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FFT.cpp
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FFT.cpp
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/*
--------------------------------------------------------------------------------
This currentWaves file is part of Hydrax.
Visit ---
Copyright (C) 2008 Xavier Verguín González <xavierverguin@hotmail.com>
<xavyiy@gmail.com>
This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 59 Temple
Place - Suite 330, Boston, MA 02111-1307, USA, or go to
http://www.gnu.org/copyleft/lesser.txt.
--------------------------------------------------------------------------------
*/
#include "FFT.h"
#include "Hydrax.h"
namespace Hydrax{namespace Noise
{
inline float uniform_deviate()
{
return rand() * ( 1.0f / ( RAND_MAX + 1.0f ) );
}
inline double sit_deviate()
{
double ud = uniform_deviate();
if(ud<=0.5)
return ud*Ogre::Math::PI;
else
return (ud-1)*Ogre::Math::PI;
}
FFT::FFT()
: Noise("FFT", true)
, resolution(128)
, re(0)
, img(0)
, maximalValue(2)
, initialWaves(0)
, currentWaves(0)
, angularFrequencies(0)
, time(10)
, mGPUNormalMapManager(0)
, spectrum(0)
{
}
FFT::FFT(const Options &Options)
: Noise("FFT", true)
, mOptions(Options)
, resolution(Options.Resolution)
, re(0)
, img(0)
, maximalValue(2)
, initialWaves(0)
, currentWaves(0)
, angularFrequencies(0)
, time(10)
, mGPUNormalMapManager(0)
, spectrum(Options.Spectrum)
{
}
FFT::~FFT()
{
remove();
HydraxLOG(getName() + " destroyed.");
}
void FFT::create()
{
if (isCreated())
{
return;
}
_initNoise();
Noise::create();
}
void FFT::remove()
{
if (areGPUNormalMapResourcesCreated())
{
Noise::removeGPUNormalMapResources(mGPUNormalMapManager);
}
if (!isCreated())
{
return;
}
if (currentWaves)
{
delete [] currentWaves;
}
if (re)
{
delete [] re;
}
if (img)
{
delete [] img;
}
if (initialWaves)
{
delete [] initialWaves;
}
if (angularFrequencies)
{
delete [] angularFrequencies;
}
maximalValue = 2;
time = 10;
Noise::remove();
}
void FFT::setOptions(const Options &Options)
{
if (isCreated())
{
if (mOptions.Resolution != Options.Resolution ||
mOptions.Amplitude != Options.Amplitude ||
mOptions.KwPower != Options.KwPower ||
mOptions.PhysicalResolution != Options.PhysicalResolution ||
mOptions.WindDirection != Options.WindDirection ||
mOptions.Spectrum !=Options.Spectrum)
{
remove();
mOptions = Options;
resolution = Options.Resolution;
spectrum =Options.Spectrum;
create();
if (mGPUNormalMapManager)
{
createGPUNormalMapResources(mGPUNormalMapManager);
}
return;
}
else
{
if (isGPUNormalMapSupported() && areGPUNormalMapResourcesCreated())
{
mGPUNormalMapManager->getNormalMapMaterial()->
getTechnique(0)->getPass(0)->
getVertexProgramParameters()->
setNamedConstant("uScale", Options.Scale);
mGPUNormalMapManager->getNormalMapMaterial()->
getTechnique(0)->getPass(0)->
getFragmentProgramParameters()->
setNamedConstant("uStrength", Options.GPU_Strength);
mGPUNormalMapManager->getNormalMapMaterial()->
getTechnique(0)->getPass(0)->
getFragmentProgramParameters()->
setNamedConstant("uLODParameters", Options.GPU_LODParameters);
}
}
}
mOptions = Options;
resolution = Options.Resolution;
spectrum =Options.Spectrum;
}
bool FFT::createGPUNormalMapResources(GPUNormalMapManager *g)
{
if (!Noise::createGPUNormalMapResources(g))
{
return false;
}
mGPUNormalMapManager = g;
// Create our FFT texture
Ogre::TexturePtr mFFTTexture
= Ogre::TextureManager::getSingleton().
