Temporarily remove Nanogui window.

also rename set_difference wrapper

.gitignore

@@ -1,288 +1,4 @@
-### C++ template
-# Prerequisites
-*.d
-
-# Compiled Object files
-*.slo
-*.lo
-*.o
-*.obj
-
-# Precompiled Headers
-*.gch
-*.pch
-
-# Compiled Dynamic libraries
-*.so
-*.dylib
-*.dll
-
-# Fortran module files
-*.mod
-*.smod
-
-# Compiled Static libraries
-*.lai
-*.la
-*.a
-*.lib
-
-# Executables
-*.exe
-*.out
-*.app
-
-### JetBrains template
-# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio, WebStorm and Rider
-# Reference: https://intellij-support.jetbrains.com/hc/en-us/articles/206544839
-
-# User-specific stuff
-.idea/**/workspace.xml
-.idea/**/tasks.xml
-.idea/**/usage.statistics.xml
-.idea/**/dictionaries
-.idea/**/shelf
-
-# AWS User-specific
-.idea/**/aws.xml
-
-# Generated files
-.idea/**/contentModel.xml
-
-# Sensitive or high-churn files
-.idea/**/dataSources/
-.idea/**/dataSources.ids
-.idea/**/dataSources.local.xml
-.idea/**/sqlDataSources.xml
-.idea/**/dynamic.xml
-.idea/**/uiDesigner.xml
-.idea/**/dbnavigator.xml
-
-# Gradle
-.idea/**/gradle.xml
-.idea/**/libraries
-
-# Gradle and Maven with auto-import
-# When using Gradle or Maven with auto-import, you should exclude module files,
-# since they will be recreated, and may cause churn.  Uncomment if using
-# auto-import.
-# .idea/artifacts
-# .idea/compiler.xml
-# .idea/jarRepositories.xml
-# .idea/modules.xml
-# .idea/*.iml
-# .idea/modules
-# *.iml
-# *.ipr
-
-# CMake
-cmake-build-*/
-
-# Mongo Explorer plugin
-.idea/**/mongoSettings.xml
-
-# File-based project format
-*.iws
-
-# IntelliJ
-out/
-
-# mpeltonen/sbt-idea plugin
-.idea_modules/
-
-# JIRA plugin
-atlassian-ide-plugin.xml
-
-# Cursive Clojure plugin
-.idea/replstate.xml
-
-# SonarLint plugin
-.idea/sonarlint/
-
-# Crashlytics plugin (for Android Studio and IntelliJ)
-com_crashlytics_export_strings.xml
-crashlytics.properties
-crashlytics-build.properties
-fabric.properties
-
-# Editor-based Rest Client
-.idea/httpRequests
-
-# Android studio 3.1+ serialized cache file
-.idea/caches/build_file_checksums.ser
-
-### CMake template
-CMakeLists.txt.user
-CMakeCache.txt
-CMakeFiles
-CMakeScripts
-Testing
-Makefile
-cmake_install.cmake
-install_manifest.txt
-compile_commands.json
-CTestTestfile.cmake
-_deps
-
-### Python template
-# Byte-compiled / optimized / DLL files
-__pycache__/
-*.py[cod]
-*$py.class
-
-# C extensions
-*.so
-
-# Distribution / packaging
-.Python
-build/
-develop-eggs/
-dist/
-downloads/
-eggs/
-.eggs/
-lib/
-lib64/
-parts/
-sdist/
-var/
-wheels/
-share/python-wheels/
-*.egg-info/
-.installed.cfg
-*.egg
-MANIFEST
-
-# PyInstaller
-#  Usually these files are written by a python script from a template
-#  before PyInstaller builds the exe, so as to inject date/other infos into it.
-*.manifest
-*.spec
-
-# Installer logs
-pip-log.txt
-pip-delete-this-directory.txt
-
-# Unit test / coverage reports
-htmlcov/
-.tox/
-.nox/
-.coverage
-.coverage.*
-.cache
-nosetests.xml
-coverage.xml
-*.cover
-*.py,cover
-.hypothesis/
-.pytest_cache/
-cover/
-
-# Translations
-*.mo
-*.pot
-
-# Django stuff:
-*.log
-local_settings.py
-db.sqlite3
-db.sqlite3-journal
-
-# Flask stuff:
-instance/
-.webassets-cache
-
-# Scrapy stuff:
-.scrapy
-
-# Sphinx documentation
-docs/_build/
-
-# PyBuilder
-.pybuilder/
-target/
-
-# Jupyter Notebook
-.ipynb_checkpoints
-
-# IPython
-profile_default/
-ipython_config.py
-
-# pyenv
-#   For a library or package, you might want to ignore these files since the code is
-#   intended to run in multiple environments; otherwise, check them in:
-# .python-version
-
-# pipenv
-#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
-#   However, in case of collaboration, if having platform-specific dependencies or dependencies
-#   having no cross-platform support, pipenv may install dependencies that don't work, or not
-#   install all needed dependencies.
-#Pipfile.lock
-
-# poetry
-#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
-#   This is especially recommended for binary packages to ensure reproducibility, and is more
-#   commonly ignored for libraries.
-#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
-#poetry.lock
-
-# pdm
-#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
-#pdm.lock
-#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
-#   in version control.
-#   https://pdm.fming.dev/#use-with-ide
-.pdm.toml
-
-# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
-__pypackages__/
-
-# Celery stuff
-celerybeat-schedule
-celerybeat.pid
-
-# SageMath parsed files
-*.sage.py
-
-# Environments
-.env
-.venv
-env/
-venv/
-ENV/
-env.bak/
-venv.bak/
-
-# Spyder project settings
-.spyderproject
-.spyproject
-
-# Rope project settings
-.ropeproject
-
-# mkdocs documentation
-/site
-
-# mypy
-.mypy_cache/
-.dmypy.json
-dmypy.json
-
-# Pyre type checker
-.pyre/
-
-# pytype static type analyzer
-.pytype/
-
-# Cython debug symbols
-cython_debug/
-
-# PyCharm
-#  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
-#  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
-#  and can be added to the global gitignore or merged into this file.  For a more nuclear
-#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
-.idea/
+.idea
 
+*.[oa]
+cmake-build*/

.gitmodules

@@ -0,0 +1,13 @@
+[submodule "vendor/toddcox"]
+	path = vendor/toddcox
+	url = https://github.com/JCRaymond/toddcox-faster.git
+[submodule "vendor/yaml-cpp"]
+	path = vendor/yaml-cpp
+	url = git://github.com/jbeder/yaml-cpp.git
+[submodule "vendor/cgl"]
+	path = vendor/cgl
+	url = git://github.com/allemangD/cgl.git
+[submodule "vendor/nanogui"]
+	path = vendor/nanogui
+	url = https://github.com/allemangD/nanogui
+	branch = master

