diff --git a/tc/include/tc/cosets.h b/tc/include/tc/cosets.h index b12385d..552e330 100644 --- a/tc/include/tc/cosets.h +++ b/tc/include/tc/cosets.h @@ -7,6 +7,7 @@ namespace tc { struct Action { int coset = -1; int gen = -1; + int target = -1; }; struct Cosets { diff --git a/tc/include/tc/groups.h b/tc/include/tc/groups.h index df17b39..5bfad37 100644 --- a/tc/include/tc/groups.h +++ b/tc/include/tc/groups.h @@ -29,8 +29,6 @@ namespace tc { [[nodiscard]] Group power(int p) const; - [[nodiscard]] Group shrink(const std::vector &gens) const; - [[nodiscard]] bool trivial() const; }; diff --git a/tc/src/cosets.cpp b/tc/src/cosets.cpp index a5fece4..5815fa9 100644 --- a/tc/src/cosets.cpp +++ b/tc/src/cosets.cpp @@ -15,7 +15,7 @@ namespace tc { data[target * ngens + gen] = coset; if (path[target].coset == -1) { - path[target] = {coset, gen}; + path[target] = {coset, gen, target}; } } @@ -26,7 +26,7 @@ namespace tc { data[target * ngens + gen] = coset; if (path[target].coset == -1) { - path[target] = {coset, gen}; + path[target] = {coset, gen, target}; } } diff --git a/tc/src/groups.cpp b/tc/src/groups.cpp index 3418e9f..b1896d4 100644 --- a/tc/src/groups.cpp +++ b/tc/src/groups.cpp @@ -66,23 +66,6 @@ namespace tc { return g; } - Group Group::shrink(const std::vector &gens) const { - Group g(ngens); - for (const auto &i : gens) { - for (const auto &j : gens) { - g._mults[i][j] = _mults[i][j]; - } - } - - std::stringstream ss; - ss << name << "{"; - for (auto e : gens) ss << " " << e; - ss << " }"; - g.name = ss.str(); - - return g; - } - bool Group::trivial() const { for (int i = 0; i < ngens; ++i) { for (int j = 0; j < ngens; ++j) { diff --git a/vis/src/main.cpp b/vis/src/main.cpp index c414a65..531dd6b 100644 --- a/vis/src/main.cpp +++ b/vis/src/main.cpp @@ -40,40 +40,71 @@ std::string utilProgramInfoLog(GLuint program) { return std::string(buffer); } -std::vector build(const tc::Group &g, std::vector gens) { - std::cout << g.name << std::endl; - if (g.trivial()) return {0}; - - std::vector res; - - auto root = tc::solve(g); - - for (size_t i = 0; i < gens.size(); ++i) { - std::vector sub(gens); - sub.erase(sub.begin() + i); - - auto base = build(g.shrink(sub), sub); - for (auto e : base) { - res.push_back(e); - } - res.push_back(0); - } - - auto map = tc::solve(g, gens); - size_t N = res.size(); - res.resize(N * map.size()); - - for (size_t i = 1; i < res.size(); ++i) { - auto action = map.path[i]; - for (size_t j = 0; j < N; ++j) { - res[i * N + j] = root.get(res[action.coset * N + j], action.gen); +template +tc::Group shrink(const tc::Group &g, const std::array &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 +std::vector raise( + const tc::Cosets &cosets, + const std::vector &path, + const std::array &gen_map +) { + std::vector res(path.size(), {0, 0, 0}); + for (size_t i = 1; i < path.size(); ++i) { + auto action = path[i]; + + auto coset = res[action.coset].target; + auto gen = gen_map[action.gen]; + auto target = cosets.get(coset, gen); + + res[i] = {coset, gen, target}; + } return res; } +std::vector targets(const std::vector &path) { + std::vector res(path.size(), 0); + for (size_t i = 0; i < path.size(); ++i) { + res[i] = path[i].target; + } + return res; +} + +std::vector tile(const tc::Cosets &map, std::vector 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 +std::vector build(const tc::Group &g, const std::array &sub) { + tc::Group h = shrink(g, sub); + auto hres = tc::solve(h); // recursion would happen here + + auto gres = tc::solve(g); + auto path = raise(gres, hres.path, sub); + + const std::vector &geom = targets(path); + + return tile(gres, geom); +} + + int main(int argc, char *argv[]) { if (!glfwInit()) { std::cerr << "Failed to initialize GLFW" << std::endl; @@ -102,7 +133,7 @@ int main(int argc, char *argv[]) { << " OpenGL version: " << glGetString(GL_VERSION) << std::endl << " Shading version: " << glGetString(GL_SHADING_LANGUAGE_VERSION) << std::endl; - auto group = tc::group::B(3); + auto group = tc::group::H(4); auto res = tc::solve(group); auto mirrors = mirror(group); auto corners = plane_intersections(mirrors); @@ -114,52 +145,10 @@ int main(int argc, char *argv[]) { points[i] = reflect(points[action.coset], mirrors[action.gen]); } - auto res0 = tc::solve(group, {0}); - auto res0_inds = std::vector(res0.size() * 2); - res0_inds[0] = res.get(0, 0); - res0_inds[1] = 0; - for (int i = 1; i < res0.size(); ++i) { - auto action = res0.path[i]; - res0_inds[i * 2 + 0] = res.get(res0_inds[action.coset * 2 + 0], action.gen); - res0_inds[i * 2 + 1] = res.get(res0_inds[action.coset * 2 + 1], action.gen); - } - - auto res1 = tc::solve(group, {1}); - auto res1_inds = std::vector(res1.size() * 2); - res1_inds[0] = res.get(0, 1); - res1_inds[1] = 0; - for (int i = 1; i < res1.size(); ++i) { - auto action = res1.path[i]; - res1_inds[i * 2 + 0] = res.get(res1_inds[action.coset * 2 + 0], action.gen); - res1_inds[i * 2 + 1] = res.get(res1_inds[action.coset * 2 + 1], action.gen); - } - - auto res2 = tc::solve(group, {2}); - auto res2_inds = std::vector(res2.size() * 2); - res2_inds[0] = res.get(0, 2); - res2_inds[1] = 0; - for (int i = 1; i < res2.size(); ++i) { - auto action = res2.path[i]; - res2_inds[i * 2 + 0] = res.get(res2_inds[action.coset * 2 + 0], action.gen); - res2_inds[i * 2 + 1] = res.get(res2_inds[action.coset * 2 + 1], action.gen); - } - -// auto res01 = tc::solve(group, {0, 1}); -// auto res01_inds = std::vector(res01.size() * 3); -// res01_inds[0] = res.get(0, 0); -// res01_inds[1] = res.get(0, 1); -// res01_inds[2] = 0; -// for (int i = 0; i < res01.size(); ++i) { -// auto action = res01.path[i]; -// for (int j = 0; j < 3; ++j) { -// res01_inds[i * 3 + j] = res.get(res01_inds[action.coset * 3 + j], action.gen); -// } -// } - - auto test_inds = build(group, {0, 1, 2}); - std::cout << "done" << std::endl; - - auto test_mode = GL_TRIANGLES; + 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, { @@ -170,9 +159,12 @@ int main(int argc, char *argv[]) { "" "layout(location=0) in vec4 pos;" "" + "out vec4 vpos;" + "" "void main() {" " int i = gl_VertexID;" - " gl_Position = proj * view * vec4(pos.xyz, 1);" + " vpos = view * pos;" + " gl_Position = proj * vec4(vpos.xyz / (1 - vpos.w), 1);" " gl_PointSize = 5;" "}" }); @@ -182,12 +174,15 @@ int main(int argc, char *argv[]) { utilShaderSource(fs, { "#version 430\n", - "layout(location=2) uniform float gray;" + "layout(location=2) uniform vec3 c;" + "" + "in vec4 vpos;" "" "out vec4 color;" "" "void main() {" - " color = vec4(gray);" + " float d = smoothstep(-2, 2, vpos.z);" + " color = vec4(c * d, 1);" "}" }); @@ -223,25 +218,25 @@ int main(int argc, char *argv[]) { glEnableVertexAttribArray(0); glVertexAttribPointer(0, 4, GL_FLOAT, false, 0, nullptr); - GLuint res0_ibo; - glGenBuffers(1, &res0_ibo); - glBindBuffer(GL_ARRAY_BUFFER, res0_ibo); - glBufferData(GL_ARRAY_BUFFER, sizeof(int) * res0_inds.size(), &res0_inds[0], GL_STATIC_DRAW); + GLuint ibo0; + glGenBuffers(1, &ibo0); + glBindBuffer(GL_ARRAY_BUFFER, ibo0); + glBufferData(GL_ARRAY_BUFFER, sizeof(int) * g0.size(), &g0[0], GL_STATIC_DRAW); - GLuint res1_ibo; - glGenBuffers(1, &res1_ibo); - glBindBuffer(GL_ARRAY_BUFFER, res1_ibo); - glBufferData(GL_ARRAY_BUFFER, sizeof(int) * res1_inds.size(), &res1_inds[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 res2_ibo; - glGenBuffers(1, &res2_ibo); - glBindBuffer(GL_ARRAY_BUFFER, res2_ibo); - glBufferData(GL_ARRAY_BUFFER, sizeof(int) * res2_inds.size(), &res2_inds[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 test_ibo; - glGenBuffers(1, &test_ibo); - glBindBuffer(GL_ARRAY_BUFFER, test_ibo); - glBufferData(GL_ARRAY_BUFFER, sizeof(int) * test_inds.size(), &test_inds[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)) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); @@ -261,23 +256,31 @@ int main(int argc, char *argv[]) { glUniformMatrix4fv(0, 1, false, glm::value_ptr(proj)); auto t = (float) glfwGetTime() / 3; - glm::mat4 view = glm::rotate(glm::identity(), t, glm::vec3(0, 1, 0)); + auto view = glm::identity(); + view = glm::rotate(view, t / 1, glm::vec3(0, 1, 0)); + 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)); - glUniform1f(2, 1.0f); + glUniform3f(2, 1.0f, 1.0f, 1.0f); glDrawArrays(GL_POINTS, 0, points.size()); -// glUniform1f(2, 0.9f); -// glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, res0_ibo); -// glDrawElements(GL_LINES, res0_inds.size(), GL_UNSIGNED_INT, nullptr); -// glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, res1_ibo); -// glDrawElements(GL_LINES, res1_inds.size(), GL_UNSIGNED_INT, nullptr); -// glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, res2_ibo); -// glDrawElements(GL_LINES, res2_inds.size(), GL_UNSIGNED_INT, nullptr); + 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); - glUniform1f(2, 0.5f); - glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, test_ibo); - glDrawElements(test_mode, test_inds.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, 0.5f, 0.5f, 0.0f); + glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo3); + glDrawElements(GL_LINES, g3.size(), GL_UNSIGNED_INT, nullptr); glfwSwapBuffers(window);