working on memoization

.gitmodules

@@ -4,3 +4,6 @@
 [submodule "vendor/glm"]
 	path = vendor/glm
 	url = https://github.com/g-truc/glm.git
+[submodule "vendor/toddcox"]
+	path = vendor/toddcox
+	url = https://github.com/JCRaymond/toddcox-faster.git

CMakeLists.txt

@@ -3,10 +3,11 @@ project(toddcox-faster)
 
 set(CMAKE_CXX_STANDARD 17)
 
+add_subdirectory(vendor/toddcox)
 add_subdirectory(vendor/glad)
 add_subdirectory(vendor/glfw)
 add_subdirectory(vendor/glm)
 
-add_subdirectory(tc)
 add_subdirectory(vis)
-add_subdirectory(example)
+
+add_subdirectory(examples)

example/CMakeLists.txt

@@ -1,5 +0,0 @@
-add_executable(bench bench.cpp)
-target_link_libraries(bench PRIVATE tc)
-
-add_executable(path path.cpp)
-target_link_libraries(path PRIVATE tc)

example/bench.cpp

@@ -1,31 +0,0 @@
-#include "tc/solver.h"
-#include "tc/groups.h"
-
-#include <ctime>
-#include <iostream>
-
-int main() {
-    std::vector<tc::Group> groups = {
-        tc::group::H(2),
-        tc::group::H(3),
-        tc::group::H(4),
-        tc::group::T(100),
-        tc::group::T(500),
-        tc::group::T(1000),
-        tc::group::E(6),
-        tc::group::E(7),
-    };
-
-    for (const auto &group : groups) {
-        auto s = std::clock(); // to measure CPU time
-        auto cosets = tc::solve(group);
-        auto e = std::clock();
-
-        double diff = (double) (e - s) / CLOCKS_PER_SEC;
-        int order = cosets.len;
-
-        std::cout << group.name << "," << order << "," << diff << std::endl;
-    }
-
-    return 0;
-}

example/path.cpp

@@ -1,17 +0,0 @@
-#include "tc/solver.h"
-#include "tc/groups.h"
-
-#include <ctime>
-#include <iostream>
-
-int main() {
-    auto cube = tc::group::B(3);
-    auto vars = tc::solve(cube, {});
-
-    for (int target = 1; target < vars.len; target++) {
-        auto &action = vars.path[target];
-        std::cout << action.coset << " " << action.gen << " " << target << std::endl;
-    }
-
-    return 0;
-}

examples/CMakeLists.txt

@@ -0,0 +1,2 @@
+add_executable(memo memotest.cpp)
+target_link_libraries(memo PRIVATE tc vis-util)

examples/memotest.cpp

@@ -0,0 +1,53 @@
+#include <geometry.hpp>
+#include <tc/groups.hpp>
+#include <iostream>
+
+int main() {
+    tc::Group g = tc::group::B(3);
+    CosetMemo m(g);
+
+    m.solve({}, {});
+    m.solve({0}, {});
+    m.solve({0}, {0});
+    m.solve({1}, {});
+    m.solve({1}, {1});
+    m.solve({2}, {});
+    m.solve({2}, {2});
+    m.solve({0, 1}, {});
+    m.solve({0, 1}, {0});
+    m.solve({0, 1}, {1});
+    m.solve({0, 1}, {0, 1});
+    m.solve({1, 2}, {});
+    m.solve({1, 2}, {1});
+    m.solve({1, 2}, {2});
+    m.solve({1, 2}, {1, 2});
+    m.solve({0, 2}, {});
+    m.solve({0, 2}, {0});
+    m.solve({0, 2}, {2});
+    m.solve({0, 2}, {0, 2});
+    m.solve({0, 1, 2}, {});
+    m.solve({0, 1, 2}, {0});
+    m.solve({0, 1, 2}, {1});
+    m.solve({0, 1, 2}, {2});
+    m.solve({0, 1, 2}, {0, 1});
+    m.solve({0, 1, 2}, {1, 2});
+    m.solve({0, 1, 2}, {0, 2});
+    m.solve({0, 1, 2}, {0, 1, 2});
+
+    tc::Group big = tc::group::B(8);
+    CosetMemo mbig(big);
+
+    auto s1 = clock();
+    m.solve({0, 1, 2, 3, 4, 5, 6, 7}, {});
+    auto e1 = clock();
+
+    double t1 = (double) (e1 - s1) / (double) CLOCKS_PER_SEC;
+    std::cout << t1 << std::endl;
+
+    auto s2 = clock();
+    m.solve({0, 1, 2, 3, 4, 5, 6, 7}, {});
+    auto e2 = clock();
+
+    double t2 = (double) (e2 - s2) / (double) CLOCKS_PER_SEC;
+    std::cout << t2 << std::endl;
+}