.idea/misc.xml

@@ -0,0 +1,19 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="CMakeWorkspace" PROJECT_DIR="$PROJECT_DIR$" />
+  <component name="CidrRootsConfiguration">
+    <sourceRoots>
+      <file path="$PROJECT_DIR$/examples" />
+      <file path="$PROJECT_DIR$/vis/include" />
+      <file path="$PROJECT_DIR$/vis/presets" />
+      <file path="$PROJECT_DIR$/vis/shaders" />
+      <file path="$PROJECT_DIR$/vis/src" />
+    </sourceRoots>
+    <libraryRoots>
+      <file path="$PROJECT_DIR$/vendor" />
+    </libraryRoots>
+  </component>
+  <component name="JavaScriptSettings">
+    <option name="languageLevel" value="ES6" />
+  </component>
+</project>

.idea/toddcox-visualize.iml

@@ -0,0 +1,2 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module classpath="CMake" type="CPP_MODULE" version="4" />

.idea/vcs.xml

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>

CMakeLists.txt

@@ -1,14 +1,19 @@
 cmake_minimum_required(VERSION 3.10)
-project(toddcox-faster)
+project(toddcox-visualize)
 
-set(CMAKE_CXX_STANDARD 20)
+set(CMAKE_CXX_STANDARD 17)
 
-file(GLOB externals ext/*.cmake)
-foreach (external ${externals})
-    include(${external})
-endforeach ()
+add_subdirectory(vendor/toddcox)
 
-include(cmake/embed.cmake)
+add_subdirectory(vendor/yaml-cpp)
+
+set(NANOGUI_BUILD_EXAMPLE OFF CACHE BOOL " " FORCE)
+set(NANOGUI_BUILD_PYTHON  OFF CACHE BOOL " " FORCE)
+set(NANOGUI_INSTALL       OFF CACHE BOOL " " FORCE)
+set(NANOGUI_USE_GLAD      ON  CACHE BOOL " " FORCE)
+add_subdirectory(vendor/nanogui)
+set_property(TARGET glfw glfw_objects nanogui PROPERTY FOLDER "dependencies")
 
-add_subdirectory(tc)
 add_subdirectory(vis)
+
+add_subdirectory(examples)

cmake/embed.cmake

@@ -1,86 +0,0 @@
-find_program(EMBED_LD ${CMAKE_LINKER})
-find_program(EMBED_OBJCOPY ${CMAKE_OBJCOPY})
-
-function(_generate_embed_source EMBED_NAME)
-  set(options)
-  set(oneValueArgs SOURCE HEADER)
-  set(multiValueArgs FILES)
-  cmake_parse_arguments(PARSE "${options}" "${oneValueArgs}" "${multiValueArgs}" ${ARGN})
-
-  set(VIEW_DECLARATIONS)
-  set(VOID_DECLARATIONS)
-  set(DEFINITIONS)
-
-  foreach (FILE IN LISTS PARSE_FILES)
-    get_filename_component(FILE_NAME "${FILE}" NAME)
-
-    string(MAKE_C_IDENTIFIER "_binary_${FILE}" SYMBOL)
-    string(MAKE_C_IDENTIFIER "${FILE_NAME}" IDENTIFIER)
-
-    string(APPEND VIEW_DECLARATIONS
-      "  /// ${FILE} Text Contents\n"
-      "  extern std::string_view const ${IDENTIFIER};\n")
-
-    string(APPEND VOID_DECLARATIONS
-      "  /// ${FILE} Binary Contents\n"
-      "  extern void* const ${IDENTIFIER};\n")
-
-    string(APPEND DEFINITIONS
-      "// ${IDENTIFIER} (${FILE})\n"
-      "extern \"C\" const char ${SYMBOL}_start[], ${SYMBOL}_end[];\n"
-      "std::string_view const ${EMBED_NAME}::${IDENTIFIER}(${SYMBOL}_start, ${SYMBOL}_end);\n"
-      "void* const ${EMBED_NAME}::bin::${IDENTIFIER} = (void *) ${SYMBOL}_start;\n\n")
-  endforeach ()
-
-  file(WRITE "${PARSE_HEADER}"
-    "#pragma once\n"
-    "#include <string>\n\n"
-    "namespace ${EMBED_NAME} {\n${VIEW_DECLARATIONS}}\n\n"
-    "namespace ${EMBED_NAME}::bin {\n${VOID_DECLARATIONS}}\n")
-
-  file(WRITE "${PARSE_SOURCE}"
-    "#include <${EMBED_NAME}.hpp>\n\n"
-    "${DEFINITIONS}")
-endfunction()
-
-function(_embed_file OUTPUT_OBJECT FILE)
-  set(OBJECT "${CMAKE_CURRENT_BINARY_DIR}/${FILE}.o")
-
-  set(${OUTPUT_OBJECT} ${OBJECT} PARENT_SCOPE)
-
-  add_custom_command(
-    COMMENT "Embedding ${FILE} in ${OBJECT}"
-    OUTPUT "${FILE}.o" DEPENDS "${FILE}"
-    WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
-    COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}
-    COMMAND ${EMBED_LD} -r -o "${OBJECT}" --format=binary "${FILE}"
-    COMMAND ${EMBED_OBJCOPY} --rename-section .data=.rodata,alloc,load,readonly,data,contents "${OBJECT}"
-    VERBATIM
-  )
-endfunction()
-
-function(add_embed_library EMBED_NAME)
-  set(FILES ${ARGN})
-
-  set(EMBED_ROOT ${CMAKE_CURRENT_BINARY_DIR}/_embed/${EMBED_NAME})
-  set(EMBED_SOURCE "${EMBED_ROOT}/${EMBED_NAME}.cpp")
-  set(EMBED_INCLUDE "${EMBED_ROOT}/include")
-  set(EMBED_HEADER "${EMBED_INCLUDE}/${EMBED_NAME}.hpp")
-
-  set(OBJECTS)
-  foreach (FILE ${ARGN})
-    _embed_file(OBJECT ${FILE})
-    list(APPEND OBJECTS ${OBJECT})
-  endforeach ()
-
-  message(STATUS "Generating embedding library ${EMBED_NAME}")
-  _generate_embed_source(
-    ${EMBED_NAME}
-    SOURCE ${EMBED_SOURCE}
-    HEADER ${EMBED_HEADER}
-    FILES ${FILES})
-
-  add_library(${EMBED_NAME} STATIC ${OBJECTS} "${EMBED_SOURCE}")
-  target_include_directories(${EMBED_NAME} PUBLIC "${EMBED_INCLUDE}")
-  set_target_properties(${EMBED_NAME} PROPERTIES POSITION_INDEPENDENT_CODE ON)
-endfunction()

