void ConstructA_CG2(const mesh& Mesh, FullMatrix& A)
{
const int NumPhysElems = Mesh.get_NumPhysElems();
const int NumBndNodes = Mesh.get_SubNumBndNodes();
const int Asize = Mesh.get_SubNumPhysNodes();
assert_eq(Asize,A.get_NumRows());
assert_eq(Asize,A.get_NumCols());
dTensor1 A1(6);
dTensor1 A2(6);
dTensor1 A3(6);
dTensor1 A4(6);
dTensor1 A5(6);
dTensor1 A6(6);
A1.set(1, -oneninth );
A1.set(2, 4.0*oneninth );
A1.set(3, -oneninth );
A1.set(4, 4.0*oneninth );
A1.set(5, 4.0*oneninth );
A1.set(6, -oneninth );
A2.set(1, -onethird );
A2.set(2, 0.0 );
A2.set(3, onethird );
A2.set(4, -4.0*onethird );
A2.set(5, 4.0*onethird );
A2.set(6, 0.0 );
A3.set(1, -onethird );
A3.set(2, -4.0*onethird );
A3.set(3, 0.0 );
A3.set(4, 0.0 );
A3.set(5, 4.0*onethird );
A3.set(6, onethird );
A4.set(1, 4.0 );
A4.set(2, -4.0 );
A4.set(3, 0.0 );
A4.set(4, -4.0 );
A4.set(5, 4.0 );
A4.set(6, 0.0 );
A5.set(1, 2.0 );
A5.set(2, -4.0 );
A5.set(3, 2.0 );
A5.set(4, 0.0 );
A5.set(5, 0.0 );
A5.set(6, 0.0 );
A6.set(1, 2.0 );
A6.set(2, 0.0 );
A6.set(3, 0.0 );
A6.set(4, -4.0 );
A6.set(5, 0.0 );
A6.set(6, 2.0 );
dTensor2 spts(3,2);
spts.set(1,1, 1.0/3.0 );
spts.set(1,2, -1.0/6.0 );
spts.set(2,1, -1.0/6.0 );
spts.set(2,2, -1.0/6.0 );
spts.set(3,1, -1.0/6.0 );
spts.set(3,2, 1.0/3.0 );
dTensor1 wgts(3);
wgts.set(1, 1.0/6.0 );
wgts.set(2, 1.0/6.0 );
wgts.set(3, 1.0/6.0 );
// Loop over all elements in the mesh
for (int i=1; i<=NumPhysElems; i++)
{
// Information for element i
iTensor1 tt(6);
for (int k=1; k<=6; k++)
{ tt.set(k, Mesh.get_node_subs(i,k) ); }
// Evaluate gradients of the Lagrange polynomials on Gauss quadrature points
dTensor2 gpx(6,3);
dTensor2 gpy(6,3);
for (int m=1; m<=3; m++)
{
double xi = spts.get(m,1);
double eta = spts.get(m,2);
for (int k=1; k<=6; k++)
{
double gp_xi = A2.get(k) + 2.0*A5.get(k)*xi + A4.get(k)*eta;
double gp_eta = A3.get(k) + A4.get(k)*xi + 2.0*A6.get(k)*eta;
gpx.set(k,m, Mesh.get_jmat(i,1,1)*gp_xi
+ Mesh.get_jmat(i,1,2)*gp_eta );
gpy.set(k,m, Mesh.get_jmat(i,2,1)*gp_xi
+ Mesh.get_jmat(i,2,2)*gp_eta );
}
}
// Entries of the stiffness matrix A
double Area = Mesh.get_area_prim(i);
for (int j=1; j<=6; j++)
for (int k=1; k<=6; k++)
{
double tmp = A.get(tt.get(j),tt.get(k));
for (int m=1; m<=3; m++)
{
tmp = tmp + 2.0*Area*wgts.get(m)*(gpx.get(j,m)*gpx.get(k,m)+gpy.get(j,m)*gpy.get(k,m));
}
A.set(tt.get(j),tt.get(k), tmp );
}
}
// Replace boundary node equations by Dirichlet boundary condition enforcement
for (int i=1; i<=NumBndNodes; i++)
{
const int j=Mesh.get_sub_bnd_node(i);
for (int k=1; k<=A.get_NumCols(); k++)
{
A.set(j,k, 0.0 );
}
for (int k=1; k<=A.get_NumRows(); k++)
{
A.set(k,j, 0.0 );
}
A.set(j,j, 1.0 );
}
// Get sparse structure representation
A.Sparsify();
}
// This routine simply glues together many of the routines that are already
// written in the Poisson solver library
//
// phi( 1:SubNumPhysNodes ) is a scalar quantity.
//
// E1 ( 1:NumElems, 1:kmax2d ) is a vector quantity.
// E2 ( 1:NumElems, 1:kmax2d ) is a vector quantity.
//
// See also: ConvertEfieldOntoDGbasis
void ComputeElectricField( const double t, const mesh& Mesh, const dTensorBC5& q,
dTensor2& E1, dTensor2& E2)
{
//
const int mx = q.getsize(1); assert_eq(mx,dogParamsCart2.get_mx());
const int my = q.getsize(2); assert_eq(my,dogParamsCart2.get_my());
const int NumElems = q.getsize(3);
const int meqn = q.getsize(4);
const int kmax = q.getsize(5);
const int space_order = dogParams.get_space_order();
// unstructured parameters:
const int kmax2d = E2.getsize(2);
const int NumBndNodes = Mesh.get_NumBndNodes();
const int NumPhysNodes = Mesh.get_NumPhysNodes();
// Quick error check
if( !Mesh.get_is_submesh() )
{
printf("ERROR: mesh needs to have subfactor set to %d\n", space_order);
printf("Go to Unstructured mesh and remesh the problem\n");
exit(-1);
}
const int SubFactor = Mesh.get_SubFactor();
assert_eq( NumElems, Mesh.get_NumElems() );
// -- Step 1: Compute rho -- //
dTensor3 rho(NumElems, 1, kmax2d );
void ComputeDensity( const mesh& Mesh, const dTensorBC5& q, dTensor3& rho );
ComputeDensity( Mesh, q, rho );
// -- Step 2: Figure out how large phi needs to be
int SubNumPhysNodes = 0;
int SubNumBndNodes = 0;
switch( dogParams.get_space_order() )
{
case 1:
SubNumPhysNodes = NumPhysNodes;
SubNumBndNodes = NumBndNodes;
break;
case 2:
SubNumPhysNodes = Mesh.get_SubNumPhysNodes();
SubNumBndNodes = Mesh.get_SubNumBndNodes();
if(SubFactor!=2)
{
printf("\n");
printf(" Error: for space_order = %i, need SubFactor = %i\n",space_order,2);
printf(" SubFactor = %i\n",SubFactor);
printf("\n");
exit(1);
}
break;
case 3:
SubNumPhysNodes = Mesh.get_SubNumPhysNodes();
SubNumBndNodes = Mesh.get_SubNumBndNodes();
if(SubFactor!=3)
{
printf("\n");
printf(" Error: for space_order = %i, need SubFactor = %i\n",space_order,3);
printf(" SubFactor = %i\n",SubFactor);
printf("\n");
exit(1);
}
break;
default:
printf("\n");
printf(" ERROR in RunDogpack_unst.cpp: space_order value not supported.\n");
printf(" space_order = %i\n",space_order);
printf("\n");
exit(1);
}
// local storage:
dTensor1 rhs(SubNumPhysNodes);
dTensor1 phi(SubNumPhysNodes);
// Get Cholesky factorization matrix R
//
// TODO - this should be saved earlier in the code rather than reading
// from file every time we with to run a Poisson solve!
