void midpointStep(ParticleSystem& ps, float step) {
const auto& x0 = ps.state();
auto n = x0.size();
auto f0 = ps.evalF(x0);
auto xm = State(n), x1 = State(n);
for (auto i = 0u; i < n; ++i) {
xm[i] = x0[i] + (0.5f * step) * f0[i];
}
auto fm = ps.evalF(xm);
for (auto i = 0u; i < n; ++i) {
x1[i] = x0[i] + step * fm[i];
}
ps.set_state(x1);
}
void trapezoidStep(ParticleSystem& ps, float step) {
// YOUR CODE HERE (R3)
// Implement a trapezoid integrator.
const auto& x0 = ps.state();
auto n = x0.size();
auto f0 = ps.evalF(x0);
auto x1 = State(n);
auto xt = State(n);
for (unsigned i = 0; i < n; i++) {
x1[i] = x0[i] + step * f0[i];
}
auto ft = ps.evalF(x1);
for (unsigned i = 0; i < n; i++) {
xt[i] = x0[i] + (0.5f * step) * (f0[i] + ft[i]);
}
ps.set_state(xt);
}
void eulerStep(ParticleSystem& ps, float step) {
// YOUR CODE HERE (R1)
// Implement an Euler integrator.
const auto& x0 = ps.state();
auto n = x0.size();
auto f0 = ps.evalF(x0);
auto x1 = State(n);
for (unsigned i = 0; i < n; i++) {
x1[i] = x0[i] + step * f0[i];
}
ps.set_state(x1);
};