entt-question.md

@@ -1,71 +0,0 @@
-I have some "composite" objects that I'm not sure how best to map into an ECS. Each composite object has multiple "parts" with various properties. But the parts of a given composite object are intrinsically linked: they transform together and use the same buffers during rendering.
-
-Note that I'm still pretty early in adopting `entt` for this project, so I'm not particularly tied to any of the architecture here. The only constraint is that, for optimization reasons, I need each composite object to get _one_ buffer on GPU, and each part owns some interval within its parent's buffer. This nested scheme seems the most straightforward way to do that.
-
----
-
-My first attempt has only one entity for each composite object, with a `Parts` component that holds an `std::vector<Part>`. 
-
-Rendering code looks something like this. In reality I save the draw commands in a separate component and re-use those on each frame.
-
-```c++
-auto view = registry.view<Parts>();
-
-for (auto [entity, parts]: view.each()) {
-  std::vector<Command> commands;
-
-  for (auto part: parts.parts) {
-    // assemble draw command
-    commands.emplace_back(...);
-  }
-
-  // bind buffers for entity
-  // issue draw command
-}
-```
-
-However it seems appropriate to give each part its own entity. My attempt for this was to switch to `std::vector<entt::entity>` where each entity has a `Part` as a component.
-
-Rendering code then looks like:
-
-```c++
-auto view = registry.view<Parts>();
-
-for (auto [entity, parts]: view.each()) {
-  std::vector<Command> commands;
-
-  for (auto part_entity: parts.parts) {
-    auto &part = registry.get<Part>(part_entity);
-    // assemble draw command
-    commands.emplace_back(...);
-  }
-
-  // bind buffers for entity
-  // issue draw command with shared buffer
-}
-```
-
----
-
-In my last attempt, I invert this so each `Part` holds only parent entity. The `Parts` component is removed. I can then use a `view<Part>` directly, but it's trickier to organize the draw calls since they must be grouped by the parent entity itself.
-
-```c++
-auto view = registry.view<Part>();
-
-for (auto [entity, part]: view.each()) {
-  // assemble draw command
-  auto &commands = registry.get<Commands>(part.parent);
-  commands.emplace_back(...);
-}
-
-for (auto [entity, commands]: view
-for (auto [entity, commands]: commands) {
-   // bind buffers for entity
-   auto &commands = registry.get<Commands>(entity);
-   // issue draw commands
-}
-```
-
----
-
-Is there any more sensible approach to this kind of many-to-one entity composition? Or some way to declare _multiple_ `Part` components on the same entity? It seems like I almost need some group-by kind of operation, but I don't see such on the registry/view docs.

examples/CMakeLists.txt

@@ -0,0 +1 @@
+# there's no examples right now.

ext/eigen.cmake

@@ -1,14 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    eigen
-    GIT_REPOSITORY https://gitlab.com/libeigen/eigen.git
-    GIT_TAG 3.4
-    GIT_PROGRESS TRUE
-)
-
-set(EIGEN_BUILD_DOC OFF CACHE INTERNAL "")
-set(BUILD_TESTING OFF CACHE INTERNAL "")
-set(EIGEN_BUILD_PKGCONFIG OFF CACHE INTERNAL "")
-
-FetchContent_MakeAvailable(eigen)

ext/entt.cmake

@@ -1,10 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    entt
-    GIT_REPOSITORY https://github.com/skypjack/entt.git
-    GIT_TAG v3.11.1
-    GIT_PROGRESS TRUE
-)
-
-FetchContent_MakeAvailable(entt)

ext/fmt.cmake

@@ -1,10 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    fmt
-    GIT_REPOSITORY https://github.com/fmtlib/fmt.git
-    GIT_TAG 9.1.0
-    GIT_PROGRESS TRUE
-)
-
-FetchContent_MakeAvailable(fmt)

ext/glad.cmake

@@ -1,14 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    glad
-    GIT_REPOSITORY https://github.com/Dav1dde/glad.git
-    GIT_TAG v0.1.36
-    GIT_PROGRESS TRUE
-)
-
-set(GLAD_PROFILE "core" CACHE INTERNAL "OpenGL profile")
-set(GLAD_API "gl=4.6" CACHE INTERNAL "API type/version pairs, like \"gl=3.2,gles=\", no version means latest")
-set(GLAD_GENERATOR "c" CACHE INTERNAL "Language to generate the binding for")
-
-FetchContent_MakeAvailable(glad)

ext/glfw.cmake

@@ -1,15 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    glfw
-    GIT_REPOSITORY https://github.com/glfw/glfw.git
-    GIT_TAG 3.3.8
-    GIT_PROGRESS TRUE
-)
-
-set(GLFW_BUILD_EXAMPLES OFF CACHE INTERNAL "")
-set(GLFW_BUILD_TESTS OFF CACHE INTERNAL "")
-set(GLFW_BUILD_DOCS OFF CACHE INTERNAL "")
-set(GLFW_INSTALL OFF CACHE INTERNAL "")
-
-FetchContent_MakeAvailable(glfw)

ext/gtest.cmake

@@ -1,12 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    gtest
-    GIT_REPOSITORY https://github.com/google/googletest.git
-    GIT_TAG release-1.12.1
-    GIT_PROGRESS TRUE
-)
-
-set(gtest_force_shared_crt ON CACHE BOOL "" FORCE)
-
-FetchContent_MakeAvailable(gtest)

ext/imgui.cmake

@@ -1,31 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    imgui
-    GIT_REPOSITORY https://github.com/ocornut/imgui
-    GIT_TAG v1.86
-    GIT_PROGRESS TRUE
-)
-
-FetchContent_GetProperties(imgui)
-if (NOT ${imgui}_POPULATED)
-    FetchContent_MakeAvailable(imgui)
-
-    add_library(
-        imgui
-        ${imgui_SOURCE_DIR}/backends/imgui_impl_glfw.cpp
-        ${imgui_SOURCE_DIR}/backends/imgui_impl_glfw.h
-        ${imgui_SOURCE_DIR}/backends/imgui_impl_opengl3.cpp
-        ${imgui_SOURCE_DIR}/backends/imgui_impl_opengl3.h
-        ${imgui_SOURCE_DIR}/imgui.cpp
-        ${imgui_SOURCE_DIR}/imgui.h
-        ${imgui_SOURCE_DIR}/imgui_demo.cpp
-        ${imgui_SOURCE_DIR}/imgui_draw.cpp
-        ${imgui_SOURCE_DIR}/imgui_tables.cpp
-        ${imgui_SOURCE_DIR}/imgui_widgets.cpp
-    )
-
-    target_include_directories(imgui PUBLIC ${imgui_SOURCE_DIR})
-    target_link_libraries(imgui PRIVATE glfw)
-endif ()
-