//
SparseCholesky R(SubNumPhysNodes);
string outputdir = dogParams.get_outputdir();
R.init(outputdir);
R.read(outputdir);
// Create right-hand side vector
void Rhs2D_unst(const int space_order,
const mesh& Mesh, const dTensor3& rhs_dg,
dTensor1& rhs);
Rhs2D_unst(space_order, Mesh, rho, rhs);
// Call Poisson solver
void PoissonSolver2D_unst(const int space_order,
const mesh& Mesh,
const SparseCholesky& R,
const dTensor1& rhs,
dTensor1& phi,
dTensor2& E1,
dTensor2& E2);
PoissonSolver2D_unst(space_order, Mesh, R, rhs, phi, E1, E2);
// Compare errors with the exact Electric field:
//
void L2Project_Unst(
const double time,
const dTensor2* vel_vec,
const int istart,
const int iend,
const int QuadOrder,
const int BasisOrder_qin,
const int BasisOrder_auxin,
const int BasisOrder_fout,
const mesh& Mesh,
const dTensor3* qin,
const dTensor3* auxin,
dTensor3* fout,
void (*Func)(const double t, const dTensor2* vel_vec, const dTensor2&,const dTensor2&,
const dTensor2&,dTensor2&));
const int sorder = dogParams.get_space_order();
dTensor3 qtmp (NumElems, 2, kmax2d ); qtmp.setall(0.);
dTensor3 auxtmp (NumElems, 0, kmax2d );
dTensor3 ExactE (NumElems, 2, kmax2d );
L2Project_Unst( t, NULL, 1, NumElems,
sorder, sorder, sorder, sorder, Mesh,
&qtmp, &auxtmp, &ExactE,
&ExactElectricField );
// Compute errors on these two:
//
double err = 0.;
for( int n=1; n <= NumElems; n++ )
for( int k=1; k <= kmax2d; k++ )
{
err += Mesh.get_area_prim(n)*pow( ExactE.get(n,1,k) - E1.get(n,k), 2 );
err += Mesh.get_area_prim(n)*pow( ExactE.get(n,2,k) - E2.get(n,k), 2 );
}
printf("error = %2.15e\n", err );
}
// Modified version of the all purpose routine L2Project specifically written
// for projecting the "time-averaged" flux function onto the basis function.
//
// This routine also returns the coefficients of the Lax Wendroff Flux
// Function when expanded with legendre basis functions, and therefore the
// basis expansions produced by this routine can be used for all of the
// Riemann solves.
//
// ---------------------------------------------------------------------
// Inputs should have the following sizes:
// TODO - document the inputs here
// ---------------------------------------------------------------------
void L2ProjectLxW_Unst( const int mterms,
const double alpha, const double beta_dt, const double charlie_dt,
const int istart, const int iend, // Start-stop indices
const int QuadOrder,
const int BasisOrder_qin,
const int BasisOrder_auxin,
const int BasisOrder_fout,
const mesh& Mesh,
const dTensor3* qin, const dTensor3* auxin, // state vector
dTensor3* F, dTensor3* G, // time-averaged Flux function
void FluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& Aux, dTensor3& flux),
void DFluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& aux, dTensor4& Dflux),
void D2FluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& aux, dTensor5& D2flux) )
{
if( fabs( alpha ) < 1e-14 && fabs( beta_dt ) < 1e-14 && fabs( charlie_dt ) < 1e-14 )
{
F->setall(0.);
G->setall(0.);
return;
}
// starting and ending indices
const int NumElems = Mesh.get_NumElems();
assert_ge(istart,1);
assert_le(iend,NumElems);
// qin variable
assert_eq(NumElems,qin->getsize(1));
const int meqn = qin->getsize(2);
const int kmax_qin = qin->getsize(3);
assert_eq(kmax_qin,(BasisOrder_qin*(BasisOrder_qin+1))/2);
// auxin variable
assert_eq(NumElems,auxin->getsize(1));
const int maux = auxin->getsize(2);
const int kmax_auxin = auxin->getsize(3);
assert_eq(kmax_auxin,(BasisOrder_auxin*(BasisOrder_auxin+1))/2);
// fout variables
assert_eq(NumElems, F->getsize(1));
const int mcomps_out = F->getsize(2);
const int kmax_fout = F->getsize(3);
assert_eq(kmax_fout, (BasisOrder_fout*(BasisOrder_fout+1))/2 );
// number of quadrature points
assert_ge(QuadOrder, 1);
assert_le(QuadOrder, 5);
// Number of quadrature points
int mpoints;
switch( QuadOrder )
{
case 1:
mpoints = 1;
break;
case 2:
mpoints = 3;
break;
case 3:
mpoints = 6;
break;
case 4:
mpoints = 12;
break;
case 5:
mpoints = 16;
break;
}
const int kmax = iMax(iMax(kmax_qin, kmax_auxin), kmax_fout);
dTensor2 phi(mpoints, kmax); // Legendre basis (orthogonal)
dTensor2 spts(mpoints, 2); // List of quadrature points
dTensor1 wgts(mpoints); // List of quadrature weights
setQuadPoints_Unst( QuadOrder, wgts, spts );
// ---------------------------------------------------------------------- //
// Evaluate the basis functions at each point
SetLegendreAtPoints_Unst(spts, phi);
// ---------------------------------------------------------------------- //
// ---------------------------------------------------------------------- //
// First-order derivatives
dTensor2 phi_xi (mpoints, kmax );
dTensor2 phi_eta(mpoints, kmax );
SetLegendreGrad_Unst( spts, phi_xi, phi_eta );
// ---------------------------------------------------------------------- //
// ---------------------------------------------------------------------- //
// Second-order derivatives
dTensor2 phi_xi2 (mpoints, kmax );
dTensor2 phi_xieta(mpoints, kmax );
dTensor2 phi_eta2 (mpoints, kmax );
LegendreDiff2_Unst(spts, &phi_xi2, &phi_xieta, &phi_eta2 );
// ---------------------------------------------------------------------- //
// ------------------------------------------------------------- //
// Loop over every grid cell indexed by user supplied parameters //
// described by istart...iend, jstart...jend //
// ------------------------------------------------------------- //
#pragma omp parallel for
for (int i=istart; i<=iend; i++)
{
// These need to be defined locally. Each mesh element carries its
// own change of basis matrix, so these need to be recomputed for
// each element. The canonical derivatives, phi_xi, and phi_eta can
// be computed and shared for each element.