tc/CMakeLists.txt

@@ -1,6 +0,0 @@
-add_library(tc STATIC
-        src/groups.cpp
-        src/solver.cpp
-        src/cosets.cpp)
-
-target_include_directories(tc PUBLIC include)

tc/include/tc/cosets.h

@@ -1,33 +0,0 @@
-#pragma once
-
-#include "groups.h"
-#include <vector>
-
-namespace tc {
-    struct Action {
-        int coset = -1;
-        int gen = -1;
-        int target = -1;
-    };
-
-    struct Cosets {
-        int ngens;
-        std::vector<int> data;
-        std::vector<Action> path;
-        int len;
-
-        explicit Cosets(int ngens);
-
-        void add_row();
-
-        void put(int coset, int gen, int target);
-
-        void put(int idx, int target);
-
-        [[nodiscard]] int get(int coset, int gen) const;
-
-        [[nodiscard]] int get(int idx) const;
-
-        [[nodiscard]] int size() const;
-    };
-}

tc/include/tc/groups.h

@@ -1,96 +0,0 @@
-#pragma once
-
-#include <array>
-#include <vector>
-
-namespace tc {
-    struct Rel {
-        std::array<int, 2> gens;
-        int mult;
-    };
-
-    /**
-     * A presentation of a coxeter group. Contains a number of generators and some relations of the form (ab)^n = e
-     */
-    struct Group {
-        const int ngens;
-        std::vector<std::vector<int>> _mults;  // lookup table for multiplicities
-        std::string name;
-
-        explicit Group(int ngens, const std::vector<Rel> &rels = {}, std::string name = "G");
-
-        void setmult(Rel rel);
-
-        [[nodiscard]] Rel rel(int a, int b) const;
-
-        [[nodiscard]] std::vector<Rel> get_rels() const;
-
-        [[nodiscard]] Group product(const Group &other) const;
-
-        [[nodiscard]] Group power(int p) const;
-
-        [[nodiscard]] bool trivial() const;
-    };
-
-    Group operator*(const Group &g, const Group &h);
-
-    Group operator^(const Group &g, const int &p);
-
-    /**
-     * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
-     * @param mults: The sequence of multiplicites between adjacent generators.
-     */
-    Group schlafli(const std::vector<int> &mults);
-
-    namespace group {
-        /**
-         * Simplex
-         */
-        Group A(int dim);
-
-        /**
-         * Cube, Orthoplex
-         */
-        Group B(int dim);
-
-        /**
-         * Demicube, Orthoplex
-         */
-        Group D(int dim);
-
-        /**
-         * E groups
-         */
-        Group E(int dim);
-
-        /**
-         * 24 Cell
-         */
-        Group F4();
-
-        /**
-         * Hexagon
-         */
-        Group G2();
-
-        /**
-         * Icosahedron
-         */
-        Group H(int dim);
-
-        /**
-         * Polygonal
-         */
-        Group I2(int n);
-
-        /**
-         * Toroidal. I2(n) * I2(m)
-         */
-        Group T(int n, int m);
-
-        /**
-         * Toroidal. T(n, n)
-         */
-        Group T(int n);
-    }
-}

tc/include/tc/solver.h

@@ -1,7 +0,0 @@
-#pragma once
-
-#include "cosets.h"
-
-namespace tc {
-    Cosets solve(const Group &g, const std::vector<int> &sub_gens = {});
-}