ext/peglib.cmake

@@ -1,20 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    peglib
-    GIT_REPOSITORY https://github.com/yhirose/cpp-peglib
-    GIT_TAG v1.8.2
-    GIT_PROGRESS TRUE
-)
-
-set(PEGLIB_BUILD_TESTS OFF CACHE INTERNAL "")
-
-FetchContent_GetProperties(peglib)
-if(NOT ${peglib}_POPULATED)
-    FetchContent_Populate(peglib)
-    find_package(Threads)
-    add_library(peglib INTERFACE ${peglib_SOURCE_DIR}/peglib.h)
-    target_include_directories(peglib INTERFACE ${peglib_SOURCE_DIR})
-    target_link_libraries(peglib INTERFACE Threads::Threads)
-    add_library(peglib::peglib ALIAS peglib)
-endif()

ext/yaml-cpp.cmake

@@ -1,15 +0,0 @@
-include(FetchContent)
-
-FetchContent_Declare(
-    yaml-cpp
-    GIT_REPOSITORY https://github.com/jbeder/yaml-cpp.git
-    GIT_TAG yaml-cpp-0.7.0
-    GIT_PROGRESS TRUE
-)
-
-set(GLFW_BUILD_EXAMPLES OFF CACHE INTERNAL "")
-set(GLFW_BUILD_TESTS OFF CACHE INTERNAL "")
-set(GLFW_BUILD_DOCS OFF CACHE INTERNAL "")
-set(GLFW_INSTALL OFF CACHE INTERNAL "")
-
-FetchContent_MakeAvailable(yaml-cpp)

tc/CMakeLists.txt

@@ -1,17 +0,0 @@
-add_library(tc
-    include/tc/core.hpp
-    include/tc/groups.hpp
-
-    src/cosets.cpp
-    src/group.cpp
-    src/groups.cpp
-    src/lang.cpp
-    src/solve.cpp
-    )
-target_link_libraries(tc peglib fmt)
-target_include_directories(tc PUBLIC include)
-
-add_library(tc::tc ALIAS tc)
-
-add_subdirectory(test)
-add_subdirectory(bench)

tc/bench/CMakeLists.txt

@@ -1,5 +0,0 @@
-add_executable(benchmark benchmark.cpp)
-target_link_libraries(benchmark PUBLIC tc fmt::fmt)
-
-add_executable(named named.cpp)
-target_link_libraries(named PUBLIC tc fmt::fmt)