// First-order derivatives
dTensor2 phi_x(mpoints, kmax_fout); // x-derivative of Legendre basis (orthogonal)
dTensor2 phi_y(mpoints, kmax_fout); // y-derivative of Legendre basis (orthogonal)
// Second-order derivatives
dTensor2 phi_xx(mpoints, kmax_fout); // xx-derivative of Legendre basis (orthogonal)
dTensor2 phi_xy(mpoints, kmax_fout); // xy-derivative of Legendre basis (orthogonal)
dTensor2 phi_yy(mpoints, kmax_fout); // yy-derivative of Legendre basis (orthogonal)
//find center of current cell
const int i1 = Mesh.get_tnode(i,1);
const int i2 = Mesh.get_tnode(i,2);
const int i3 = Mesh.get_tnode(i,3);
// Corners:
const double x1 = Mesh.get_node(i1,1);
const double y1 = Mesh.get_node(i1,2);
const double x2 = Mesh.get_node(i2,1);
const double y2 = Mesh.get_node(i2,2);
const double x3 = Mesh.get_node(i3,1);
const double y3 = Mesh.get_node(i3,2);
// Center of current cell:
const double xc = (x1+x2+x3)/3.0;
const double yc = (y1+y2+y3)/3.0;
// Variables that need to be written to, and therefore are
// created for each thread
dTensor2 xpts (mpoints, 2);
dTensor2 qvals (mpoints, meqn);
dTensor2 auxvals(mpoints, maux);
// local storage for Flux function its Jacobian, and the Hessian:
dTensor3 fvals(mpoints, meqn, 2); // flux function (vector)
dTensor4 A(mpoints, meqn, meqn, 2); // Jacobian of flux
dTensor5 H(mpoints, meqn, meqn, meqn, 2); // Hessian of flux
// Compute q, aux and fvals at each Gaussian Quadrature point
// for this current cell indexed by (i,j)
// Save results into dTensor2 qvals, auxvals and fvals.
for (int m=1; m<= mpoints; m++)
{
// convert phi_xi and phi_eta derivatives
// to phi_x and phi_y derivatives through Jacobian
//
// Note that:
//
// pd_x = J11 pd_xi + J12 pd_eta and
// pd_y = J21 pd_xi + J22 pd_eta.
//
// Squaring these operators yields the second derivatives.
for (int k=1; k<=kmax_fout; k++)
{
phi_x.set(m,k, Mesh.get_jmat(i,1,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,1,2)*phi_eta.get(m,k) );
phi_y.set(m,k, Mesh.get_jmat(i,2,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,2,2)*phi_eta.get(m,k) );
phi_xx.set(m,k, Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,1,1)*phi_xi2.get(m,k)
+ Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,1,2)*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,1,2)*phi_eta2.get(m,k)
);
phi_xy.set(m,k, Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,2,1)*phi_xi2.get(m,k)
+(Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,2,1)
+ Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,2,2))*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,2,2)*phi_eta2.get(m,k)
);
phi_yy.set(m,k, Mesh.get_jmat(i,2,1)*Mesh.get_jmat(i,2,1)*phi_xi2.get(m,k)
+ Mesh.get_jmat(i,2,1)*Mesh.get_jmat(i,2,2)*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,2,2)*Mesh.get_jmat(i,2,2)*phi_eta2.get(m,k)
);
}
// point on the unit triangle
const double s = spts.get(m,1);
const double t = spts.get(m,2);
// point on the physical triangle
xpts.set(m,1, xc + (x2-x1)*s + (x3-x1)*t );
xpts.set(m,2, yc + (y2-y1)*s + (y3-y1)*t );
// Solution values (q) at each grid point
for (int me=1; me<=meqn; me++)
{
qvals.set(m,me, 0.0 );
for (int k=1; k<=kmax_qin; k++)
{
qvals.set(m,me, qvals.get(m,me)
+ phi.get(m,k) * qin->get(i,me,k) );
}
}
// Auxiliary values (aux) at each grid point
for (int ma=1; ma<=maux; ma++)
{
auxvals.set(m,ma, 0.0 );
for (int k=1; k<=kmax_auxin; k++)
{
auxvals.set(m,ma, auxvals.get(m,ma)
+ phi.get(m,k) * auxin->get(i,ma,k) );
}
}
}
// ----------------------------------------------------------------- //
//
// Part I:
//
// Project the flux function onto the basis
// functions. This is the term of order O( 1 ) in the
// "time-averaged" Taylor expansion of f and g.
//
// ----------------------------------------------------------------- //
// Call user-supplied function to set fvals
FluxFunc(xpts, qvals, auxvals, fvals);
// Evaluate integral on current cell (project onto Legendre basis)
// using Gaussian Quadrature for the integration
//
// TODO - do we want to optimize this by looking into using transposes,
// as has been done in the 2d/cart code? (5/14/2014) -DS
for (int me=1; me<=mcomps_out; me++)
for (int k=1; k<=kmax; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int mp=1; mp <= mpoints; mp++)
{
tmp1 += wgts.get(mp)*fvals.get(mp, me, 1)*phi.get(mp, k);
tmp2 += wgts.get(mp)*fvals.get(mp, me, 2)*phi.get(mp, k);
}
F->set(i, me, k, 2.0*tmp1 );
G->set(i, me, k, 2.0*tmp2 );
}
// ----------------------------------------------------------------- //
//
// Part II:
//
// Project the derivative of the flux function onto the basis
// functions. This is the term of order O( \dt ) in the
// "time-averaged" Taylor expansion of f and g.
//
// ----------------------------------------------------------------- //
// ----------------------------------------------------------------- //
// Compute pointwise values for fx+gy:
//
// We can't multiply fvals of f, and g,
// by alpha, otherwise we compute the wrong derivative here!