createManual("_Hydrax_FFT_Noise",
HYDRAX_RESOURCE_GROUP,
Ogre::TEX_TYPE_2D,
resolution, resolution, 0,
Ogre::PF_L16,
Ogre::TU_DYNAMIC_WRITE_ONLY);
mGPUNormalMapManager->addTexture(mFFTTexture);
// Create our normal map generator material
MaterialManager *mMaterialManager = g->getHydrax()->getMaterialManager();
Ogre::String VertexProgramData, FragmentProgramData;
Ogre::GpuProgramParametersSharedPtr VP_Parameters, FP_Parameters;
Ogre::String EntryPoints[2] = {"main_vp", "main_fp"};
Ogre::String GpuProgramsData[2]; Ogre::String GpuProgramNames[2];
// Vertex program
switch (g->getHydrax()->getShaderMode())
{
case MaterialManager::SM_HLSL: case MaterialManager::SM_CG:
{
VertexProgramData +=
Ogre::String(
"void main_vp(\n") +
// IN
"float4 iPosition : POSITION,\n" +
// OUT
"out float4 oPosition : POSITION,\n" +
"out float3 oPosition_ : TEXCOORD0,\n" +
"out float4 oWorldUV : TEXCOORD1,\n" +
"out float oScale : TEXCOORD2,\n" +
"out float3 oCameraPos : TEXCOORD3,\n" +
"out float3 oCameraToPixel : TEXCOORD4,\n" +
// UNIFORM
"uniform float4x4 uWorldViewProj,\n" +
"uniform float4x4 uWorld, \n" +
"uniform float3 uCameraPos,\n"+
"uniform float uScale)\n" +
"{\n" +
"oPosition = mul(uWorldViewProj, iPosition);\n" +
"oPosition_ = iPosition.xyz;\n" +
"float2 Scale = uScale*mul(uWorld, iPosition).xz*0.0078125;\n" +
"oWorldUV.xy = Scale;\n" +
"oWorldUV.zw = Scale*16;\n" +
"oScale = uScale;\n" +
"oCameraPos = uCameraPos,\n" +
"oCameraToPixel = iPosition - uCameraPos;\n"+
"}\n";
}
break;
case MaterialManager::SM_GLSL:
{}
break;
}
// Fragment program
switch (g->getHydrax()->getShaderMode())
{
case MaterialManager::SM_HLSL: case MaterialManager::SM_CG:
{
FragmentProgramData +=
Ogre::String(
"void main_fp(\n") +
// IN
"float3 iPosition : TEXCOORD0,\n" +
"float4 iWorldCoord : TEXCOORD1,\n" +
"float iScale : TEXCOORD2,\n" +
"float3 iCameraPos : TEXCOORD3,\n" +
"float3 iCameraToPixel : TEXCOORD4,\n" +
// OUT
"out float4 oColor : COLOR,\n" +
// UNIFORM
"uniform float uStrength,\n" +
"uniform float3 uLODParameters,\n" + // x: Initial derivation, y: Final derivation, z: Step
"uniform float3 uCameraPos,\n" +
"uniform sampler2D uFFT : register(s0))\n" +
"{\n" +
"float Distance = length(iCameraToPixel);\n" +
"float Attenuation = saturate(Distance/uLODParameters.z);\n" +
"uLODParameters.x += (uLODParameters.y-uLODParameters.x)*Attenuation;\n"+
"uLODParameters.x *= iScale;\n" +
"float AngleAttenuation = 1/abs(normalize(iCameraToPixel).y);\n"+
"uLODParameters.x *= AngleAttenuation;\n"+
"float2 dx = float2(uLODParameters.x*0.0078125, 0);\n" +
"float2 dy = float2(0, dx.x);\n" +
"float3 p_dx, m_dx, p_dy, m_dy;\n" +
"p_dx = float3(\n" +
// x+
"iPosition.x+uLODParameters.x,\n" +
// y+
"tex2D(uFFT, iWorldCoord.xy+dx).x,\n" +
// z
"iPosition.z);\n" +
"m_dx = float3(\n" +
// x-
"iPosition.x-uLODParameters.x,\n" +
// y-
"tex2D(uFFT, iWorldCoord.xy-dx).x, \n" +
// z
"iPosition.z);\n" +
"p_dy = float3(\n" +
// x
"iPosition.x,\n" +
// y+
"tex2D(uFFT, iWorldCoord.xy+dy).x,\n" +
// z+