tc/bench/benchmark.cpp

@@ -1,138 +0,0 @@
-#include <ctime>
-#include <string>
-#include <vector>
-
-#include <fmt/core.h>
-#include <fmt/ranges.h>
-
-#include <tc/core.hpp>
-#include <tc/groups.hpp>
-
-void bench(
-    const std::string &group_expr,
-    const std::string &symbol,
-    const std::vector<size_t> &gens,
-    const size_t bound = SIZE_MAX
-) {
-    tc::Group<> group = tc::coxeter(symbol);
-    
-    std::clock_t s = std::clock();
-    tc::Cosets<> cosets = group.solve(gens, bound);
-    std::clock_t e = std::clock();
-
-    auto time = (double) (e - s) / CLOCKS_PER_SEC;
-    size_t order = cosets.order();
-    auto cos_s = (size_t) (order / time);
-
-    bool complete = cosets.complete();
-
-    std::string name = fmt::format("{}/{}", group_expr, gens);
-    std::string row = fmt::format(
-        "{:>24},{:>10},{:>6},{:>8.3f}s,{:>10L}",
-        name, order, complete, time, cos_s
-    );
-    fmt::print("{}\n", row);
-}
-
-int main(int argc, char *argv[]) {
-    std::vector<std::string> args(argv + 1, argv + argc);
-
-    fmt::print("{:>24},{:>10},{:>6},{:>9},{:>10}\n", "NAME", "ORDER", "COMPL", "TIME", "COS/S");
-
-    // Finite Groups
-    
-    // A_n: 3 * `n-1`           ; n >= 1
-    bench("A_5", "3 * 4", {});
-    bench("A_6", "3 * 5", {});
-    bench("A_7", "3 * 6", {});
-    bench("A_8", "3 * 7", {});
-    // B_n: 4 3 * `n-2`         ; n >= 2
-    bench("B_5", "4 3 * 3", {});
-    bench("B_6", "4 3 * 4", {});
-    bench("B_7", "4 3 * 5", {});
-    bench("B_8", "4 3 * 6", {});
-    // D_n: 3 * [1 1 `n-3`]     ; n >= 4
-    bench("D_5", "3 * [1 1 2]", {});
-    bench("D_6", "3 * [1 1 3]", {});
-    bench("D_7", "3 * [1 1 4]", {});
-    bench("D_8", "3 * [1 1 5]", {});
-    // E_n: 3 * [1 2 `n-4`]     ; n >= 6
-    bench("E_6", "3 * [1 2 2]", {});
-    bench("E_7", "3 * [1 2 3]", {});
-//    bench("E_8", "3 * [1 2 4]", {}); // too big
-    // H_n: 5 3 * `n-2`         ; n >= 2
-    bench("H_3", "5 3 * 0", {});
-    bench("H_4", "5 3 * 1", {});
-    bench("H_5", "5 3 * 2", {});
-    // grid: `p` `q`            ; 2(p+q) > pq
-    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r > 1
-
-    // Special Finite Groups
-    bench("F_4", "3 4 3", {});
-    bench("G_2", "6", {});
-    // I_2(p): `p`              ; p >= 2
-    bench("I_2(100)", "100", {});
-    bench("I_2(1000)", "1000", {});
-    // "Torus": `p` 2 `q`       ; p, q >= 2
-    bench("T(100)", "100 2 100", {});
-    bench("T(1000)", "1000 2 1000", {});
-
-    // Affine Groups
-    
-    // ~A_n: {3 * `n+1`}
-    bench("~A_5", "{3 * 6}", {}, 10'000'000);
-    bench("~A_6", "{3 * 7}", {}, 10'000'000);
-    bench("~A_7", "{3 * 8}", {}, 10'000'000);
-    bench("~A_8", "{3 * 9}", {}, 10'000'000);
-    // ~B_n: 4 3 * `n-3` 3 * [1 1]
-    bench("~B_5", "4 3 * 2 3 * [1 1]", {}, 10'000'000);
-    bench("~B_6", "4 3 * 3 3 * [1 1]", {}, 10'000'000);
-    bench("~B_7", "4 3 * 4 3 * [1 1]", {}, 10'000'000);
-    bench("~B_8", "4 3 * 5 3 * [1 1]", {}, 10'000'000);
-    // ~B_n: 4 3 * `n-2` 4
-    bench("~C_5", "4 3 * 3 4", {}, 10'000'000);
-    bench("~C_6", "4 3 * 4 4", {}, 10'000'000);
-    bench("~C_7", "4 3 * 5 4", {}, 10'000'000);
-    bench("~C_8", "4 3 * 6 4", {}, 10'000'000);
-    // ~D_n: 3 * [1 1] 3 * `n-4` 3 * [1 1]
-    bench("~D_5", "3 * [1 1] 3 * 1 3 * [1 1]", {}, 10'000'000);
-    bench("~D_6", "3 * [1 1] 3 * 2 3 * [1 1]", {}, 10'000'000);
-    bench("~D_7", "3 * [1 1] 3 * 3 3 * [1 1]", {}, 10'000'000);
-    bench("~D_8", "3 * [1 1] 3 * 4 3 * [1 1]", {}, 10'000'000);
-    // grid: `p` `q`            ; 2(p+q) = pq
-    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r = 1
-    
-    // Special Affine Groups
-    bench("~I_1", "-", {}, 10'000'000);
-    bench("~E_6", "3 * [2 2 2]", {}, 10'000'000);
-    bench("~E_7", "3 * [1 3 3]", {}, 10'000'000);
-    bench("~E_8", "3 * [1 2 5]", {}, 10'000'000);
-//    bench("E_9",  "3 * [1 2 5]", {}, 10'000'000);  // ~E_8 == E_9
-    bench("~F_4", "3 4 3 3", {}, 10'000'000);
-    bench("~G_2", "6 3", {}, 10'000'000);
-
-    // Hyperbolic Groups
-    // grid: `p` `q`            ; 2(p+q) < pq
-    // triangle: `p` `q` `r`    ; 1/p + 1/q + 1/r < 1
-    
-    // Special Hyperbolic Groups
-    bench("-BH_3", "4 3 5", {}, 10'000'000);
-    bench("-K_3", "5 3 5", {}, 10'000'000);
-    bench("-J_3", "3 5 3", {}, 10'000'000);
-//    bench("~H_3", "3 5 3", {}, 10'000'000);  // -J_3 == ~H_3
-    bench("-DH_3", "5 3 * [1 1]", {}, 10'000'000);
-    bench("^AB_3", "{3 3 3 4}", {}, 10'000'000);
-    bench("^AH_3", "{3 3 3 5}", {}, 10'000'000);
-    bench("^BB_3", "{3 4 3 4}", {}, 10'000'000);
-    bench("^BH_3", "{3 4 3 5}", {}, 10'000'000);
-    bench("^HH_3", "{3 5 3 5}", {}, 10'000'000);
-    bench("-H_4", "5 3 3 3", {}, 10'000'000);
-//    bench("~H_4", "5 3 3 3", {}, 10'000'000);  // -H_4 == ~H_4 == H_5 
-//    bench("H_5", "5 3 3 3", {}, 10'000'000);
-    bench("-BH_4", "4 3 3 5", {}, 10'000'000);
-    bench("-K_4", "5 3 3 5", {}, 10'000'000);
-    bench("-DH_4", "5 3 3 * [1 1]", {}, 10'000'000);
-    bench("^AF_4", "{3 3 3 3 4}", {}, 10'000'000);
-    
-    return EXIT_SUCCESS;
-}

tc/bench/named.cpp

@@ -1,149 +0,0 @@
-#include <string>
-#include <vector>
-
-#include <fmt/core.h>
-#include <fmt/ranges.h>
-
-#include <tc/core.hpp>
-
-using namespace std::string_literals;
-
-template<typename Gen_>
-struct fmt::formatter<tc::Group<Gen_>> {
-    template<typename ParseContext>
-    constexpr auto parse(ParseContext &ctx) {
-        return ctx.begin();
-    }
-
-    template<typename FormatContext>
-    constexpr auto format(tc::Group<Gen_> const &g, FormatContext &ctx) {
-        auto gens = g.gens();
-
-        fmt::format_to(ctx.out(), "  | ");
-        for (const auto &gen: gens) {
-            fmt::format_to(ctx.out(), "{} ", gen);
-        }
-        fmt::format_to(ctx.out(), "\n");
-
-        for (int i = 0; i < gens.size(); ++i) {
-            auto u = gens[i];
-
-            fmt::format_to(ctx.out(), "{} | ", u);
-
-            for (int j = 0; j < gens.size(); ++j) {
-                auto v = gens[j];
-
-                if (i <= j) {
-                    fmt::format_to(ctx.out(), "{} ", g.get(u, v));
-                } else {
-                    fmt::format_to(ctx.out(), "  ");
-                }
-            }
-
-            fmt::format_to(ctx.out(), "\n");
-        }
-
-        return ctx.out();
-    }
-};
-
-template<typename Gen_>
-struct fmt::formatter<tc::Cosets<Gen_>> {
-    template<typename ParseContext>
-    constexpr auto parse(ParseContext &ctx) {
-        return ctx.begin();
-    }
-
-    template<typename FormatContext>
-    constexpr auto format(tc::Cosets<Gen_> const &c, FormatContext &ctx) {
-        auto gens = c.gens();
-
-        auto width = (size_t) (std::log10(c.order() + 1));
-
-        fmt::format_to(ctx.out(), "{:>{}} | ", "-", width);
-        for (const auto &gen: gens) {
-            fmt::format_to(ctx.out(), "{:>{}} ", gen, width);
-        }
-        fmt::format_to(ctx.out(), "\n");
-
-        for (size_t cos = 0; cos < c.order(); ++cos) {
-            fmt::format_to(ctx.out(), "{:>{}} | ", cos, width);
-
-            for (const auto &gen: gens) {
-                auto target = c.get(cos, gen);
-
-                fmt::format_to(ctx.out(), "{:>{}} ", target, width);
-            }
-
-            fmt::format_to(ctx.out(), "\n");
-        }
-
-        return ctx.out();
-    }
-};
-
-int main() {
-    tc::Group<char> group(4, {'r', 'g', 'b', 'y'});
-
-    group.set('r', 'g', 5);
-    group.set('g', 'b', 3);
-    group.set('b', 'y', 3);
-
-    fmt::print("{}\n", group);
-
-//    auto res = group.sub({'r', 'g', 'b', 'y'}).solve();
-    auto res = group.sub({'r', 'g'}).solve();
-    fmt::print("rank: {}, order: {}\n{}\n",
-               res.rank(), res.order(), res);
-
-//    tc::Path<> path(res);
-//    auto gens = group.gens();
-//    std::vector<std::string> words(path.order());
-//    path.walk(
-//        "-"s,
-//        [&](const std::string &cos, size_t gen) -> std::string {
-//            return cos + gens[gen];
-//        },
-//        words.begin());
-
-    tc::Path<char> typed(res);
-    std::vector<std::string> words(typed.order());
-    typed.walk("-"s, std::plus<>(), words.begin());
-
-    fmt::print("words: {}\n", words);
-    fmt::print("size: {}\n", words.size());
-
-//    path.walk(
-//        words.begin(),
-//        "-",
-//        [&gens](const std::string &cos, size_t gen) {
-//            return cos + gens[gen];
-//        }
-//    );
-//    for (const auto &word: words) {
-//        fmt::print("'{}'\n", word);
-//    }
-
-//    auto sub = group.sub({'r', 'g', 'y'});
-//    fmt::print("{}\n", sub);
-//
-//    auto res = sub.solve({});
-//    fmt::print("res order: {}\n", res.order());
-//
-//    auto cos = sub.solve({'r', 'y'});
-
-//    fmt::print("order: {}\n", cos.order());
-//
-//    fmt::print("{}\n", cos);
-
-//    tc::Group<u_int8_t> group(4, {0, 1, 2, 3});
-//
-//    group.set(0, 1, 5);
-//    group.set(1, 2, 4);
-//    group.set(2, 3, 3);
-//
-//    show(group);
-//
-//    auto sub = group.sub({3, 2, 0, 1});
-//    show(sub);
-}