//
dTensor2 fx_plus_gy( mpoints, meqn ); fx_plus_gy.setall(0.);
for( int mp=1; mp <= mpoints; mp++ )
for( int me=1; me <= meqn; me++ )
{
double tmp = 0.;
for( int k=2; k <= kmax; k++ )
{
tmp += F->get( i, me, k ) * phi_x.get( mp, k );
tmp += G->get( i, me, k ) * phi_y.get( mp, k );
}
fx_plus_gy.set( mp, me, tmp );
}
// Call user-supplied Jacobian to set f'(q) and g'(q):
DFluxFunc( xpts, qvals, auxvals, A );
// place-holders for point values of
// f'(q)( fx + gy ) and g'(q)( fx + gy ):
dTensor2 dt_times_fdot( mpoints, meqn );
dTensor2 dt_times_gdot( mpoints, meqn );
// Compute point values for f'(q) * (fx+gy) and g'(q) * (fx+gy):
for( int mp=1; mp <= mpoints; mp++ )
for( int m1=1; m1 <= meqn; m1++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += A.get(mp, m1, m2, 1 ) * fx_plus_gy.get(mp, m2);
tmp2 += A.get(mp, m1, m2, 2 ) * fx_plus_gy.get(mp, m2);
}
dt_times_fdot.set( mp, m1, -beta_dt*tmp1 );
dt_times_gdot.set( mp, m1, -beta_dt*tmp2 );
}
// --- Third-order terms --- //
//
// These are the terms that are O( \dt^2 ) in the "time-averaged"
// flux function.
dTensor2 f_tt( mpoints, meqn ); f_tt.setall(0.);
dTensor2 g_tt( mpoints, meqn ); g_tt.setall(0.);
if( mterms > 2 )
{
// Construct the Hessian at each (quadrature) point
D2FluxFunc( xpts, qvals, auxvals, H );
// Second-order derivative terms
dTensor2 qx_vals (mpoints, meqn); qx_vals.setall(0.);
dTensor2 qy_vals (mpoints, meqn); qy_vals.setall(0.);
dTensor2 fxx_vals(mpoints, meqn); fxx_vals.setall(0.);
dTensor2 gxx_vals(mpoints, meqn); gxx_vals.setall(0.);
dTensor2 fxy_vals(mpoints, meqn); fxy_vals.setall(0.);
dTensor2 gxy_vals(mpoints, meqn); gxy_vals.setall(0.);
dTensor2 fyy_vals(mpoints, meqn); fyy_vals.setall(0.);
dTensor2 gyy_vals(mpoints, meqn); gyy_vals.setall(0.);
for( int m=1; m <= mpoints; m++ )
for( int me=1; me <= meqn; me++ )
{
// Can start at k=1, because derivative of a constant is
// zero.
double tmp_qx = 0.;
double tmp_qy = 0.;
for( int k=2; k <= kmax; k++ )
{
tmp_qx += phi_x.get(m,k) * qin->get(i,me,k);
tmp_qy += phi_y.get(m,k) * qin->get(i,me,k);
}
qx_vals.set(m,me, tmp_qx );
qy_vals.set(m,me, tmp_qy );
// First non-zero terms start at third-order.
for( int k=4; k <= kmax; k++ )
{
fxx_vals.set(m,me, fxx_vals.get(m,me) + phi_xx.get(m,k)*F->get(i,me,k) );
gxx_vals.set(m,me, gxx_vals.get(m,me) + phi_xx.get(m,k)*G->get(i,me,k) );
fxy_vals.set(m,me, fxy_vals.get(m,me) + phi_xy.get(m,k)*F->get(i,me,k) );
gxy_vals.set(m,me, gxy_vals.get(m,me) + phi_xy.get(m,k)*G->get(i,me,k) );
fyy_vals.set(m,me, fyy_vals.get(m,me) + phi_yy.get(m,k)*F->get(i,me,k) );
gyy_vals.set(m,me, gyy_vals.get(m,me) + phi_yy.get(m,k)*G->get(i,me,k) );
}
}
// ----------------------------------- //
// Part I: Compute (f_x + g_y)_{,t}
// ----------------------------------- //
// Compute terms that get multiplied by \pd2{ f }{ q } and \pd2{ g }{ q }.
dTensor2 fx_plus_gy_t( mpoints, meqn );
for( int m = 1; m <= mpoints; m++ )
for( int me = 1; me <= meqn; me++ )
{
double tmp = 0.;
// Terms that get multiplied by the Hessian:
for( int m1=1; m1 <= meqn; m1++ )
for( int m2=1; m2 <= meqn; m2++ )
{
tmp += H.get(m,me,m1,m2,1)*qx_vals.get(m,m1)*fx_plus_gy.get(m,m2);
tmp += H.get(m,me,m1,m2,2)*qy_vals.get(m,m1)*fx_plus_gy.get(m,m2);
}
// Terms that get multiplied by f'(q) and g'(q):
for( int m1=1; m1 <= meqn; m1++ )
{
tmp += A.get(m,me,m1,1)*( fxx_vals.get(m,m1)+gxy_vals.get(m,m1) );
tmp += A.get(m,me,m1,2)*( fxy_vals.get(m,m1)+gyy_vals.get(m,m1) );
}
fx_plus_gy_t.set( m, me, tmp );
}
// ----------------------------------- //
// Part II: Compute
// f'(q) * fx_plus_gy_t and
// g'(q) * fx_plus_gy_t
// ----------------------------------- //
// Add in the third term that gets multiplied by A:
for( int m=1; m <= mpoints; m++ )
for( int m1=1; m1 <= meqn; m1++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += A.get(m,m1,m2,1)*fx_plus_gy_t.get(m,m2);
tmp2 += A.get(m,m1,m2,2)*fx_plus_gy_t.get(m,m2);
}
f_tt.set( m, m1, tmp1 );
g_tt.set( m, m1, tmp2 );
}
// ----------------------------------------------- //
// Part III: Add in contributions from
// f''(q) * (fx_plus_gy, fx_plus_gy ) and
// g''(q) * (fx_plus_gy, fx_plus_gy ).
