void
v_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
a = SBasis(f.us, Linear());
b = SBasis(f.us, Linear());
for (unsigned u=0; u<f.us; u++){
a[u] = Linear(f.index(deg,u)[0], f.index(deg,u)[1]);
b[u] = Linear(f.index(deg,u)[2], f.index(deg,u)[3]);
}
}
//see a sb2d as an sb of u with coef in sbasis of v.
void
u_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
a = SBasis(f.vs, Linear());
b = SBasis(f.vs, Linear());
for (unsigned v=0; v<f.vs; v++){
a[v] = Linear(f.index(deg,v)[0], f.index(deg,v)[2]);
b[v] = Linear(f.index(deg,v)[1], f.index(deg,v)[3]);
}
}
void
v_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
a = SBasis();
b = SBasis();
for (unsigned u=0; u<f.us; u++){
a.push_back(Linear(f.index(deg,u)[0], f.index(deg,u)[1]));
b.push_back(Linear(f.index(deg,u)[2], f.index(deg,u)[3]));
}
}
//see a sb2d as an sb of u with coef in sbasis of v.
void
u_coef(SBasis2d f, unsigned deg, SBasis &a, SBasis &b) {
a = SBasis();
b = SBasis();
for (unsigned v=0; v<f.vs; v++){
a.push_back(Linear(f.index(deg,v)[0], f.index(deg,v)[2]));
b.push_back(Linear(f.index(deg,v)[1], f.index(deg,v)[3]));
}
}
SBasis2d partial_derivative(SBasis2d const &f, int dim) {
SBasis2d result;
for(unsigned i = 0; i < f.size(); i++) {
result.push_back(Linear2d(0,0,0,0));
}
result.us = f.us;
result.vs = f.vs;
for(unsigned i = 0; i < f.us; i++) {
for(unsigned j = 0; j < f.vs; j++) {
Linear2d lin = f.index(i,j);
Linear2d dlin(lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3-dim]-lin[2*(1-dim)], lin[3]-lin[2-dim]);
result[i+j*result.us] += dlin;
unsigned di = dim?j:i;
if (di>=1){
float motpi = dim?-1:1;
Linear2d ds_lin_low( lin[0], -motpi*lin[1], motpi*lin[2], -lin[3] );
result[(i+dim-1)+(j-dim)*result.us] += di*ds_lin_low;
Linear2d ds_lin_hi( lin[1+dim]-lin[0], lin[1+2*dim]-lin[dim], lin[3]-lin[2-dim], lin[3-dim]-lin[2-dim] );
result[i+j*result.us] += di*ds_lin_hi;
}
}
}
return result;
}
SBasis extract_u(SBasis2d const &a, double u) {
SBasis sb(a.vs, Linear());
double s = u*(1-u);
for(unsigned vi = 0; vi < a.vs; vi++) {
double sk = 1;
Linear bo(0,0);
for(unsigned ui = 0; ui < a.us; ui++) {
bo += (extract_u(a.index(ui, vi), u))*sk;
sk *= s;
}
sb[vi] = bo;
}
return sb;
}
SBasis extract_v(SBasis2d const &a, double v) {
SBasis sb(a.us, Linear());
double s = v*(1-v);
for(unsigned ui = 0; ui < a.us; ui++) {
double sk = 1;
Linear bo(0,0);
for(unsigned vi = 0; vi < a.vs; vi++) {
bo += (extract_v(a.index(ui, vi), v))*sk;
sk *= s;
}
sb[ui] = bo;
}
return sb;
}