tc/include/tc/core.hpp

@@ -1,194 +0,0 @@
-#pragma once
-
-#include <vector> //todo clean up includes. lots of duplicate cstdint, cassert.
-#include <cstdint>
-#include <cassert>
-#include <tuple>
-
-#include <limits>
-
-namespace tc {
-    using Mult = std::uint16_t;
-    constexpr Mult FREE = 0;
-
-    /**
-     * @brief Complete representation of a quotient group. Describes the action of each generator on each coset.
-     */
-    struct Cosets;
-
-    /** 
-     * @brief Manage the presentation of a Coxeter group and enforce constraints
-     * on the multiplicities of its relations.
-     * <ul>
-     *   <li>
-     *     <code>m_ij = 1</code> iff <code>i != j</code>
-     *   </li>
-     *   <li>
-     *     <code>m_ij = m_ji</code>
-     *   </li>
-     *   <li>
-     *     If <code>m_ij == inf</code> (<code>tc::FREE</code>) then no relation is imposed.
-     *   </li>
-     * </ul>
-     * @see
-     * <a href="https://en.wikipedia.org/wiki/Coxeter_group#Definition">Coxeter Group (Wikipedia)</a>
-     */
-    struct Group;
-
-    /**
-     * @brief Support generating values given a Cosets and transformation callback.
-     * @tparam Gen_ 
-     */
-    template<typename Gen_=void>
-    struct Path;
-
-    struct Cosets {
-        static constexpr size_t UNSET = std::numeric_limits<size_t>::max();
-
-    private:
-        size_t _rank;
-        size_t _order;
-        bool _complete;
-        std::vector<size_t> _data;
-
-    public:
-        Cosets(Cosets const &) = default;
-
-        Cosets(Cosets &&) noexcept = default;
-
-        ~Cosets() = default;
-
-        void set(size_t coset, size_t gen, size_t target);
-
-        [[nodiscard]] size_t get(size_t coset, size_t gen) const;
-
-        [[nodiscard]] bool isset(size_t coset, size_t gen) const;
-
-        [[nodiscard]] size_t rank() const;
-
-        [[nodiscard]] size_t order() const;
-
-        [[nodiscard]] bool complete() const;
-
-        [[nodiscard]] size_t size() const;
-
-        friend Group;  // only constructible via Group<>::solve
-
-    private:
-        explicit Cosets(size_t rank);
-
-        void add_row();
-
-        void set(size_t idx, size_t target);
-
-        [[nodiscard]] size_t get(size_t idx) const;
-
-        [[nodiscard]] bool isset(size_t idx) const;
-    };
-
-    struct Group {
-        using Rel = std::tuple<size_t, size_t, Mult>;
-
-    private:
-        size_t _rank;
-        std::vector<size_t> _mults;
-        std::vector<size_t> _gens;
-
-    public:
-        Group(Group const &) = default;
-
-        Group(Group &&) noexcept = default;
-
-        ~Group() = default;
-
-        explicit Group(size_t rank);
-
-        void set(size_t, size_t, Mult);
-
-        [[nodiscard]] Mult get(size_t, size_t) const;
-
-        [[nodiscard]] size_t rank() const;
-
-        [[nodiscard]] std::vector<size_t> gens() const;
-
-        [[nodiscard]] Group sub(std::vector<size_t> const &gens) const;
-
-        [[nodiscard]] std::vector<Group> subs(size_t rank) const;
-
-        [[nodiscard]] Cosets solve(std::vector<size_t> const &idxs = {}, size_t bound = SIZE_MAX) const;
-    };
-
-    template<>
-    struct Path<> {
-        using Action = std::tuple<size_t, size_t>;  // coset, gen
-
-    private:
-        std::vector<Action> _data;
-
-    public:
-        // todo be smarter about move semantics
-
-        explicit Path(Cosets const &cosets) : _data() {
-            _data.resize(cosets.order());
-
-            std::vector<bool> complete(cosets.order(), false);
-
-            complete[0] = true;
-
-            for (size_t cos = 0; cos < cosets.order(); ++cos) {
-                for (size_t gen = 0; gen < cosets.rank(); ++gen) {
-                    size_t tgt = cosets.get(cos, gen);
-                    if (!complete[tgt]) {
-                        _data[tgt] = {cos, gen};
-                        complete[tgt] = true;
-                    }
-                }
-            }
-        }
-
-        template<typename Elem, typename BinaryOp, std::random_access_iterator It>
-        void walk(Elem const &start, BinaryOp op, It out) {
-            // todo how to work for std::back_insert_iterator?
-            // todo how to work for non-default-constructible values?
-
-            out[0] = start;
-
-            for (int tgt = 1; tgt < _data.size(); ++tgt) {
-                auto [cos, gen] = _data[tgt];
-                out[tgt] = op(out[cos], gen);
-            }
-        }
-
-        template<typename Elem, typename BinaryOp, std::random_access_iterator It, std::random_access_iterator Gens>
-        void walk(Elem const &start, BinaryOp op, It out, Gens const &gens) {
-            out[0] = start;
-
-            for (int tgt = 1; tgt < _data.size(); ++tgt) {
-                auto [cos, gen] = _data[tgt];
-                out[tgt] = op(out[cos], gens[gen]);
-            }
-        }
-
-        [[nodiscard]] size_t order() const {
-            return _data.size();
-        }
-    };
-
-    template<typename Gen_>
-    struct Path : public Path<> {
-        using Gen = Gen_;
-
-    private:
-        std::vector<Gen> _index;
-
-    public:
-        template<typename T>
-        Path(Cosets const &cosets, T &&gens)
-            : Path<>(cosets), _index(std::forward<T>(gens).begin(), std::forward<T>(gens).end()) {}
-
-        template<typename Elem, typename BinaryOp, std::random_access_iterator It>
-        void walk(Elem const &start, BinaryOp op, It out) {
-            Path<>::walk(start, op, out, _index.begin());
-        }
-    };
-}