// ----------------------------------------------- //
for( int m =1; m <= mpoints; m++ )
for( int me =1; me <= meqn; me++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
// Terms that get multiplied by the Hessian:
for( int m1=1; m1 <= meqn; m1++ )
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += H.get(m,me,m1,m2,1)*fx_plus_gy.get(m,m1)*fx_plus_gy.get(m,m2);
tmp2 += H.get(m,me,m1,m2,2)*fx_plus_gy.get(m,m1)*fx_plus_gy.get(m,m2);
}
f_tt.set( m, me, f_tt.get(m,me) + tmp1 );
g_tt.set( m, me, g_tt.get(m,me) + tmp2 );
}
} // End of computing "third"-order terms
// ---------------------------------------------------------- //
//
// Construct basis coefficients (integrate_on_current_cell)
//
// ---------------------------------------------------------- //
for (int me=1; me<=mcomps_out; me++)
for (int k=1; k<=kmax; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int mp=1; mp<=mpoints; mp++)
{
tmp1 += wgts.get(mp)*phi.get(mp,k)*(
dt_times_fdot.get(mp, me) + charlie_dt*f_tt.get(mp, me) );
tmp2 += wgts.get(mp)*phi.get(mp,k)*(
dt_times_gdot.get(mp, me) + charlie_dt*g_tt.get(mp, me) );
}
F->set(i,me,k, F->get(i,me,k) + 2.0*tmp1 );
G->set(i,me,k, G->get(i,me,k) + 2.0*tmp2 );
}
}
}
// This is the positivity preserving limiter proposed in
// "Maximum-Principle-Satisfying and Positivity-Preserving
// High Order Discontinuous Galerkin Schemes
// for Conservation Laws on Triangular Meshes", Zhang, Xia and Shu
// J. Sci. Comput. (2012).
//
// THIS METHOD ASSUMES THAT EVERY COMPONENT OF CONSERVED VARIABLES SHOULD STAY
// POSITIVE.
//
// In order to implement this for a different scheme, one should rewrite, or
// redefine what components should remain positiive. This will require
// reworking the control flow logic for how time step lengths are chosen.
void ApplyPosLimiter_Unst(const mesh& Mesh, const dTensor3& aux, dTensor3& q)
{
const int NumElems = Mesh.get_NumElems();
const int NumPhysElems = Mesh.get_NumPhysElems();
const int NumEdges = Mesh.get_NumEdges();
const int meqn = q.getsize(2);
const int kmax = q.getsize(3);
const int maux = aux.getsize(2);
const int space_order = dogParams.get_space_order();
// Do nothing in the case of piecewise constants
if( space_order == 1 )
{ return; }
// ------------------------------------------------ //
// number of points where we want to check solution //
// ------------------------------------------------ //
const int space_order_sq = space_order*space_order;
const int mpts_vec[] = {0, 3*space_order_sq, 18, 3*space_order_sq, 3*space_order_sq }; // TODO - FILL IN 2ND-ORDER CASE
const int mpoints = mpts_vec[space_order-1];
// ---------------------------------------------------------- //
// sample basis at all points where we want to check solution //
// ---------------------------------------------------------- //
dTensor2 spts(mpoints, 2);
void SetPositivePoints_Unst(const int& space_order, dTensor2& spts);
SetPositivePoints_Unst(space_order, spts);
void SamplePhiAtPositivePoints_Unst(const int& space_order,
const dTensor2& spts, dTensor2& phi);
dTensor2 phi(mpoints, kmax);
SamplePhiAtPositivePoints_Unst(space_order, spts, phi);
// -------------------------------------------------------------- //
// q_limited = Q1 + \theta ( q(xi,eta) - Q1 ) //
// where theta = min(1, |Q1| / |Q1-m|; m = min_{i} q(xi_i, eta_i) //
// -------------------------------------------------------------- //
#pragma omp parallel for
for(int i=1; i <= NumPhysElems; i++)
for(int me=1; me <= meqn; me++)
{
double m = 0.0;
for(int mp=1; mp <= mpoints; mp++)
{
// evaluate q at spts(mp) //
double qnow = 0.0;
for( int k=1; k <= kmax; k++ )
{
qnow += q.get(i,me,k) * phi.get(mp,k);
}
m = Min(m, qnow);
}
double theta = 0.0;
double Q1 = q.get(i,me,1); assert_ge( Q1, -1e-13 );
if( fabs( Q1 - m ) < 1.0e-14 ){ theta = 1.0; }
else{ theta = Min( 1.0, fabs( Q1 / (Q1 - m) ) ); }
// limit q //
for( int k=2; k <= kmax; k++ )
{
q.set(i,me,k, q.get(i,me,k) * theta );
}
}
}
// GAUSS-LOBATTO QUADRATURE ALONG EDGE
void SetEdgeDataGL_Unst(const mesh& Mesh,
int NumQuadPoints,
int NumBasisOrder,
edge_data_Unst* EdgeData)
{
// Quick error check
if (NumQuadPoints<2 || NumQuadPoints>6 || NumBasisOrder<1 || NumBasisOrder>5)
{
printf(" \n");
printf(" Error in SetEdgeData_Unst.cpp \n");
printf(" NumQuadPoints must be 2,3,4,5, or 6.\n");
printf(" NumBasisOrder must be 1,2,3,4, or 5.\n");
printf(" NumQuadPoints = %i\n",NumQuadPoints);
printf(" NumBasisOrder = %i\n",NumBasisOrder);
printf("\n");
exit(1);
}
// ---------------------------------
// Set quadrature weights and points
// ---------------------------------
switch( NumQuadPoints )
{
case 2:
EdgeData->GL_wgts1d->set(1, 1.0 );
EdgeData->GL_wgts1d->set(2, 1.0 );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, -1.0 );
break;
case 3:
EdgeData->GL_wgts1d->set(1, onethird );
EdgeData->GL_wgts1d->set(2, 4.0*onethird );
EdgeData->GL_wgts1d->set(3, onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, 0.0 );
EdgeData->GL_xpts1d->set(3, -1.0 );
break;
case 4:
EdgeData->GL_wgts1d->set(1, 0.5*onethird );
EdgeData->GL_wgts1d->set(2, 2.5*onethird );
EdgeData->GL_wgts1d->set(3, 2.5*onethird );
EdgeData->GL_wgts1d->set(4, 0.5*onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, osq5 );
EdgeData->GL_xpts1d->set(3, -osq5 );