"iPosition.z+uLODParameters.x);\n" +
"m_dy = float3(\n" +
// x
"iPosition.x,\n" +
// y-
"tex2D(uFFT, iWorldCoord.xy-dy).x,\n" +
// z-
"iPosition.z-uLODParameters.x);\n" +
"uStrength *= (1-Attenuation);\n" +
"p_dx.y *= uStrength; m_dx.y *= uStrength;\n" +
"p_dy.y *= uStrength; m_dy.y *= uStrength;\n" +
"float3 normal = normalize(cross(p_dx-m_dx, p_dy-m_dy));\n" +
"oColor = float4(saturate(1-(0.5+0.5*normal)),1);\n" +
"}\n";
}
break;
case MaterialManager::SM_GLSL:
{}
break;
}
// Build our material
Ogre::MaterialPtr &mNormalMapMaterial = mGPUNormalMapManager->getNormalMapMaterial();
mNormalMapMaterial = Ogre::MaterialManager::getSingleton().create("_Hydrax_GPU_Normal_Map_Material", HYDRAX_RESOURCE_GROUP);
Ogre::Pass *Technique0_Pass0 = mNormalMapMaterial->getTechnique(0)->getPass(0);
Technique0_Pass0->setLightingEnabled(false);
Technique0_Pass0->setCullingMode(Ogre::CULL_NONE);
Technique0_Pass0->setDepthWriteEnabled(true);
Technique0_Pass0->setDepthCheckEnabled(true);
GpuProgramsData[0] = VertexProgramData; GpuProgramsData[1] = FragmentProgramData;
GpuProgramNames[0] = "_Hydrax_GPU_Normal_Map_VP"; GpuProgramNames[1] = "_Hydrax_GPU_Normal_Map_FP";
mMaterialManager->fillGpuProgramsToPass(Technique0_Pass0, GpuProgramNames, g->getHydrax()->getShaderMode(), EntryPoints, GpuProgramsData);
VP_Parameters = Technique0_Pass0->getVertexProgramParameters();
VP_Parameters->setNamedAutoConstant("uWorldViewProj", Ogre::GpuProgramParameters::ACT_WORLDVIEWPROJ_MATRIX);
VP_Parameters->setNamedAutoConstant("uWorld", Ogre::GpuProgramParameters::ACT_WORLD_MATRIX);
VP_Parameters->setNamedAutoConstant("uCameraPos", Ogre::GpuProgramParameters::ACT_CAMERA_POSITION_OBJECT_SPACE);
VP_Parameters->setNamedConstant("uScale", mOptions.Scale);
FP_Parameters = Technique0_Pass0->getFragmentProgramParameters();
FP_Parameters->setNamedConstant("uStrength", mOptions.GPU_Strength);
FP_Parameters->setNamedConstant("uLODParameters", mOptions.GPU_LODParameters);
Technique0_Pass0->createTextureUnitState(mGPUNormalMapManager->getTexture(0)->getName(), 0)
->setTextureAddressingMode(Ogre::TextureUnitState::TAM_WRAP);
mNormalMapMaterial->load();
mGPUNormalMapManager->create();
return true;
}
void FFT::_updateGPUNormalMapResources()
{
unsigned short *Data;
Ogre::HardwarePixelBufferSharedPtr PixelBuffer
= mGPUNormalMapManager->getTexture(0)->getBuffer();
PixelBuffer->lock(Ogre::HardwareBuffer::HBL_DISCARD);
const Ogre::PixelBox& PixelBox = PixelBuffer->getCurrentLock();
Data = static_cast<unsigned short*>(PixelBox.data);
for (int u = 0; u < resolution*resolution; u++)
{
Data[u] = static_cast<int>(re[u]*65535);
}
PixelBuffer->unlock();
}
// void FFT::saveCfg(Ogre::String &Data)
// {
// Noise::saveCfg(Data);
// Data += CfgFileManager::_getCfgString("FFT_Resolution", mOptions.Resolution);
// Data += CfgFileManager::_getCfgString("FFT_PhysycalResolution", mOptions.PhysicalResolution);
// Data += CfgFileManager::_getCfgString("FFT_Scale", mOptions.Scale);
// Data += CfgFileManager::_getCfgString("FFT_WindDirection", mOptions.WindDirection);