tc/include/tc/groups.hpp

@@ -1,24 +0,0 @@
-#pragma once
-
-#include <vector>
-#include <string>
-
-#include <tc/core.hpp>
-
-namespace tc {
-    /**
-     * 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<unsigned int> &mults);
-
-    Group coxeter(const std::string &symbol);
-
-    Group vcoxeter(const std::string &symbol, const std::vector<unsigned int> &values);
-
-    template<typename ...Args>
-    Group coxeter(const std::string &symbol, const Args &... args) {
-        std::vector<unsigned int> values = {{args...}};
-        return vcoxeter(symbol, values);
-    }
-}

tc/src/cosets.cpp

@@ -1,55 +0,0 @@
-#include <tc/core.hpp>
-
-namespace tc {
-    Cosets::Cosets(size_t rank)
-        : _rank(rank), _order(0), _complete(false), _data() {}
-
-    void Cosets::set(size_t coset, size_t gen, size_t target) {
-        set(coset * rank() + gen, target);
-    }
-
-    [[nodiscard]] size_t Cosets::get(size_t coset, size_t gen) const {
-        return get(coset * rank() + gen);
-    }
-
-    [[nodiscard]] bool Cosets::isset(size_t coset, size_t gen) const {
-        return isset(coset * rank() + gen);
-    }
-
-    [[nodiscard]] size_t Cosets::rank() const {
-        return _rank;
-    }
-
-    [[nodiscard]] size_t Cosets::order() const {
-        return _order;
-    }
-
-    [[nodiscard]] bool Cosets::complete() const {
-        return _complete;
-    }
-
-    [[nodiscard]] size_t Cosets::size() const {
-        return _data.size();
-    }
-
-    void Cosets::add_row() {
-        _data.resize(_data.size() + rank(), UNSET);
-        _order++;
-    }
-
-    void Cosets::set(size_t idx, size_t target) {
-        size_t coset = idx / rank();
-        size_t gen = idx % rank();
-        _data[idx] = target;
-        _data[target * rank() + gen] = coset;
-    }
-
-    [[nodiscard]] size_t Cosets::get(size_t idx) const {
-        return _data[idx];
-    }
-
-    [[nodiscard]] bool Cosets::isset(size_t idx) const {
-        return get(idx) != UNSET;
-    }
-
-}

tc/src/group.cpp

@@ -1,72 +0,0 @@
-#include <tc/core.hpp>
-
-#include <cassert>
-#include <numeric>
-
-namespace tc {
-    Group::Group(size_t rank) : _rank(rank), _mults(_rank * _rank, 2), _gens(_rank) {
-        std::iota(_gens.begin(), _gens.end(), 0);
-
-        for (int idx = 0; idx < rank; ++idx) {
-            set(idx, idx, 1);
-        }
-    }
-
-    void Group::set(size_t u, size_t v, Mult m) {
-        assert(u < rank());
-        assert(v < rank());
-
-        _mults[u * rank() + v] = m;
-        _mults[v * rank() + u] = m;
-    }
-
-    [[nodiscard]] Mult Group::get(size_t u, size_t v) const {
-        assert(u < rank());
-        assert(v < rank());
-
-        return _mults[u * rank() + v];
-    }
-
-    [[nodiscard]] size_t Group::rank() const {
-        return _rank;
-    }
-
-    [[nodiscard]] std::vector<size_t> Group::gens() const {
-        return _gens;
-    }
-
-    [[nodiscard]] Group Group::sub(std::vector<size_t> const &gens) const {
-        Group res(gens.size());
-        res._gens = gens;
-
-        for (int i = 0; i < gens.size(); ++i) {
-            for (int j = i; j < gens.size(); ++j) {
-                res.set(i, j, get(gens[i], gens[j]));
-            }
-        }
-
-        return res;
-    }
-
-    [[nodiscard]] std::vector<Group> Group::subs(size_t rank) const {
-        std::vector<bool> mask(_rank, false);
-        std::fill(mask.begin(), mask.begin() + rank, true);
-
-        std::vector<size_t> sub_gens(rank);
-
-        std::vector<Group> res;
-
-        do {
-            for (int i = 0, j = 0; i < _rank; ++i) {
-                if (mask[i]) sub_gens[j++] = i;
-            }
-            res.push_back(sub(sub_gens));
-        } while (std::next_permutation(
-            mask.begin(),
-            mask.end(),
-            std::greater<>()
-        ));
-
-        return res;
-    }
-}

tc/src/groups.cpp

@@ -1,25 +0,0 @@
-#include <tc/groups.hpp>
-
-#include <fmt/args.h>
-#include <fmt/core.h>
-#include <numeric>
-
-namespace tc {
-    Group schlafli(const std::vector<unsigned int> &mults) {
-        Group res(mults.size() + 1);
-        for (size_t i = 0; i < mults.size(); ++i) {
-            res.set(i, i + 1, mults[i]);
-        }
-        return res;
-    }
-
-    Group vcoxeter(const std::string &symbol, const std::vector<unsigned int> &values) {
-        fmt::dynamic_format_arg_store<fmt::format_context> ds;
-
-        for (const auto &value: values) {
-            ds.push_back(value);
-        }
-
-        return coxeter(fmt::vformat(symbol, ds));
-    }
-}