tc/src/cosets.cpp

@@ -1,44 +0,0 @@
-#include "tc/cosets.h"
-
-namespace tc {
-    Cosets::Cosets(int ngens) : ngens(ngens), len(0) {
-    }
-
-    void Cosets::add_row() {
-        len++;
-        data.resize(data.size() + ngens, -1);
-        path.resize(path.size() + 1);
-    }
-
-    void Cosets::put(int coset, int gen, int target) {
-        data[coset * ngens + gen] = target;
-        data[target * ngens + gen] = coset;
-
-        if (path[target].coset == -1) {
-            path[target] = {coset, gen, target};
-        }
-    }
-
-    void Cosets::put(int idx, int target) {
-        int coset = idx / ngens;
-        int gen = idx % ngens;
-        data[idx] = target;
-        data[target * ngens + gen] = coset;
-
-        if (path[target].coset == -1) {
-            path[target] = {coset, gen, target};
-        }
-    }
-
-    int Cosets::get(int coset, int gen) const {
-        return data[coset * ngens + gen];
-    }
-
-    int Cosets::get(int idx) const {
-        return data[idx];
-    }
-
-    int Cosets::size() const {
-        return len;
-    }
-}

tc/src/groups.cpp

@@ -1,207 +0,0 @@
-#include "tc/groups.h"
-
-#include <iterator>
-#include <sstream>
-
-namespace tc {
-    Group::Group(int ngens, const std::vector<Rel> &rels, std::string name) : ngens(ngens), name(std::move(name)) {
-        _mults.resize(ngens);
-        for (int i = 0; i < ngens; i++) {
-            _mults[i].resize(ngens, 2);
-        }
-
-        for (Rel rel : rels) {
-            setmult(rel);
-        }
-    }
-
-    void Group::setmult(Rel rel) {
-        _mults[rel.gens[0]][rel.gens[1]] = rel.mult;
-        _mults[rel.gens[1]][rel.gens[0]] = rel.mult;
-    }
-
-    Rel Group::rel(int a, int b) const {
-        return {a, b, _mults[a][b]};
-    }
-
-    std::vector<Rel> Group::get_rels() const {
-        std::vector<Rel> rels;
-        for (int i = 0; i < ngens - 1; i++) {
-            for (int j = i + 1; j < ngens; j++) {
-                rels.push_back({i, j, _mults[i][j]});
-            }
-        }
-        return rels;
-    }
-
-    Group Group::product(const Group &other) const {
-        int off = ngens;
-
-        Group g(ngens + other.ngens, get_rels());
-
-        for (Rel rel : other.get_rels()) {
-            g.setmult({off + rel.gens[0], off + rel.gens[1], rel.mult});
-        }
-
-        std::stringstream ss;
-        ss << name << "*" << other.name;
-        g.name = ss.str();
-
-        return g;
-    }
-
-    Group Group::power(int p) const {
-        Group g(ngens * p);
-
-        for (Rel rel : get_rels()) {
-            for (int off = 0; off < g.ngens; off += ngens) {
-                g.setmult({off + rel.gens[0], off + rel.gens[1], rel.mult});
-            }
-        }
-
-        std::stringstream ss;
-        ss << name << "^" << p;
-        g.name = ss.str();
-
-        return g;
-    }
-
-    bool Group::trivial() const {
-        for (int i = 0; i < ngens; ++i) {
-            for (int j = 0; j < ngens; ++j) {
-                if (_mults[i][j] != 2) {
-                    return false;
-                }
-            }
-        }
-
-        return true;
-    }
-
-    Group operator*(const Group &g, const Group &h) {
-        return g.product(h);
-    }
-
-    Group operator^(const Group &g, const int &p) {
-        return g.power(p);
-    }
-
-    Group schlafli(const std::vector<int> &mults, const std::string &name) {
-        int ngens = (int) mults.size() + 1;
-
-        Group g(ngens, {}, name);
-
-        for (int i = 0; i < (int) mults.size(); i++) {
-            g.setmult({i, i + 1, mults[i]});
-        }
-
-        return g;
-    }
-
-    Group schlafli(const std::vector<int> &mults) {
-        std::stringstream ss;
-        ss << "[";
-        if (!mults.empty()) {
-            copy(mults.begin(), mults.end() - 1, std::ostream_iterator<int>(ss, ","));
-            ss << mults.back();
-        }
-        ss << "]";
-
-        return schlafli(mults, ss.str());
-    }
-
-    namespace group {
-        Group A(const int dim) {
-            if (dim == 0)
-                return Group(0, {}, "A(0)");
-
-            const std::vector<int> &mults = std::vector<int>(dim - 1, 3);
-
-            std::stringstream ss;
-            ss << "A(" << dim << ")";
-
-            return schlafli(mults, ss.str());
-        }
-
-        Group B(const int dim) {
-            std::vector<int> mults(dim - 1, 3);
-            mults[0] = 4;
-
-            std::stringstream ss;
-            ss << "B(" << dim << ")";
-
-            return schlafli(mults, ss.str());
-        }
-
-        Group D(const int dim) {
-            std::vector<int> mults(dim - 1, 3);
-            mults[dim - 2] = 2;
-            Group g = schlafli(mults);
-            g.setmult({1, dim - 1, 3});
-
-            std::stringstream ss;
-            ss << "D(" << dim << ")";
-            g.name = ss.str();
-
-            return g;
-        }
-
-        Group E(const int dim) {
-            std::vector<int> mults(dim - 1, 3);
-            mults[dim - 2] = 2;
-            Group g = schlafli(mults);
-            g.setmult({2, dim - 1, 3});
-
-            std::stringstream ss;
-            ss << "E(" << dim << ")";
-            g.name = ss.str();
-
-            return g;
-        }
-
-        Group F4() {
-            return schlafli({3, 4, 3}, "F4");
-        }
-
-        Group G2() {
-            return schlafli({6}, "G2");
-        }
-
-        Group H(const int dim) {
-            std::vector<int> mults(dim - 1, 3);
-            mults[0] = 5;
-
-            std::stringstream ss;
-            ss << "H(" << dim << ")";
-
-            return schlafli(mults, ss.str());
-        }
-
-        Group I2(const int n) {
-            std::stringstream ss;
-            ss << "I2(" << n << ")";
-
-            return schlafli({n}, ss.str());
-        }
-
-        Group T(const int n, const int m) {
-            Group g = I2(n) * I2(m);
-
-            std::stringstream ss;
-            ss << "T(" << n << "," << m << ")";
-            g.name = ss.str();
-
-            return g;
-        }
-
-        Group T(const int n) {
-            Group g = I2(n) ^2;
-
-            std::stringstream ss;
-            ss << "T(" << n << ")";
-            g.name = ss.str();
-
-            return g;
-        }
-    }
-}