// Data += CfgFileManager::_getCfgString("FFT_AnimationSpeed", mOptions.AnimationSpeed);
// Data += CfgFileManager::_getCfgString("FFT_KwPower", mOptions.KwPower);
// Data += CfgFileManager::_getCfgString("FFT_Amplitude", mOptions.Amplitude); Data += "\n";
// }
// bool FFT::loadCfg(Ogre::ConfigFile &CfgFile)
// {
// if (!Noise::loadCfg(CfgFile))
// {
// return false;
// }
// setOptions(
// Options(CfgFileManager::_getIntValue(CfgFile,"FFT_Resolution"),
// CfgFileManager::_getFloatValue(CfgFile,"FFT_PhysycalResolution"),
// CfgFileManager::_getFloatValue(CfgFile,"FFT_Scale"),
// CfgFileManager::_getVector2Value(CfgFile,"FFT_WindDirection"),
// CfgFileManager::_getFloatValue(CfgFile,"FFT_AnimationSpeed"),
// CfgFileManager::_getFloatValue(CfgFile,"FFT_KwPower"),
// CfgFileManager::_getFloatValue(CfgFile,"FFT_Amplitude")));
// return true;
// }
void FFT::update(const Ogre::Real &timeSinceLastFrame)
{
_calculeNoise(timeSinceLastFrame);
if (areGPUNormalMapResourcesCreated())
{
_updateGPUNormalMapResources();
}
}
void FFT::_initNoise()
{
initialWaves = new std::complex<float>[resolution*resolution];
currentWaves = new std::complex<float>[resolution*resolution];
angularFrequencies = new float[resolution*resolution];
re = new float[resolution*resolution];
img = new float[resolution*resolution];
Ogre::Vector2 wave = Ogre::Vector2(0,0);
std::complex<float>* pInitialWavesData = initialWaves;
float* pAngularFrequenciesData = angularFrequencies;
int u, v;
float temp;
// for (u = 0; u < resolution; u++)
// {
// wave.x = (-0.5f * resolution + u) * (2.0f* Ogre::Math::PI / mOptions.PhysicalResolution);
// for (v = 0; v < resolution; v++)
// {
// wave.y = (-0.5f * resolution + v) * (2.0f* Ogre::Math::PI / mOptions.PhysicalResolution);
// temp = Ogre::Math::Sqrt(0.5f * _getPhillipsSpectrum(wave, mOptions.WindDirection, mOptions.KwPower));
// *pInitialWavesData++ = std::complex<float>(_getGaussianRandomFloat() * temp, _getGaussianRandomFloat() * temp);
// temp=9.81f * wave.length();
// *pAngularFrequenciesData++ = Ogre::Math::Sqrt(temp);
// }
// }
float sitarr[128];
for (int sit=1; sit<128 ; sit++){
sitarr[sit]=(sitarr[sit-1]+Ogre::Math::TWO_PI/128);
}
for (u = 0; u < resolution; u++)
{
wave.x = (-0.5f * resolution + u) * (2.0f* Ogre::Math::PI / mOptions.Resolution);
for (v = 0; v < resolution; v++)
{
wave.y = (-0.5f * resolution + v) * (2.0f* Ogre::Math::PI / mOptions.Resolution);
switch (spectrum) {
case 1:
temp =10* Ogre::Math::Sqrt(0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2) * _getPhillipsSpectrum(wave, mOptions.WindDirection, mOptions.KwPower));
break;
case 2:
// temp =Ogre::Math::Sqrt(0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2)*_getP_MSpectrum(wave,mOptions.WindDirection,mOptions.Winds)*2*Ogre::Math::Pow(cos(sitarr[v]),2)/Ogre::Math::PI);
temp =10*Ogre::Math::Sqrt(0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2)*_getP_MSpectrum(wave,mOptions.WindDirection,70-mOptions.Winds));
