f, 100.0f );
// Compose the 2 matrices together to obtain the final matrix that transforms world coordinates into projected 2D coordinates
return camera2World.Inverse * camera2Proj;
}
// Filtering stolen from http://csc.lsu.edu/~kooima/sht/sh.hpp
// Apply a Hanning window of width w (usually the SH order).
public static void FilterHanning( float3[] _SH, int w )
{
for (int l = 0; l < 3; l++)
if ( l > w )
Filter( _SH, l, 0 );
else
Filter( _SH, l, (float) ((Math.Cos(Math.PI * l / w) + 1.0) * 0.5) );
}
// void timer1_Tick(object sender, System.EventArgs e) {
// throw new System.NotImplementedException();
// }
//////////////////////////////////////////////////////////////////////////
// Test methods compile
static void TestFloat3x3()
{
if ( System.Runtime.InteropServices.Marshal.SizeOf(typeof(float3x3)) != 36 )
throw new Exception( "Not the appropriate size!" );
float3x3 test1 = new float3x3( new float[9] { 9, 8, 7, 6, 5, 4, 3, 2, 1 } );
float3x3 test2 = new float3x3( new float3( 1, 0, 0 ), new float3( 0, 1, 0 ), new float3( 0, 0, 1 ) );
float3x3 test3 = new float3x3( 0, 1, 2, 3, 4, 5, 6, 7, 8 );
float3x3 test0;
test0 = test3;
test2.Scale( new float3( 2, 2, 2 ) );
float3x3 mul0 = test1 * test2;
float3x3 mul1 = 3.0f * test2;
float3 mul2 = new float3( 1, 1, 1 ) * test3;
float3 access0 = test3[2];
test3[1] = new float3( 12, 13, 14 );
float access1 = test3[1,2];
test3[1,2] = 18;
// float coFactor = test3.CoFactor( 0, 2 );
float det = test3.Determinant;
float3x3 inv = test2.Inverse;
float3x3 id = float3x3.Identity;
test3.BuildRotationX( 0.5f );
test3.BuildRotationY( 0.5f );
test3.BuildRotationZ( 0.5f );
test3.BuildFromAngleAxis( 0.5f, float3.UnitY );
}
/// <summary>
/// Initializes the provided vector with the SH coefficients corresponding to the specified direction
/// </summary>
/// <param name="_Order">The order of the SH vector</param>
/// <param name="_Direction">The direction of the SH sampling</param>
/// <param name="_Coefficients">The array of coefficients to fill up</param>
public static void InitializeSHCoefficients( int _Order, float3 _Direction, double[] _Coefficients )
{
int Index = 0;
for ( int l=0; l < _Order; l++ )
for ( int m=-l; m <= +l; m++ )
_Coefficients[Index++] = Ylm( l, m, _Direction );
}
protected override void OnLoad(EventArgs e)
{
base.OnLoad(e);
// Initialize the device
m_device.Init( panelOutput1.Handle, false, true );
// Build cube primitive
{
float3 colorXp = new float3( 1, 0, 0 );
float3 colorXn = new float3( 1, 1, 0 );
float3 colorYp = new float3( 0, 1, 0 );
float3 colorYn = new float3( 0, 1, 1 );
float3 colorZp = new float3( 0, 0, 1 );
float3 colorZn = new float3( 1, 0, 1 );
VertexP3N3G3T2[] vertices = new VertexP3N3G3T2[6*4] {
// +X
new VertexP3N3G3T2() { P = new float3( 1, 1, 1 ), N = new float3( 1, 0, 0 ), T = colorXp, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, 1 ), N = new float3( 1, 0, 0 ), T = colorXp, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, -1 ), N = new float3( 1, 0, 0 ), T = colorXp, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, 1, -1 ), N = new float3( 1, 0, 0 ), T = colorXp, UV = new float2( 1, 0 ) },
// -X
new VertexP3N3G3T2() { P = new float3( -1, 1, -1 ), N = new float3( -1, 0, 0 ), T = colorXn, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( -1, -1, -1 ), N = new float3( -1, 0, 0 ), T = colorXn, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( -1, -1, 1 ), N = new float3( -1, 0, 0 ), T = colorXn, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( -1, 1, 1 ), N = new float3( -1, 0, 0 ), T = colorXn, UV = new float2( 1, 0 ) },
// +Y