tc/src/solver.cpp

@@ -1,135 +0,0 @@
-#include "tc/solver.h"
-
-#include <algorithm>
-
-namespace tc {
-    struct RelTable {
-        Rel rel;
-
-        std::vector<int *> lst_ptr;
-        std::vector<int> gen;
-
-        int &mult = rel.mult;
-        std::array<int, 2> &gens = rel.gens;
-
-        explicit RelTable(Rel rel) : rel(rel) {
-        }
-
-        int add_row() {
-            int idx = lst_ptr.size();
-            lst_ptr.push_back(nullptr);
-            gen.push_back(-1);
-            return idx;
-        }
-    };
-
-    struct RelationSet {
-        const Cosets &cosets;
-
-        std::vector<RelTable> tables;
-        std::vector<std::vector<RelTable *>> gen_map; // which relations involve which generators
-
-        explicit RelationSet(const Group &g, const Cosets &cosets) : gen_map(g.ngens), cosets(cosets) {
-            const std::vector<Rel> &rels = g.get_rels();
-            tables.reserve(rels.size());
-            for (const auto &rel : rels) {
-                RelTable &table = tables.emplace_back(rel);
-                gen_map[rel.gens[0]].push_back(&table);
-                gen_map[rel.gens[1]].push_back(&table);
-            }
-        }
-
-        void add_row() {
-            for (auto &table : tables) {
-                table.add_row();
-            }
-        }
-
-        void fill_row(int idx) {
-            for (auto &table : tables) {
-                if (table.lst_ptr[idx] != nullptr) continue;
-
-                table.lst_ptr[idx] = new int;
-
-                if ((cosets.get(idx, table.gens[0]) != idx) and
-                    (cosets.get(idx, table.gens[1]) != idx)) {
-                    table.gen[idx] = 0;
-                } else {
-                    table.gen[idx] = -1;
-                }
-            }
-        }
-    };
-
-    Cosets solve(const Group &group, const std::vector<int> &sub_gens) {
-        Cosets cosets(group.ngens);
-        cosets.add_row();
-        for (const auto &i : sub_gens) {
-            cosets.put(0, i, 0);
-        }
-
-        RelationSet rels(group, cosets);
-        rels.add_row();
-        rels.fill_row(0);
-
-        int idx = 0;
-        int coset, gen, target, fact_idx, lst, gen_;
-        while (true) {
-            while (idx < cosets.data.size() and cosets.get(idx) >= 0)
-                idx++;
-
-            if (idx == cosets.data.size())
-                break;
-
-            target = cosets.len;
-
-            cosets.add_row();
-            rels.add_row();
-
-            std::vector<int> facts = {idx};
-
-            while (!facts.empty()) {
-                fact_idx = facts.back();
-                facts.pop_back();
-
-                if (cosets.get(fact_idx) != -1)
-                    continue;
-
-                cosets.put(fact_idx, target);
-
-                coset = fact_idx / group.ngens;
-                gen = fact_idx % group.ngens;
-
-                for (RelTable *pTable : rels.gen_map[gen]) {
-                    RelTable &table = *pTable;
-
-                    if (table.lst_ptr[target] == nullptr) {
-                        table.lst_ptr[target] = table.lst_ptr[coset];
-                        table.gen[target] = table.gen[coset] + 1;
-
-                        if (table.gen[coset] < 0)
-                            table.gen[target] -= 2;
-
-                        if (table.gen[target] == table.rel.mult) {
-                            lst = *(table.lst_ptr[target]);
-                            delete table.lst_ptr[target];
-                            gen_ = table.gens[table.gens[0] == gen];
-                            facts.push_back(lst * group.ngens + gen_);
-                        } else if (table.gen[target] == -table.mult) {
-                            gen_ = table.gens[table.gens[0] == gen];
-                            facts.push_back(target * group.ngens + gen_);
-                        } else if (table.gen[target] == table.mult - 1) {
-                            *(table.lst_ptr[target]) = target;
-                        }
-                    }
-                }
-
-                std::sort(facts.begin(), facts.end(), std::greater<>());
-            }
-
-            rels.fill_row(target);
-        }
-
-        return cosets;
-    }
-}