// temp =Ogre::Math::Sqrt(0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2)*_getPM1sSpectrum(wave,mOptions.WindDirection,mOptions.KwPower,mOptions.Winds));
break;
case 3:
temp =10*Ogre::Math::Sqrt(0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2)*(_getJONSWAPSpectrum(wave,mOptions.WindDirection,70-mOptions.Winds,mOptions.Fetch)));
//temp =Ogre::Math::Sqrt(0.5f* _getJONSWAPSpectrum(wave,mOptions.WindDirection,mOptions.Winds,mOptions.Fetch));
break;
case 4:
temp =10*Ogre::Math::Sqrt( 0.5f* Ogre::Math::Pow(Ogre::Math::TWO_PI/resolution,2)*_getTMASpectrum(wave,mOptions.WindDirection,70-mOptions.Winds,mOptions.Fetch,mOptions.Depth));
break;
default:
temp = 0;
break;
}
//*pInitialWavesData++ = std::complex<float>(Ogre::Math::Cos(Ogre::Math::RangeRandom(0,Ogre::Math::TWO_PI)) * temp, Ogre::Math::Sin(Ogre::Math::RangeRandom(0,Ogre::Math::TWO_PI))* temp);
*pInitialWavesData++ = std::complex<float>(_getGaussianRandomFloat() * temp, _getGaussianRandomFloat() * temp);
// *pInitialWavesData++ = std::complex<float>( temp, temp);
// HydraxLOG(Ogre::StringConverter::toString(_getPhillipsSpectrum(wave,mOptions.WindDirection,mOptions.KwPower)));
// HydraxLOG(Ogre::StringConverter::toString(4.004f*Ogre::Math::Sqrt(_getJONSWAPSpectrum(wave,Ogre::Vector2(0,0),22.26f,367.6*1000))));
if(spectrum==4){
temp= 9.81f *wave.length()*tanh(wave.length()*mOptions.Depth);
*pAngularFrequenciesData++ = Ogre::Math::Sqrt(temp);
}
else{
temp= 9.81f * wave.length();
*pAngularFrequenciesData++ = Ogre::Math::Sqrt(temp);
}
}
}
_calculeNoise(0);
}
void FFT::_calculeNoise(const float &delta)
{
time += delta*mOptions.AnimationSpeed;
std::complex<float>* pData = currentWaves;
int u, v;
float wt,
coswt, sinwt,
realVal, imagVal;
for (u = 0; u < resolution; u++)
{
for (v = 0; v< resolution ; v++)
{
const std::complex<float>& positive_h0 = initialWaves[u * (resolution)+v];
const std::complex<float>& negative_h0 = initialWaves[(resolution-1 - u) * (resolution) + (resolution-1- v)];
wt = angularFrequencies[u * (resolution) + v] * time;
coswt = Ogre::Math::Cos(wt);
sinwt = Ogre::Math::Sin(wt);
realVal =
positive_h0.real() * coswt - positive_h0.imag() * sinwt + negative_h0.real() * coswt - (-negative_h0.imag()) * (-sinwt),
imagVal =
positive_h0.real() * sinwt + positive_h0.imag() * coswt + negative_h0.real() * (-sinwt) + (-negative_h0.imag()) * coswt;
*pData++ = std::complex<float>(realVal, imagVal);
}
}
_executeInverseFFT();
_normalizeFFTData(0);
}
const float FFT::_getGaussianRandomFloat() const
{
float x1, x2, w, y1;
do
{
x1 = 2.0f * uniform_deviate() - 1.0f;
x2 = 2.0f * uniform_deviate() - 1.0f;
w = x1 * x1 + x2 * x2;
} while ( w >= 1.0f );
w = Ogre::Math::Sqrt( (-2.0f * Ogre::Math::Log( w ) ) / w );
y1 = x1 * w;
return y1;
}
const float FFT::_getPhillipsSpectrum(const Ogre::Vector2& waveVector, const Ogre::Vector2& wind, const float& kwPower_) const
{
// Compute the length of the vector
float k = waveVector.length();
// To avoid division by 0
if (k < 0.0000001f)
{
return 0;
}
else
{
float windVelocity = mOptions.Winds,//wind.length(),