new VertexP3N3G3T2() { P = new float3( -1, 1, -1 ), N = new float3( 0, 1, 0 ), T = colorYp, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( -1, 1, 1 ), N = new float3( 0, 1, 0 ), T = colorYp, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, 1, 1 ), N = new float3( 0, 1, 0 ), T = colorYp, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, 1, -1 ), N = new float3( 0, 1, 0 ), T = colorYp, UV = new float2( 1, 0 ) },
// -Y
new VertexP3N3G3T2() { P = new float3( -1, -1, 1 ), N = new float3( 0, -1, 0 ), T = colorYn, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( -1, -1, -1 ), N = new float3( 0, -1, 0 ), T = colorYn, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, -1 ), N = new float3( 0, -1, 0 ), T = colorYn, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, 1 ), N = new float3( 0, -1, 0 ), T = colorYn, UV = new float2( 1, 0 ) },
// +Z
new VertexP3N3G3T2() { P = new float3( -1, 1, 1 ), N = new float3( 0, 0, 1 ), T = colorZp, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( -1, -1, 1 ), N = new float3( 0, 0, 1 ), T = colorZp, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, 1 ), N = new float3( 0, 0, 1 ), T = colorZp, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( 1, 1, 1 ), N = new float3( 0, 0, 1 ), T = colorZp, UV = new float2( 1, 0 ) },
// -Z
new VertexP3N3G3T2() { P = new float3( 1, 1, -1 ), N = new float3( 0, 0, -1 ), T = colorZn, UV = new float2( 0, 0 ) },
new VertexP3N3G3T2() { P = new float3( 1, -1, -1 ), N = new float3( 0, 0, -1 ), T = colorZn, UV = new float2( 0, 1 ) },
new VertexP3N3G3T2() { P = new float3( -1, -1, -1 ), N = new float3( 0, 0, -1 ), T = colorZn, UV = new float2( 1, 1 ) },
new VertexP3N3G3T2() { P = new float3( -1, 1, -1 ), N = new float3( 0, 0, -1 ), T = colorZn, UV = new float2( 1, 0 ) },
};
uint[] indices = new uint[3*2*6] {
4*0+0, 4*0+1, 4*0+2, 4*0+0, 4*0+2, 4*0+3,
4*1+0, 4*1+1, 4*1+2, 4*1+0, 4*1+2, 4*1+3,
4*2+0, 4*2+1, 4*2+2, 4*2+0, 4*2+2, 4*2+3,
4*3+0, 4*3+1, 4*3+2, 4*3+0, 4*3+2, 4*3+3,
4*4+0, 4*4+1, 4*4+2, 4*4+0, 4*4+2, 4*4+3,
4*5+0, 4*5+1, 4*5+2, 4*5+0, 4*5+2, 4*5+3,
};
m_prim_cube = new Primitive( m_device, 6*4, VertexP3N3G3T2.FromArray( vertices ), indices, Primitive.TOPOLOGY.TRIANGLE_LIST, VERTEX_FORMAT.P3N3G3T2 );
}
// Build the shader to render the cube
m_shader_renderCube = new Shader( m_device, new ShaderFile( new System.IO.FileInfo( @".\Shaders\RenderCube.hlsl" ) ), VERTEX_FORMAT.P3N3G3T2, "VS", null, "PS", null );
// Build constant buffer to provide camera transform
m_CB_Camera = new ConstantBuffer<CBCamera>( m_device, 0 );
Application.Idle += Application_Idle;
}
public float3[] MapSequenceToSphere( double[,] _Sequence, double _MaxTheta )
{
if ( _Sequence.GetLength( 1 ) != 2 )
throw new Exception( "Expecting a 2-dimensional sequence !" );
double cosMaxTheta = Math.Cos( _MaxTheta );
float3[] Result = new float3[_Sequence.GetLength( 0 )];
for ( int i=0; i < Result.Length; i++ )
{
// Pick a uniformly random VDOT, which must be between -1 and 1.
// This represents the dot product of the random vector with the Y unit vector.
//
// Note: this works because the surface area of the sphere between
// Y and Y + dY is independent of Y. So choosing Y uniformly chooses
// a patch of area uniformly.
//
double vdot = cosMaxTheta + (1.0 - cosMaxTheta) * _Sequence[i,0];
double theta = Math.Acos( vdot );
// Pick a uniformly random rotation between 0 and 2 Pi around the axis of the Y vector.
//
double phi = 2.0 * Math.PI * _Sequence[i,1];
Result[i] = new float3()
{
x = (float) (Math.Sin( phi ) * Math.Sin( theta )),
y = (float) Math.Cos( theta ),
z = (float) (Math.Cos( phi ) * Math.Sin( theta ))
};
}
return Result;
}
public Point2D(float3 _Source)
{
Set(_Source);
}