EdgeData->GL_xpts1d->set(4, -1.0 );
break;
case 5:
EdgeData->GL_wgts1d->set(1, 0.1 );
EdgeData->GL_wgts1d->set(2, 49.0/90.0 );
EdgeData->GL_wgts1d->set(3, 32.0/45.0 );
EdgeData->GL_wgts1d->set(4, 49.0/90.0 );
EdgeData->GL_wgts1d->set(5, 0.1 );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, sq3*osq7 );
EdgeData->GL_xpts1d->set(3, 0.0 );
EdgeData->GL_xpts1d->set(4, -sq3*osq7 );
EdgeData->GL_xpts1d->set(5, -1.0 );
break;
case 6:
EdgeData->GL_wgts1d->set(1, 0.2*onethird );
EdgeData->GL_wgts1d->set(2, (1.4 - 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(3, (1.4 + 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(4, (1.4 + 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(5, (1.4 - 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(6, 0.2*onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, (1/21.0)*sqrt(147.0+42.0*sq7) );
EdgeData->GL_xpts1d->set(3, (1/21.0)*sqrt(147.0-42.0*sq7) );
EdgeData->GL_xpts1d->set(4, -(1/21.0)*sqrt(147.0-42.0*sq7) );
EdgeData->GL_xpts1d->set(5, -(1/21.0)*sqrt(147.0+42.0*sq7) );
EdgeData->GL_xpts1d->set(6, -1.0 );
break;
}
// ---------------------------------
// Legendre basis functions on the
// left and right of each edge
// ---------------------------------
const int NumEdges = Mesh.get_NumEdges();
const int NumBasisComps = (NumBasisOrder*(NumBasisOrder+1))/2;
dTensor1 xp1(3);
dTensor1 yp1(3);
dTensor1 xp2(3);
dTensor1 yp2(3);
dTensor1 xy1(2);
dTensor1 xy2(2);
dTensor1 mu1(NumBasisComps);
dTensor1 mu2(NumBasisComps);
for (int i=1; i<=NumEdges; i++)
{
// Get edge information
const double x1 = Mesh.get_edge(i,1);
const double y1 = Mesh.get_edge(i,2);
const double x2 = Mesh.get_edge(i,3);
const double y2 = Mesh.get_edge(i,4);
const int e1 = Mesh.get_eelem(i,1);
const int e2 = Mesh.get_eelem(i,2);
// Get element information about
// the two elements that meet at
// the current edge
const double Area1 = Mesh.get_area_prim(e1);
const double Area2 = Mesh.get_area_prim(e2);
for (int k=1; k<=3; k++)
{
xp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),1) );
yp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),2) );
xp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),1) );
yp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),2) );
}
const double xc1 = (xp1.get(1) + xp1.get(2) + xp1.get(3))/3.0;
const double yc1 = (yp1.get(1) + yp1.get(2) + yp1.get(3))/3.0;
const double xc2 = (xp2.get(1) + xp2.get(2) + xp2.get(3))/3.0;
const double yc2 = (yp2.get(1) + yp2.get(2) + yp2.get(3))/3.0;
// quadrature points on the edge
for (int m=1; m<=NumQuadPoints; m++)
{
// Take integration point s (in [-1,1])
// and map to physical domain
const double s = EdgeData->GL_xpts1d->get(m);
const double x = x1 + 0.5*(s+1.0)*(x2-x1);
const double y = y1 + 0.5*(s+1.0)*(y2-y1);
// Take physical point (x,y)
// and map into the coordinates
// of the two triangles that are
// adjacent to the current edge
xy1.set(1, ((yp1.get(3)-yp1.get(1))*(x-xc1)
+ (xp1.get(1)-xp1.get(3))*(y-yc1))/(2.0*Area1) );
xy1.set(2, ((yp1.get(1)-yp1.get(2))*(x-xc1)
+ (xp1.get(2)-xp1.get(1))*(y-yc1))/(2.0*Area1) );
xy2.set(1, ((yp2.get(3)-yp2.get(1))*(x-xc2)
+ (xp2.get(1)-xp2.get(3))*(y-yc2))/(2.0*Area2) );
xy2.set(2, ((yp2.get(1)-yp2.get(2))*(x-xc2)
+ (xp2.get(2)-xp2.get(1))*(y-yc2))/(2.0*Area2) );
// Evaluate monomials at locations xy1
double xi = xy1.get(1);
double xi2 = xi*xi;
double xi3 = xi*xi2;
double xi4 = xi*xi3;
double eta = xy1.get(2);
double eta2 = eta*eta;
double eta3 = eta*eta2;
double eta4 = eta*eta3;
switch( NumBasisOrder )
{
case 5: // fifth order
mu1.set(15, eta4 );
mu1.set(14, xi4 );
mu1.set(13, xi2*eta2 );
mu1.set(12, eta3*xi );
mu1.set(11, xi3*eta );
case 4: // fourth order
mu1.set(10, eta3 );
mu1.set(9, xi3 );
mu1.set(8, xi*eta2 );
mu1.set(7, eta*xi2 );
case 3: // third order
mu1.set(6, eta2 );
mu1.set(5, xi2 );
mu1.set(4, xi*eta );
case 2: // second order
mu1.set(3, eta );
mu1.set(2, xi );
case 1: // first order
mu1.set(1, 1.0 );
break;
}
// Evaluate monomials at locations xy2
xi = xy2.get(1);
xi2 = xi*xi;
xi3 = xi*xi2;
xi4 = xi*xi3;
eta = xy2.get(2);
eta2 = eta*eta;
eta3 = eta*eta2;
eta4 = eta*eta3;
switch( NumBasisOrder )
{
case 5: // fifth order
mu2.set(15, eta4 );
mu2.set(14, xi4 );
mu2.set(13, xi2*eta2 );
mu2.set(12, eta3*xi );
mu2.set(11, xi3*eta );
case 4: // fourth order
mu2.set(10, eta3 );
mu2.set(9, xi3 );
mu2.set(8, xi*eta2 );
mu2.set(7, eta*xi2 );
case 3: // third order
mu2.set(6, eta2 );
mu2.set(5, xi2 );
mu2.set(4, xi*eta );
case 2: // second order
mu2.set(3, eta );
mu2.set(2, xi );
case 1: // first order
mu2.set(1, 1.0 );
break;
}
// Finally, convert monomials to Legendre Polys
// on the two adjacent triangle
for (int k=1; k<=NumBasisComps; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int j=1; j<=k; j++)
{
tmp1 = tmp1 + Mmat[k-1][j-1]*mu1.get(j);
tmp2 = tmp2 + Mmat[k-1][j-1]*mu2.get(j);
}
EdgeData->GL_phi_left->set(i,m,k, tmp1 );
EdgeData->GL_phi_right->set(i,m,k, tmp2 );
}
}
}
}
void ConstructL_Unst(
const double t,
const dTensor2* vel_vec,
const mesh& Mesh,
const edge_data_Unst& EdgeData,
dTensor3& aux, // SetBndValues_Unst modifies ghost cells
dTensor3& q, // SetBndValues_Unst modifies ghost cells
dTensor3& Lstar,
dTensor1& smax)
{
const int NumElems = Mesh.get_NumElems();
const int NumPhysElems = Mesh.get_NumPhysElems();