l = pow(windVelocity,2.0f)/9.81f,
dot=waveVector.dotProduct(wind);
return mOptions.Amplitude*
(Ogre::Math::Exp(-1 / pow(k * l,2)) / (Ogre::Math::Pow(k,2) *
Ogre::Math::Pow(k,2))) * Ogre::Math::Pow(-dot/ (k * windVelocity), kwPower_);
}
}
const float FFT::_getPM1sSpectrum(const Ogre::Vector2& waveVector, const Ogre::Vector2& wind, const float& kwPower_,const float& winds) const
{
// Compute the length of the vector
float k = waveVector.length();
// To avoid division by 0
if (k < 0.0000001f)
{
return 0;
}
else
{
float windVelocity = winds,//wind.length(),
l = pow(windVelocity,2.0f)/9.81f,
dot=waveVector.dotProduct(wind);
double wk = Ogre::Math::Sqrt(k*9.81f);
double wp=0.855f*9.81f/winds;
return mOptions.Amplitude*
(Ogre::Math::Exp(-1 / pow(k * l,2)) / (Ogre::Math::Pow(k,2) *
Ogre::Math::Pow(k,2)))* Ogre::Math::Exp(-1.2500f*Ogre::Math::Pow((wp/wk),4))* Ogre::Math::Pow(-dot/ (k * windVelocity), kwPower_);
}
}
const double FFT:: _getP_MSpectrum(const Ogre::Vector2& waveVector,const Ogre::Vector2& wind, const float& winds) const
{
double g = 9.81f;
double k = waveVector.length(); // ||K||
double Apm,alfpm,betpm,Jpm,D,Bs,e,wp,wk;
alfpm=0.0081f;
// Apm=alfpm/Ogre::Math::TWO_PI;
betpm=0.74f;
float dot=waveVector.dotProduct(wind);
// To avoid division by 0
if ((k < 0.0000001f)||(winds<0.00001f))
{
return 0;
}
else{
wk = Ogre::Math::Sqrt(k*g);
wp=0.855f*g/winds;
Bs=2.6100f*Ogre::Math::Pow((wk/wp),1.30f);
Jpm=0.0081f*(g*g/(Ogre::Math::Pow(wk,5)))*Ogre::Math::Exp(-1.2500f*Ogre::Math::Pow((wp/wk),4));
//( 1.00f/Ogre::Math::Pow(g*Ogre::Math::Pow(k,5),1.00f/2.00f))*
//Ogre::Math::Exp((-betpm)*(Ogre::Math::Pow(g,2))/((Ogre::Math::Pow(winds,4))*k*k)); HydraxLOG(Ogre::StringConverter::toString(Jpm));/*
// Ogre::Math::Pow(Ogre::Math::Cos((uniform_deviate()*Ogre::Math::TWO_PI-atan2(wind.y,wind.x))/2),2);*/
//D=(Bs*Ogre::Math::Pow((1.00f/cosh(Bs*-uniform_deviate()*Ogre::Math::TWO_PI)),2))/(2.00f*tanh(Bs*Ogre::Math::PI));
//D=2*Ogre::Math::Pow(cos(uniform_deviate()*Ogre::Math::TWO_PI),2)/Ogre::Math::PI;
//HydraxLOG(Ogre::StringConverter::toString(D));
return Jpm*(1.00f/(2.00f*k))*Ogre::Math::Sqrt(g/k)*Ogre::Math::Pow(-dot/ (k * winds), 6);
}
}
const double FFT:: _getJONSWAPSpectrum(const Ogre::Vector2& waveVector, const Ogre::Vector2& wind, const float& winds, const float &fetch) const
{
double g = 9.81f;
double gam = 3.30f;
double k = waveVector.length(); // ||K||
double Aj,alfj,Xtilde,wk,wp,Jk,sig,aj;
Xtilde=Ogre::Math::Pow(winds,2)/(g*fetch*1000.00f);
alfj=0.076f*Ogre::Math::Pow(Xtilde,0.22f);
Aj=alfj/Ogre::Math::TWO_PI;
float dot=waveVector.dotProduct(wind);
// To avoid division by 0
if (k < 0.0000001f)
{
return 0;
}
else
{
wk = sqrt(k*g); // deep water frequencies (empirical parameter)
wp = 22.00f*Ogre::Math::Pow(Ogre::Math::Pow(g,2)/(winds*fetch*1000.0f),(1.00f/3.00f));//wp = 22.0*(g/winds)*Ogre::Math::Pow(Xtilde,-0.33);
if (wk <= wp)
{
sig = 0.07f;
}
else
{
sig = 0.09f;
}
Jk=alfj*(g*g/(Ogre::Math::Pow(wk,5)))*Ogre::Math::Exp(-1.2500f*Ogre::Math::Pow((wp/wk),4))*