vis/CMakeLists.txt

@@ -10,3 +10,6 @@ add_custom_command(
 )
 
 add_dependencies(vis shaders)
+
+add_library(vis-util INTERFACE)
+target_include_directories(vis-util INTERFACE include)

vis/include/geometry.hpp

@@ -0,0 +1,38 @@
+#pragma once
+
+#include <tc/core.hpp>
+#include <optional>
+#include <cmath>
+
+size_t key(const std::vector<int> &gens) {
+    size_t bits = 0;
+    for (const auto &gen : gens) {
+        bits |= 1U << gen;
+    }
+    return bits;
+}
+
+struct CosetMemo {
+    const tc::Group &parent;
+    std::vector<std::vector<std::optional<tc::Cosets>>> results;
+
+    explicit CosetMemo(const tc::Group &parent)
+        : parent(parent) {
+        size_t W = std::pow(2, parent.ngens);
+
+        for (size_t i = 0; i < W; ++i) {
+            results.emplace_back(W, std::nullopt);
+        }
+    }
+
+    tc::Cosets solve(const std::vector<int> &group_gens, const std::vector<int> &sub_gens) {
+        size_t group_key = key(group_gens);
+        size_t sub_key = key(sub_gens);
+
+        if (!results[group_key][sub_key]) {
+            results[group_key][sub_key] = parent.subgroup(group_gens).solve(sub_gens);
+        }
+
+        return results[group_key][sub_key].value();
+    }
+};

vis/include/mirror.hpp

@@ -1,6 +1,6 @@
 #pragma once
 
-#include <tc/cosets.h>
+#include <tc/core.hpp>
 #include <glm/glm.hpp>
 #include <cmath>
 #include <vector>
@@ -27,7 +27,7 @@ std::vector<glm::vec4> mirror(const tc::Group &group) {
         glm::vec4 vp{};
         for (int m = 0; m < p; ++m) {
             glm::vec4 vq = mirrors[m];
-            vp[m] = (cos(M_PI / group.rel(p, m).mult) - dot(m, vp, vq)) / vq[m];
+            vp[m] = (cos(M_PI / group.get(p, m)) - dot(m, vp, vq)) / vq[m];
         }
         vp[p] = std::sqrt(1 - glm::dot(vp, vp));
 