const int NumEdges = Mesh.get_NumEdges();
const int meqn = q.getsize(2);
const int kmax = q.getsize(3);
const int maux = aux.getsize(2);
const int space_order = dogParams.get_space_order();
dTensor3 EdgeFluxIntegral(NumElems,meqn,kmax);
dTensor3 ElemFluxIntegral(NumElems,meqn,kmax);
dTensor3 Psi(NumElems,meqn,kmax);
// ---------------------------------------------------------
// Boundary Conditions
SetBndValues_Unst(Mesh,&q,&aux);
// Positivity limiter
void ApplyPosLimiter_Unst(const mesh& Mesh, const dTensor3& aux, dTensor3& q);
if( dogParams.using_moment_limiter() )
{ ApplyPosLimiter_Unst(Mesh, aux, q); }
// ---------------------------------------------------------
// ---------------------------------------------------------
// Part I: compute flux integral on element edges
// ---------------------------------------------------------
// Loop over all interior edges and solve Riemann problems
// dTensor1 nvec(2);
// Loop over all interior edges
EdgeFluxIntegral.setall(0.);
ElemFluxIntegral.setall(0.);
// Loop over all interior edges
#pragma omp parallel for
for (int i=1; i<=NumEdges; i++)
{
// Edge coordinates
double x1 = Mesh.get_edge(i,1);
double y1 = Mesh.get_edge(i,2);
double x2 = Mesh.get_edge(i,3);
double y2 = Mesh.get_edge(i,4);
// Elements on either side of edge
int ileft = Mesh.get_eelem(i,1);
int iright = Mesh.get_eelem(i,2);
double Areal = Mesh.get_area_prim(ileft);
double Arear = Mesh.get_area_prim(iright);
// Scaled normal to edge
dTensor1 nhat(2);
nhat.set(1, (y2-y1) );
nhat.set(2, (x1-x2) );
// Variables to store flux integrals along edge
dTensor2 Fr_tmp(meqn,dogParams.get_space_order());
dTensor2 Fl_tmp(meqn,dogParams.get_space_order());
// Loop over number of quadrature points along each edge
for (int ell=1; ell<=dogParams.get_space_order(); ell++)
{
dTensor1 Ql(meqn),Qr(meqn);
dTensor1 Auxl(maux),Auxr(maux);
// Riemann data - q
for (int m=1; m<=meqn; m++)
{
Ql.set(m, 0.0 );
Qr.set(m, 0.0 );
for (int k=1; k<=kmax; k++)
{
Ql.set(m, Ql.get(m) + EdgeData.phi_left->get(i,ell,k)
*q.get(ileft, m,k) );
Qr.set(m, Qr.get(m) + EdgeData.phi_right->get(i,ell,k)
*q.get(iright,m,k) );
}
}
// Riemann data - aux
for (int m=1; m<=maux; m++)
{
Auxl.set(m, 0.0 );
Auxr.set(m, 0.0 );
for (int k=1; k<=kmax; k++)
{
Auxl.set(m, Auxl.get(m) + EdgeData.phi_left->get(i,ell,k)
*aux.get(ileft, m,k) );
Auxr.set(m, Auxr.get(m) + EdgeData.phi_right->get(i,ell,k)
*aux.get(iright,m,k) );
}
}
// Solve Riemann problem
dTensor1 xedge(2);
double s = EdgeData.xpts1d->get(ell);
xedge.set(1, x1 + 0.5*(s+1.0)*(x2-x1) );
xedge.set(2, y1 + 0.5*(s+1.0)*(y2-y1) );
dTensor1 Fl(meqn),Fr(meqn);
const double smax_edge = RiemannSolve(vel_vec, nhat, xedge, Ql, Qr, Auxl, Auxr, Fl, Fr);
smax.set(i, Max(smax_edge,smax.get(i)) );
// Construct fluxes
for (int m=1; m<=meqn; m++)
{
Fr_tmp.set(m,ell, Fr.get(m) );
Fl_tmp.set(m,ell, Fl.get(m) );
}
}
// Add edge integral to line integral around the full element
for (int m=1; m<=meqn; m++)
for (int k=1; k<=kmax; k++)
{
double Fl_sum = 0.0;
double Fr_sum = 0.0;
for (int ell=1; ell<=dogParams.get_space_order(); ell++)
{
Fl_sum = Fl_sum + 0.5*EdgeData.wgts1d->get(ell)
*EdgeData.phi_left->get(i,ell,k) *Fl_tmp.get(m,ell);
Fr_sum = Fr_sum + 0.5*EdgeData.wgts1d->get(ell)
*EdgeData.phi_right->get(i,ell,k)*Fr_tmp.get(m,ell);
}
EdgeFluxIntegral.set(ileft, m,k, EdgeFluxIntegral.get(ileft, m,k) + Fl_sum/Areal );
EdgeFluxIntegral.set(iright,m,k, EdgeFluxIntegral.get(iright,m,k) - Fr_sum/Arear );
}
}
// ---------------------------------------------------------
// ---------------------------------------------------------
// Part II: compute intra-element contributions
// ---------------------------------------------------------
L2ProjectGrad_Unst(vel_vec, 1,NumPhysElems,
space_order,space_order,space_order,space_order,
Mesh,&q,&aux,&ElemFluxIntegral,&FluxFunc);
// ---------------------------------------------------------
// ---------------------------------------------------------
// Part III: compute source term
// ---------------------------------------------------------
if ( dogParams.get_source_term()>0 )
{
// Set source term on computational grid
// Set values and apply L2-projection
L2Project_Unst(t, vel_vec, 1,NumPhysElems,
space_order,space_order,space_order,space_order,
Mesh,&q,&aux,&Psi,&SourceTermFunc);
}
// ---------------------------------------------------------
// ---------------------------------------------------------
// Part IV: construct Lstar
// ---------------------------------------------------------
if (dogParams.get_source_term()==0) // Without Source Term
{
#pragma omp parallel for
for (int i=1; i<=NumPhysElems; i++)
for (int m=1; m<=meqn; m++)
for (int k=1; k<=kmax; k++)
{
double tmp = ElemFluxIntegral.get(i,m,k) - EdgeFluxIntegral.get(i,m,k);
Lstar.set(i,m,k, tmp );
}
}
else // With Source Term
{
#pragma omp parallel for
for (int i=1; i<=NumPhysElems; i++)
for (int m=1; m<=meqn; m++)
for (int k=1; k<=kmax; k++)
{
double tmp = ElemFluxIntegral.get(i,m,k)
- EdgeFluxIntegral.get(i,m,k)
+ Psi.get(i,m,k);
Lstar.set(i,m,k, tmp );
}
}
// ---------------------------------------------------------
// ---------------------------------------------------------
// Part V: add extra contributions to Lstar
// ---------------------------------------------------------