Ogre::Math::Pow(gam,Ogre::Math::Exp(-(Ogre::Math::Pow(wk-wp,2))/(2.0f*sig*sig*wp*wp)));
return Jk*(1.00f/(2.00f*k))*Ogre::Math::Sqrt(g/k)*Ogre::Math::Pow(-dot/ (k * winds), 6);
}
}
const double FFT:: _getTMASpectrum(const Ogre::Vector2& waveVector,const Ogre::Vector2& wind, const float& winds,const float& fetch,const float& depth) const
{ double g = 9.81f;
double k = waveVector.length(); // ||K||
double phi,wk,wp,Xtilde,alfj,wh,TMA,sig;
wk = Ogre::Math::Sqrt(k*g*tanh(k*depth)); // deep water frequencies (empirical parameter)
wh=wk*Ogre::Math::Sqrt(depth/g);
if(wh<=1)
phi=(1/2)*pow(wh,2);
else
phi=1-((1/2)*pow((2-wh),2));
Xtilde=g*fetch/Ogre::Math::Pow(winds,2);
alfj=0.076f*Ogre::Math::Pow(Xtilde,-0.22f);
float dot=waveVector.dotProduct(wind);
double gam = 3.3;
if (k < 0.0000001f)
{
return 0;
}
else
{
wp = 22.00f*Ogre::Math::Pow(Ogre::Math::Pow(g,2)/(winds*fetch*1000.0f),(1.00f/3.00f));//wp = 22.0*(g/winds)*Ogre::Math::Pow(Xtilde,-0.33);
if (wk <= wp)
{
sig = 0.07f;
}
else
{
sig = 0.09f;
}
TMA=alfj*(g*g/(Ogre::Math::Pow(wk,5)))*Ogre::Math::Exp(-1.2500f*Ogre::Math::Pow((wp/wk),4))*
Ogre::Math::Pow(3.30f,Ogre::Math::Exp(-(Ogre::Math::Pow(wk-wp,2))/(2.0f*sig*sig*wp*wp)))*
phi;
return TMA*(1.00f/(2.00f*k))*Ogre::Math::Sqrt(g/k)*Ogre::Math::Pow(-dot/ (k * winds), 6);}
}
void FFT::_executeInverseFFT()
{
int l2n = 0, p = 1;
while (p < resolution)
{
p *= 2; l2n++;
}
int l2m = 0; p = 1;
while (p < resolution)
{
p *= 2; l2m++;
}
resolution = 1<<l2m;
resolution = 1<<l2n;
int x, y, i;
for(x = 0; x <resolution; x++)
{
for(y = 0; y <resolution; y++)
{
re[resolution * x + y] = currentWaves[resolution * x + y].real();
img[resolution * x + y] = currentWaves[resolution * x + y].imag();
}
}
//Bit reversal of each row
int j, k;
for(y = 0; y < resolution; y++) //for each row
{
j = 0;
for(i = 0; i < resolution - 1; i++)
{
re[resolution * i + y] = currentWaves[resolution * j + y].real();
img[resolution * i + y] = currentWaves[resolution * j + y].imag();
k = resolution / 2;
while (k <= j)
{
j -= k;
k/= 2;
}
j += k;
}
}
//Bit reversal of each column
float tx = 0, ty = 0;
for(x = 0; x < resolution; x++) //for each column
{
j = 0;
for(i = 0; i < resolution - 1; i++)
{
if(i < j)
{
tx = re[resolution * x + i];
ty = img[resolution * x + i];
re[resolution * x + i] = re[resolution * x + j];
img[resolution * x + i] = img[resolution * x + j];
re[resolution * x + j] = tx;
img[resolution * x + j] = ty;
}
k = resolution / 2;
while (k <= j)
{
j -= k;
k/= 2;
}
j += k;
}
}
//Calculate the FFT of the columns
float ca, sa,
u1, u2,
t1, t2,
z;
int l1, l2,
l, i1;
for(x = 0; x < resolution; x++) //for each column
{
//This is the 1D FFT:
ca = -1.0;
sa = 0.0;
l1 = 1, l2 = 1;
for(l=0;l<l2n;l++)
{
l1 = l2;
l2 *= 2;
u1 = 1.0;
u2 = 0.0;
for(j = 0; j < l1; j++)
{
for(i = j; i < resolution; i += l2)
{
i1 = i + l1;
t1 = u1 * re[resolution * x + i1] - u2 * img[resolution * x + i1];
t2 = u1 * img[resolution * x + i1] + u2 * re[resolution * x + i1];
re[resolution * x + i1] = re[resolution * x + i] - t1;
