//-----------------------------------------------------------------------------
// Name: D3DXQuaternionAxisToAxis
// Desc: Axis to axis quaternion
// Takes two points on unit sphere an angle THETA apart, returns
// quaternion that represents a rotation around cross product by theta.
//-----------------------------------------------------------------------------
inline D3DXQUATERNION* WINAPI D3DXQuaternionAxisToAxis
( D3DXQUATERNION *pOut, const D3DXVECTOR3 *pvFrom, const D3DXVECTOR3 *pvTo)
{
D3DXVECTOR3 vA, vB;
D3DXVec3Normalize(&vA, pvFrom);
D3DXVec3Normalize(&vB, pvTo);
D3DXVECTOR3 vHalf(vA + vB);
D3DXVec3Normalize(&vHalf, &vHalf);
return D3DXQuaternionUnitAxisToUnitAxis2(pOut, &vA, &vHalf);
}
// `创建模型`
int CGutParticle::BuildMesh(Matrix4x4 &camera_matrix)
{
Vector4 vHalf(0.5f);
for ( int i=0; i<m_iNumParticles; i++ )
{
int base = i*4;
float size = m_pParticleArray[i].m_fSize;
Vector4 vPos = m_pParticleArray[i].m_vPosition;
Vector4 vVec0 = camera_matrix[0] * size;
Vector4 vVec1 = camera_matrix[1] * size;
Vector4 v0 = vPos - vVec0 * vHalf + vVec1 * vHalf;
Vector4 v1 = v0 - vVec1;
Vector4 v2 = v0 + vVec0;
Vector4 v3 = v0 + vVec0 - vVec1;
sParticleVertex *p = m_pVertexArray + base;
float fFadeout = m_pParticleArray[i].m_fLife * 5;
if ( fFadeout > 1.0f ) fFadeout = 1.0f;
int intensity = fFadeout * 255;
unsigned int color = intensity<<24 | intensity<<16 | intensity<<8 | intensity;
p[0].m_Color = color;
p[1].m_Color = color;
p[2].m_Color = color;
p[3].m_Color = color;
v0.StoreXYZ(p[0].m_fPosition);
v1.StoreXYZ(p[1].m_fPosition);
v2.StoreXYZ(p[2].m_fPosition);
v3.StoreXYZ(p[3].m_fPosition);
}
return m_iNumParticles * 4;
}
void GrayScott::step()
{
// update step
++currStep_;
// u and v at the half step
std::vector<double> uHalf(Ntot_);
std::vector<double> vHalf(Ntot_);
// right hand sides for u and for v
std::vector<double> uRhs(N_);
std::vector<double> vRhs(N_);
double uCoeff = Du_*dt_/(2.*dx_*dx_);
double vCoeff = Dv_*dt_/(2.*dx_*dx_);
/****************** DIFFUSION (ADI) ***************************************/
// perform the first half-step
// loop over all rows
// j=0
for (int i=0; i<N_; ++i) {
uRhs[i] = U(i,0) + uCoeff * (U(i,1) - U(i,0));
vRhs[i] = V(i,0) + vCoeff * (V(i,1) - V(i,0));
}
TriDiagMatrixSolver::solve(N_, matU1_, uRhs, &UHALF(0,0), 1);
TriDiagMatrixSolver::solve(N_, matV1_, vRhs, &VHALF(0,0), 1);
// inner grid points
for (int j=1; j<N_-1; ++j) {
// create right-hand side of the systems
for (int i=0; i<N_; ++i) {
uRhs[i] = U(i,j) + uCoeff * (U(i,j+1) - 2.*U(i,j) + U(i,j-1));
vRhs[i] = V(i,j) + vCoeff * (V(i,j+1) - 2.*V(i,j) + V(i,j-1));
}
TriDiagMatrixSolver::solve(N_, matU1_, uRhs, &UHALF(0,j), 1);
TriDiagMatrixSolver::solve(N_, matV1_, vRhs, &VHALF(0,j), 1);
}
// j=N_-1
for (int i=0; i<N_; ++i) {
uRhs[i] = U(i,N_-1) + uCoeff * (- U(i,N_-1) + U(i,N_-2));
vRhs[i] = V(i,N_-1) + vCoeff * (- V(i,N_-1) + V(i,N_-2));
}
TriDiagMatrixSolver::solve(N_, matU1_, uRhs, &UHALF(0,N_-1), 1);
TriDiagMatrixSolver::solve(N_, matV1_, vRhs, &VHALF(0,N_-1), 1);
// perform the second half-step
// loop over all columns
// i=0
for (int j=0; j<N_; ++j) {
uRhs[j] = UHALF(0,j) + uCoeff * (UHALF(1,j) - UHALF(0,j));
vRhs[j] = VHALF(0,j) + vCoeff * (VHALF(1,j) - VHALF(0,j));
}
TriDiagMatrixSolver::solve(N_, matU2_, uRhs, &U(0,0), N_);
TriDiagMatrixSolver::solve(N_, matV2_, vRhs, &V(0,0), N_);
// inner grid points
for (int i=1; i<N_-1; ++i) {
// create right-hand side of the systems
for (int j=0; j<N_; ++j) {
uRhs[j] = UHALF(i,j) + uCoeff * (UHALF(i+1,j) - 2.*UHALF(i,j) + UHALF(i-1,j));
vRhs[j] = VHALF(i,j) + vCoeff * (VHALF(i+1,j) - 2.*VHALF(i,j) + VHALF(i-1,j));
}
TriDiagMatrixSolver::solve(N_, matU2_, uRhs, &U(i,0), N_);
TriDiagMatrixSolver::solve(N_, matV2_, vRhs, &V(i,0), N_);
}
// i=N_-1
for (int j=0; j<N_; ++j) {
uRhs[j] = UHALF(N_-1,j) + uCoeff * (- UHALF(N_-1,j) + UHALF(N_-2,j));
vRhs[j] = VHALF(N_-1,j) + vCoeff * (- VHALF(N_-1,j) + VHALF(N_-2,j));
}
TriDiagMatrixSolver::solve(N_, matU2_, uRhs, &U(N_-1,0), N_);
TriDiagMatrixSolver::solve(N_, matV2_, vRhs, &V(N_-1,0), N_);
/****************** REACTION **********************************************/
double tmp;
for (int i=0; i<N_; ++i) {
for (int j=0; j<N_; ++j) {
tmp = U(i,j);
U(i,j) += dt_ * ( -U(i,j)*V(i,j)*V(i,j) + F_*(1.-U(i,j)) );
V(i,j) += dt_ * ( tmp*V(i,j)*V(i,j) - (F_+k_)*V(i,j) );
}
}
}
