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#include <list>
#include <eigen3/Eigen/Dense>
#include <eigen3/Eigen/src/Core/CwiseNullaryOp.h>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
template <int D> using Vector = Eigen::Matrix<int, D, 1>;
template <int D> using Matrix = Eigen::Matrix<int, D, D>;
using Rng = randutils::random_generator<pcg32>;
int iPow(int x, unsigned p) {
if (p == 0)
return 1;
if (p == 1)
return x;
int tmp = iPow(x, p / 2);
if (p % 2 == 0) {
return tmp * tmp;
} else {
return x * tmp * tmp;
}
}
unsigned mod(signed a, unsigned b) { return ((a < 0) ? (a + (1 - a / (signed)b) * b) : a) % b; }
template <int D, typename Derived> Vector<D> mod(const Eigen::MatrixBase<Derived>& v, unsigned b) {
Vector<D> u;
for (unsigned i = 0; i < D; i++) {
u(i) = mod(v(i), b);
}
return u;
}
template <int D> void one_sequences(std::list<std::array<double, D>>& sequences, unsigned level) {
if (level > 0) {
unsigned new_level = level - 1;
unsigned old_length = sequences.size();
for (std::array<double, D>& sequence : sequences) {
std::array<double, D> new_sequence = sequence;
new_sequence[new_level] = -1;
sequences.push_front(new_sequence);
}
one_sequences<D>(sequences, new_level);
}
}
template <unsigned D> std::vector<Matrix<D>> generateTorusMatrices() {
std::vector<Matrix<D>> mats;
std::array<double, D> ini_sequence;
ini_sequence.fill(1);
std::list<std::array<double, D>> sequences;
sequences.push_back(ini_sequence);
one_sequences<D>(sequences, D);
sequences.pop_back(); // don't want the identity matrix!
for (std::array<double, D> sequence : sequences) {
Matrix<D> m;
for (unsigned i = 0; i < D; i++) {
for (unsigned j = 0; j < D; j++) {
if (i == j) {
m(i, j) = sequence[i];
} else {
m(i, j) = 0;
}
}
}
mats.push_back(m);
}
for (unsigned i = 0; i < D; i++) {
for (unsigned j = 0; j < D; j++) {
if (i != j) {
Matrix<D> m;
for (unsigned k = 0; k < D; k++) {
for (unsigned l = 0; l < D; l++) {
if ((k == i && l == j) || (k == j && l == i)) {
if (i < j) {
m(k, l) = 1;
} else {
m(k, l) = -1;
}
} else if (k == l && (k != i && k != j)) {
m(k, l) = 1;
} else {
m(k, l) = 0;
}
}
}
mats.push_back(m);
}
}
}
return mats;
}
template <unsigned D> class Transformation {
public:
unsigned L;
Matrix<D> m;
Vector<D> v;
Transformation(unsigned L) : L(L) {
m.setIdentity();
v.setZero();
}
Transformation(unsigned L, const Matrix<D>& m, const Vector<D>& v) : L(L), m(m), v(v) {}
Transformation(unsigned L, const std::vector<Matrix<D>>& ms, Rng& r) : m(r.pick(ms)), L(L) {
for (unsigned i = 0; i < D; i++) {
v[i] = r.uniform((unsigned)0, L - 1);
}
v = v - m * v;
}
Vector<D> apply(const Vector<D>& x) const { return mod<D>(v + m * x, L); }
Transformation<D> apply(const Transformation<D>& t) const {
Transformation<D> tNew(L);
tNew.m = m * t.m;
tNew.v = apply(t.v);
return tNew;
}
Transformation<D> inverse() const {
return Transformation<D>(L, m.transpose(), -m.transpose() * v);
}
};
template <typename T> concept State = requires(T v) {
{ v.empty() } -> std::same_as<bool>;
{v.remove()};
};
template <unsigned D, State S> class HalfEdge;
template <unsigned D, State S> class Vertex {
public:
Vector<D> position;
Vector<D> initialPosition;
S state;
std::vector<HalfEdge<D, S>> adjacentEdges;
bool marked;
bool empty() const { return state.empty(); }
};
template <unsigned D, State S> class HalfEdge {
public:
Vertex<D, S>& neighbor;
Vector<D> Δx;
HalfEdge(Vertex<D, S>& n, const Vector<D>& d) : neighbor(n), Δx(d) {}
};
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