img[resolution * x + i1] = img[resolution * x + i] - t2;
re[resolution * x + i] += t1;
img[resolution * x + i] += t2;
}
z = u1 * ca - u2 * sa;
u2 = u1 * sa + u2 * ca;
u1 = z;
}
sa = Ogre::Math::Sqrt((1.0f - ca) / 2.0f);
ca = Ogre::Math::Sqrt((1.0f+ca) / 2.0f);
}
}
//Calculate the FFT of the rows
for(y = 0; y < resolution; y++) //for each row
{
//This is the 1D FFT:
ca = -1.0;
sa = 0.0;
l1= 1, l2 = 1;
for(l = 0; l < l2m; l++)
{
l1 = l2;
l2 *= 2;
u1 = 1.0;
u2 = 0.0;
for(j = 0; j < l1; j++)
{
for(i = j; i < resolution; i += l2)
{
i1 = i + l1;
t1 = u1 * re[resolution * i1 + y] - u2 * img[resolution * i1 + y];
t2 = u1 * img[resolution * i1 + y] + u2 * re[resolution* i1 + y];
re[resolution * i1 + y] = re[resolution * i + y] - t1;
img[resolution * i1 + y] = img[resolution * i + y] - t2;
re[resolution * i + y] += t1;
img[resolution * i + y] += t2;
}
z = u1 * ca - u2 * sa;
u2 = u1 * sa + u2 * ca;
u1 = z;
}
sa = Ogre::Math::Sqrt((1.0f - ca) / 2.0f);
ca = Ogre::Math::Sqrt((1.0f+ca) / 2.0f);
}
}
for(x=0;x<resolution;x++)
{
for(y=0;y<resolution;y++)
{
if (((x+y) & 0x1)==1)
{
re[x*resolution+y]*=1;
}
else
{
re[x*resolution+y]*=-1;
}
}
}
}
void FFT::_normalizeFFTData(const float& scale)
{
float scaleCoef = 0.000001f;
int i;
// Perform automatic detection of maximum value
if (scale == 0.0f)
{
float min=re[0], max=re[0],
currentMax=maximalValue;;
for(i=1;i<resolution*resolution;i++)
{
if (min>re[i]) min=re[i];
if (max<re[i]) max=re[i];
}
min=Ogre::Math::Abs(min);
max=Ogre::Math::Abs(max);
currentMax = (min>max) ? min : max;
if (currentMax>maximalValue) maximalValue=currentMax;
scaleCoef += maximalValue;
}
else
{ // User defined scale
scaleCoef=scale;
}
// Scale all the value, and clamp to [0,1] range
int x, y;
for(x=0;x<resolution;x++)
{
for(y=0;y<resolution;y++)
{
i=x*resolution+y;
re[i]=(re[i]+scaleCoef)/(scaleCoef*2);
}
}
}
float FFT::getValue(const float &x, const float &y)
{
// Scale world coords
float xScale = x*mOptions.Scale,
yScale = y*mOptions.Scale;
// Convert coords from world-space to data-space
int xs = static_cast<int>(xScale)%resolution,
ys = static_cast<int>(yScale)%resolution;
// If data-space coords are negative, transform it to positive
if (x<0) xs += resolution-1;
if (y<0) ys += resolution-1;
// Determine x and y diff for linear interpolation
int xINT = (x>0) ? static_cast<int>(xScale) : static_cast<int>(xScale-1),
yINT = (y>0) ? static_cast<int>(yScale) : static_cast<int>(yScale-1);
// Calculate interpolation coeficients
float xDIFF = xScale-xINT,
yDIFF = yScale-yINT,
_xDIFF = 1-xDIFF,
_yDIFF = 1-yDIFF;
// To adjust the index if coords are out of range
int xxs = (xs==resolution-1) ? -1 : xs,
yys = (ys==resolution-1) ? -1 : ys;
// A B
//
//
// C D
float A = re[(ys*resolution+xs)],
B = re[(ys*resolution+xxs+1)],
C = re[((yys+1)*resolution+xs)],
D = re[((yys+1)*resolution+xxs+1)];
// Return the result of the linear interpolation
return (A*_xDIFF*_yDIFF +
B* xDIFF*_yDIFF +
C*_xDIFF* yDIFF +
D* xDIFF* yDIFF) // Range [-0.3, 0.3]
*0.6f-0.3f;
}
}}