// Call LstarExtra
LstarExtra_Unst(Mesh,&q,&aux,&Lstar);
// ---------------------------------------------------------
}
int setupTextureShader(GLuint &textureID, const mesh& object)
{
glewInit();
if(!glewIsSupported("GL_VERSION_2_0 GL_ARB_multitexture GL_EXT_framebuffer_object"))
{
fprintf(stderr, "Required OpenGL extensions missing\n");
return -1;
}
/* create texture */
glGenTextures(1, &textureID);
glActiveTexture(GL_TEXTURE0);
glBindTexture(GL_TEXTURE_2D, textureID);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
/* load texture file */
int width, height, components;
unsigned char *data = stbi_load("static/uv_color_map.png",
&width, &height, &components, 0);
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB,
GL_UNSIGNED_BYTE, data);
stbi_image_free(data);
/* load UV data from mesh */
std::vector<glm::vec2> texture_uvs = object.getTextureUVs();
unsigned int uvsize = texture_uvs.size();
unsigned int uvmem = 2*uvsize*sizeof(GLfloat);
GLfloat *uv_buffer_data = (GLfloat *)malloc(uvmem);
for(int i = 0; i < uvsize; i++)
{
uv_buffer_data[2*i] = texture_uvs.at(i).x;
uv_buffer_data[2*i + 1] = texture_uvs.at(i).y;
}
/* pass data to shader */
GLuint uvBuffer;
glGenBuffers(1, &uvBuffer);
glBindBuffer(GL_ARRAY_BUFFER, uvBuffer);
glBufferData(GL_ARRAY_BUFFER, uvmem, uv_buffer_data, GL_STATIC_DRAW);
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 2, GL_FLOAT, GL_FALSE, 0, (void*)0);
free(uv_buffer_data);
glm::ivec2 shaders = loadShaders("src/texture.vert", "src/texture.frag");
GLuint vertexShader = shaders.x;
GLuint fragmentShader = shaders.y;
/* create and link program */
int program = glCreateProgram();
glBindAttribLocation(program, 0, "vertexUV");
int loc = glGetUniformLocation(program, "texsampler");
glUniform1i(loc, 0);
glAttachShader(program, vertexShader);
glAttachShader(program, fragmentShader);
glLinkProgram(program);
GLint pstatus;
glGetProgramiv(program, GL_LINK_STATUS, &pstatus);
if(pstatus != GL_TRUE)
{
char log[2048];
int len;
glGetProgramInfoLog(program, 2048, (GLsizei*)&len, log);
fprintf(stderr, "%s", log);
glDeleteProgram(program);
return -1;
}
return program;
}
void draw_3D_graphics()
{
static double Px, Py, Pz, roll, pitch, yaw, yawA;
static int initilization = 0;
int i;
static double x = 0.0, dx; // x - an offset for the object
static double y = 0.0, dy; // z offset controlled by keyboard input
static double t; // clock time from t0
static double t0; // initial clock time
static double T, fps, tp, dt, t_sim;
// Declare and load x-file mesh object for later
static mesh m1("car.x");
// Change scale
m1.Scale = 0.5;
// Set initial position for mesh (proper positioning)
m1.Roll_0 = 1.645;
// Initialize everything here (once)
if (!initilization)
{
t0 = high_resolution_time();
tp = 0.0;
t_sim = 0.0;
initilization = 1;
}
// set_view();
set_2D_view(50.0, 50.0);
// draw the axes (red = x, y = green, z = blue)
draw_XYZ(5.0); // set axes of 5 m length
t = high_resolution_time() - t0; // Time since start, as measured by a clock
T = t - tp; // calculate dt frame or period
fps = 1 / T;
tp = t; // save previous time for later
dt = 0.001; // we can pick a small dt for performance / stability
while (t_sim < t) {
sim_step(dt, x, y, yaw);
t_sim += dt;
}
// Use keyboard input to change yaw (upper keys for alphabet)
if (KEY('Z')) yaw -= 0.001;
if (KEY('X')) yaw += 0.001;
// connect graphics parameters with the simulation output
// NOTE: BECAUSE OF THE WAY WE'VE WRITTEN OUR SIMULATION CODE, THE SIGN NOTATION IS DIFFERENT!
// HENCE THE NEED FOR YAWA = YAW ACTUAL
Px = x;
Py = y;
Pz = 0;
roll = 0;
pitch = 0;
yawA = -yaw;
// draw x-file / mesh object
m1.draw(Px, Py, Pz, yawA, pitch, roll);
}
bool load_content()
{
// Construct geometry object
geometry geom;
geom.set_type(GL_QUADS);
// Create quad data
// Positions
vector<vec3> positions
{
vec3(-1.0f, 1.0f, 0.0f),
vec3(-1.0f, -1.0f, 0.0f),
vec3(1.0f, -1.0f, 0.0f),
vec3(1.0f, 1.0f, 0.0f)
};
// Texture coordinates
vector<vec2> tex_coords
{
vec2(0.0f, 1.0f),
vec2(0.0f, 0.0f),
vec2(1.0f, 0.0f),
vec2(1.0f, 1.0f)
};
// Add to the geometry
geom.add_buffer(positions, BUFFER_INDEXES::POSITION_BUFFER);
geom.add_buffer(tex_coords, BUFFER_INDEXES::TEXTURE_COORDS_0);
// Create mesh object
m = mesh(geom);
// Scale geometry
m.get_transform().scale = vec3(10.0f, 10.0f, 10.0f);
// ********************
// Load in blend shader
// ********************
eff.add_shader("..\\resources\\shaders\\blend.vert", GL_VERTEX_SHADER); // vertex
eff.add_shader("..\\resources\\shaders\\blend.frag", GL_FRAGMENT_SHADER); // fragment
// ************
// Build effect
// ************
eff.build();
// **********************
// Load main two textures
// **********************
texs[0] = new texture("..\\resources\\textures\\grass.png", false, false);
texs[1] = new texture("..\\resources\\textures\\stonygrass.jpg", false, false);
// **************
// Load blend map
// **************
blend_map = texture("..\\resources\\textures\\blend_map.jpg", false, false);
// Set camera properties
cam.set_position(vec3(0.0f, 0.0f, 30.0f));
cam.set_target(vec3(0.0f, 0.0f, 0.0f));
auto aspect = static_cast<float>(renderer::get_screen_width()) / static_cast<float>(renderer::get_screen_height());
cam.set_projection(quarter_pi<float>(), aspect, 2.414f, 1000.0f);
return true;
}