vis/include/util.hpp

@@ -0,0 +1,42 @@
+#pragma once
+
+#include <string>
+#include <vector>
+#include <glad/glad.h>
+
+#include <sstream>
+
+void utilShaderSource(GLuint shader, const std::vector<std::string> &sources) {
+    char const *ptrs[sources.size()];
+    for (size_t i = 0; i < sources.size(); ++i) {
+        ptrs[i] = sources[i].c_str();
+    }
+    glShaderSource(shader, sources.size(), ptrs, nullptr);
+}
+
+std::string utilShaderInfoLog(GLuint shader) {
+    int len;
+    glGetShaderiv(shader, GL_INFO_LOG_LENGTH, &len);
+    char buffer[len];
+    glGetShaderInfoLog(shader, len, nullptr, buffer);
+    return std::string(buffer);
+}
+
+std::string utilProgramInfoLog(GLuint program) {
+    int len;
+    glGetProgramiv(program, GL_INFO_LOG_LENGTH, &len);
+    char buffer[len];
+    glGetProgramInfoLog(program, len, nullptr, buffer);
+    return std::string(buffer);
+}
+
+std::string utilInfo() {
+    std::stringstream ss;
+    ss
+        << "Graphics Information:" << std::endl
+        << "    Vendor:          " << glGetString(GL_VENDOR) << std::endl
+        << "    Renderer:        " << glGetString(GL_RENDERER) << std::endl
+        << "    OpenGL version:  " << glGetString(GL_VERSION) << std::endl
+        << "    Shading version: " << glGetString(GL_SHADING_LANGUAGE_VERSION) << std::endl;
+    return ss.str();
+}

vis/src/main.cpp

@@ -2,106 +2,24 @@
 #include <GLFW/glfw3.h>
 #include <iostream>
 
-#include <tc/groups.h>
-#include <tc/solver.h>
-
-#include "geom.h"
-
 #include <glm/gtc/type_ptr.hpp>
 #include <glm/gtx/string_cast.hpp>
 
+#include <tc/groups.hpp>
+
+#include "util.hpp"
+#include "mirror.hpp"
+#include "geometry.hpp"
+
 #ifdef _WIN32
 extern "C" {
 __attribute__((unused)) __declspec(dllexport) int NvOptimusEnablement = 0x00000001;
 }
 #endif
 
-void utilShaderSource(GLuint shader, const std::vector<std::string> &sources) {
-    char const *ptrs[sources.size()];
-    for (size_t i = 0; i < sources.size(); ++i) {
-        ptrs[i] = sources[i].c_str();
-    }
-    glShaderSource(shader, sources.size(), ptrs, nullptr);
-}
-
-std::string utilShaderInfoLog(GLuint shader) {
-    int len;
-    glGetShaderiv(shader, GL_INFO_LOG_LENGTH, &len);
-    char buffer[len];
-    glGetShaderInfoLog(shader, len, nullptr, buffer);
-    return std::string(buffer);
-}
-
-std::string utilProgramInfoLog(GLuint program) {
-    int len;
-    glGetProgramiv(program, GL_INFO_LOG_LENGTH, &len);
-    char buffer[len];
-    glGetProgramInfoLog(program, len, nullptr, buffer);
-    return std::string(buffer);
-}
-
-
-template<int D>
-tc::Group shrink(const tc::Group &g, const std::array<int, D> &sub) {
-    tc::Group h(D);
-    for (int i = 0; i < D; ++i) {
-        for (int j = 0; j < D; ++j) {
-            h.setmult({i, j, g.rel(sub[i], sub[j]).mult});
-        }
-    }
-    return h;
-}
-
-template<int D>
-std::vector<int> raise(
-    const tc::Cosets &g_res,
-    const tc::Cosets &h_res,
-    const std::array<int, D> &gen_map,
-    const std::vector<int> &path
-) {
-    std::vector<int> res(path.size(), 0);
-    for (size_t i = 1; i < path.size(); ++i) {
-        auto action = h_res.path[path[i]];
-
-        res[i] = g_res.get(res[action.coset], gen_map[action.gen]);
-    }
-    return res;
-}
-
-std::vector<int> targets(const std::vector<tc::Action> &path) {
-    std::vector<int> res(path.size(), 0);
-    for (size_t i = 0; i < path.size(); ++i) {
-        res[i] = path[i].target;
-    }
-    return res;
-}
-
-std::vector<int> tile(const tc::Cosets &map, std::vector<int> geom) {
-    int K = geom.size();
-    geom.resize(K * map.size());
-    for (int i = 1; i < map.size(); ++i) { // tile
-        auto gaction = map.path[i];
-        for (int j = 0; j < K; ++j) {
-            geom[i * K + j] = map.get(geom[gaction.coset * K + j], gaction.gen);
-        }
-    }
-    return geom;
-}
-
-template<int D>
-std::vector<int> build(const tc::Group &g, const std::array<int, D> &sub) {
-    tc::Group h = shrink<D>(g, sub);
-    auto hres = tc::solve(h); // recursion would happen here
-
-    auto gres = tc::solve(g);
-    std::vector<int> geom = targets(hres.path);
-    geom = raise<D>(gres, hres, sub, geom);
-
-    return tile(gres, geom);
-}
-
-
 int main(int argc, char *argv[]) {
+    //region init window
+
     if (!glfwInit()) {
         std::cerr << "Failed to initialize GLFW" << std::endl;
         return EXIT_FAILURE;
@@ -122,46 +40,12 @@ int main(int argc, char *argv[]) {
     gladLoadGLLoader((GLADloadproc) glfwGetProcAddress);
     glfwSwapInterval(0);
 
-    std::cout
+    //endregion
-        << "Graphics Information:" << std::endl
-        << "    Vendor:          " << glGetString(GL_VENDOR) << std::endl
-        << "    Renderer:        " << glGetString(GL_RENDERER) << std::endl
-        << "    OpenGL version:  " << glGetString(GL_VERSION) << std::endl
-        << "    Shading version: " << glGetString(GL_SHADING_LANGUAGE_VERSION) << std::endl;
 
-    auto group = tc::group::B(2);
+    std::cout << utilInfo();
-    auto res = tc::solve(group);
-    auto mirrors = mirror(group);
-    auto corners = plane_intersections(mirrors);
-
-    auto points = std::vector<glm::vec4>(res.size());
-    points[0] = barycentric(corners, {1.00f, 0.50f, 0.50f, 0.50f});
-    for (int i = 1; i < res.size(); ++i) {
-        auto action = res.path[i];
-        points[i] = reflect(points[action.coset], mirrors[action.gen]);
-    }
-
-    auto h = shrink<2>(group, {0, 1});
-    auto i = shrink<1>(h, {0});
-
-    auto g_map = res;
-    auto h_map = tc::solve(h);
-    auto i_map = tc::solve(i);
-
-    auto g0 = targets(i_map.path);
-    g0 = raise<1>(h_map, i_map, {0}, g0);
-    g0 = tile(h_map, g0);
-    g0 = raise<2>(g_map, h_map, {0, 1}, g0);
-
-//    auto g0 = build<2>(group, {0});
-//    auto g1 = build<2>(group, {1});
-//    auto g2 = build<2>(group, {2});
-//    auto g3 = build<2>(group, {3});
-
-    GLuint vs = glCreateShader(GL_VERTEX_SHADER);
-    utilShaderSource(vs, {
-        "#version 430\n",
 
+    const std::string VS_SOURCE =
+        "#version 430\n"
         "layout(location=0) uniform mat4 proj;"
         "layout(location=1) uniform mat4 view;"
         ""
@@ -175,14 +59,10 @@ int main(int argc, char *argv[]) {
         //        "   gl_Position = proj * vec4(vpos.xyz / (1), 1);"
         "   gl_Position = proj * vec4(vpos.xyz / (1 - vpos.w), 1);"
         "   gl_PointSize = 5;"
-        "}"
+        "}";
-    });
-    glCompileShader(vs);
-
-    GLuint fs = glCreateShader(GL_FRAGMENT_SHADER);
-    utilShaderSource(fs, {
-        "#version 430\n",
 
+    const std::string FS_SOURCE =
+        "#version 430\n"
         "layout(location=2) uniform vec3 c;"
         ""
         "in vec4 vpos;"
@@ -192,8 +72,15 @@ int main(int argc, char *argv[]) {
         "void main() {"
         "   float d = smoothstep(-2, 2, vpos.z);"
         "   color = vec4(c * d, 1);"
-        "}"
+        "}";
-    });
+
+    //region init shaders
+    GLuint vs = glCreateShader(GL_VERTEX_SHADER);
+    utilShaderSource(vs, {VS_SOURCE});
+    glCompileShader(vs);
+
+    GLuint fs = glCreateShader(GL_FRAGMENT_SHADER);
+    utilShaderSource(fs, {FS_SOURCE});
 
     GLuint pgm = glCreateProgram();
     glAttachShader(pgm, vs);
@@ -218,6 +105,15 @@ int main(int argc, char *argv[]) {
         glfwTerminate();
         return EXIT_FAILURE;
     }
+    //endregion
+
+    auto group = tc::group::B(4);
+    auto res = group.solve();
+    auto mirrors = mirror(group);
+    auto corners = plane_intersections(mirrors);
+
+    auto start = barycentric(corners, {1.00f, 0.50f, 0.50f, 0.50f});
+    auto points = res.path.walk<glm::vec4, glm::vec4>(start, mirrors, reflect);
 
     GLuint vbo;
     glGenBuffers(1, &vbo);
@@ -227,27 +123,11 @@ int main(int argc, char *argv[]) {
     glEnableVertexAttribArray(0);
     glVertexAttribPointer(0, 4, GL_FLOAT, false, 0, nullptr);
 
-    GLuint ibo0;
-    glGenBuffers(1, &ibo0);
-    glBindBuffer(GL_ARRAY_BUFFER, ibo0);
-    glBufferData(GL_ARRAY_BUFFER, sizeof(int) * g0.size(), &g0[0], GL_STATIC_DRAW);
-
-//    GLuint ibo1;
-//    glGenBuffers(1, &ibo1);
-//    glBindBuffer(GL_ARRAY_BUFFER, ibo1);
-//    glBufferData(GL_ARRAY_BUFFER, sizeof(int) * g1.size(), &g1[0], GL_STATIC_DRAW);
-//
-//    GLuint ibo2;
-//    glGenBuffers(1, &ibo2);
-//    glBindBuffer(GL_ARRAY_BUFFER, ibo2);
-//    glBufferData(GL_ARRAY_BUFFER, sizeof(int) * g2.size(), &g2[0], GL_STATIC_DRAW);
-//
-//    GLuint ibo3;
-//    glGenBuffers(1, &ibo3);
-//    glBindBuffer(GL_ARRAY_BUFFER, ibo3);
-//    glBufferData(GL_ARRAY_BUFFER, sizeof(int) * g3.size(), &g3[0], GL_STATIC_DRAW);
-
     while (!glfwWindowShouldClose(window)) {
+        int width, height;
+        glfwGetFramebufferSize(window, &width, &height);
+        glViewport(0, 0, width, height);
+
         glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
 
         glUseProgram(pgm);
@@ -255,9 +135,7 @@ int main(int argc, char *argv[]) {
         glEnable(GL_POINT_SMOOTH);
         glEnable(GL_DEPTH_TEST);
 
-        int width, height;
+        //region uniforms
-        glfwGetFramebufferSize(window, &width, &height);
-        glViewport(0, 0, width, height);
         auto aspect = (float) width / (float) height;
         auto pheight = 1.4f;
         auto pwidth = aspect * pheight;
@@ -270,27 +148,11 @@ int main(int argc, char *argv[]) {
         view = glm::rotate(view, t / 3, glm::vec3(0, 0, 1));
         view = glm::rotate(view, t / 4, glm::vec3(1, 0, 0));
         glUniformMatrix4fv(1, 1, false, glm::value_ptr(view));
+        //endregion
 
         glUniform3f(2, 1.0f, 1.0f, 1.0f);
         glDrawArrays(GL_POINTS, 0, points.size());
 
-        glLineWidth(2.0f);
-        glUniform3f(2, 1.0f, 0.0f, 0.0f);
-        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo0);
-        glDrawElements(GL_LINES, g0.size(), GL_UNSIGNED_INT, nullptr);
-
-//        glUniform3f(2, 0.0f, 1.0f, 0.0f);
-//        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo1);
-//        glDrawElements(GL_LINES, g1.size(), GL_UNSIGNED_INT, nullptr);
-//
-//        glUniform3f(2, 0.0f, 0.0f, 1.0f);
-//        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo2);
-//        glDrawElements(GL_LINES, g2.size(), GL_UNSIGNED_INT, nullptr);
-//
-//        glUniform3f(2, 0.7f, 0.7f, 0.0f);
-//        glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo3);
-//        glDrawElements(GL_LINES, g3.size(), GL_UNSIGNED_INT, nullptr);
-
         glfwSwapBuffers(window);
 
         glfwPollEvents();