tc/src/lang.cpp

@@ -1,299 +0,0 @@
-#include <vector>
-#include <stack>
-#include <string>
-#include <cassert>
-
-#include <tc/core.hpp>
-#include <tc/groups.hpp>
-
-#include <peglib.h>
-
-#include <fmt/core.h>
-#include <fmt/ranges.h>
-#include <numeric>
-
-struct Graph {
-    size_t rank{};
-    std::vector<tc::Group::Rel> edges{};
-};
-
-struct Op {
-    enum Code {
-        LINK,
-        PUSH,
-        POP,
-        LOOP,
-        FREE,
-    };
-
-    Code code: 4;
-    unsigned int value: 12;
-
-    explicit Op(Code code, unsigned int value = 0)
-        : code(code), value(value) {}
-};
-
-template<>
-struct fmt::formatter<Op> {
-    template<typename ParseContext>
-    constexpr auto parse(ParseContext &ctx) {
-        return ctx.begin();
-    }
-
-    template<typename FormatContext>
-    auto format(const Op &op, FormatContext &ctx) {
-        switch (op.code) {
-            case Op::LINK:
-                return fmt::format_to(ctx.out(), "link({})",
-                                      (unsigned int) op.value);
-            case Op::PUSH:
-                return fmt::format_to(ctx.out(), "push()");
-            case Op::POP:
-                return fmt::format_to(ctx.out(), "pop()");
-            case Op::LOOP:
-                return fmt::format_to(ctx.out(), "loop()");
-            case Op::FREE:
-                return fmt::format_to(ctx.out(), "free()");
-            default:
-                return fmt::format_to(ctx.out(), "[{}]({})",
-                                      (unsigned int) op.code,
-                                      (unsigned int) op.value);
-        }
-    }
-};
-
-struct Factor {
-    unsigned int mode;
-    std::vector<unsigned int> orders;
-};
-
-struct codegen {
-    std::vector<Op> ops;
-
-    void link(unsigned int order) {
-        ops.emplace_back(Op::LINK, order);
-    }
-
-    void push() {
-        ops.emplace_back(Op::PUSH);
-    }
-
-    void pop() {
-        ops.emplace_back(Op::POP);
-    }
-
-    void loop() {
-        ops.emplace_back(Op::LOOP);
-    }
-
-    void free() {
-        ops.emplace_back(Op::FREE);
-    }
-
-    template<typename It>
-    void insert(It begin, It end) {
-        std::copy(begin, end, std::back_inserter(ops));
-    }
-
-    void insert(const codegen &o) {
-        insert(o.ops.begin(), o.ops.end());
-    }
-};
-
-static const std::string GRAMMAR = R"(
-    root    <- term+
-    term    <- product / op
-    op      <- block / link
-    block   <- '(' root ')' / '{' root '}' / '[' root ']'
-    link    <- int / '-'
-    product <- op '*' factor
-    factor  <- int / '{' int+ '}' / '[' int+ ']'
-    int     <- < [0-9]+ >
-
-    %whitespace <- [ \t\n\r]*
-)";
-
-peg::parser build_parser() {
-    peg::parser parser;
-    parser.set_logger([](size_t line, size_t col, const std::string &msg, const std::string &rule) {
-        fmt::print(stderr, "{}:{} [{}] {}\n", line, col, rule, msg);
-    });
-    auto ok = parser.load_grammar(GRAMMAR);
-    assert(ok);
-
-    parser["int"] = [](const peg::SemanticValues &vs) -> std::any {
-        return vs.token_to_number<unsigned int>();
-    };
-
-    parser["link"] = [](const peg::SemanticValues &vs) -> std::any {
-        codegen cg;
-
-        if (vs.choice() == 0) {
-            auto order = std::any_cast<unsigned int>(vs[0]);
-            cg.link(order);
-        } else {
-            cg.free();
-        }
-
-        return cg;
-    };
-
-    parser["root"] = [](const peg::SemanticValues &vs) -> std::any {
-        codegen cg;
-
-        for (const auto &sub: vs) {
-            cg.insert(std::any_cast<codegen>(sub));
-        }
-
-        return cg;
-    };
-
-    parser["block"] = [](const peg::SemanticValues &vs) -> std::any {
-        if (vs.choice() == 0) return vs[0];
-
-        codegen cg;
-
-        cg.push();
-        cg.insert(std::any_cast<codegen>(vs[0]));
-        if (vs.choice() == 1) cg.loop();
-        cg.pop();
-
-        return cg;
-    };
-
-    parser["factor"] = [](const peg::SemanticValues &vs) -> std::any {
-        return Factor{
-            (unsigned int) vs.choice(),
-            vs.transform<unsigned int>(),
-        };
-    };
-
-    parser["product"] = [](const peg::SemanticValues &vs) -> std::any {
-        auto sub = std::any_cast<codegen>(vs[0]);
-        auto fac = std::any_cast<Factor>(vs[1]);
-
-        codegen cg;
-
-        for (const auto &order: fac.orders) {
-            if (fac.mode == 0) {
-                for (unsigned int i = 0; i < order; ++i) {
-                    cg.insert(sub);
-                }
-            } else {
-                cg.push();
-                for (unsigned int i = 0; i < order; ++i) {
-                    cg.insert(sub);
-                }
-                if (fac.mode == 1) cg.loop();
-                cg.pop();
-            }
-        }
-
-        return cg;
-    };
-
-    return parser;
-}
-
-#ifndef NDEBUG
-
-peg::parser build_ast_parser() {
-    peg::parser parser;
-    parser.set_logger([](size_t line, size_t col, const std::string &msg, const std::string &rule) {
-        fmt::print(stderr, "{}:{} [{}] {}\n", line, col, rule, msg);
-    });
-    auto ok = parser.load_grammar(GRAMMAR);
-    assert(ok);
-
-    parser.enable_ast();
-
-    return parser;
-}
-
-#endif
-
-std::vector<Op> compile(const std::string &source) {
-#ifndef NDEBUG
-    static peg::parser ast_parser = build_ast_parser();
-    std::shared_ptr<peg::Ast> ast;
-    bool ast_ok = ast_parser.parse(source, ast);
-    assert(ast_ok);
-//    std::cout << peg::ast_to_s(ast) << std::endl;
-#endif
-
-    static peg::parser parser = build_parser();
-    codegen cg;
-    bool ok = parser.parse(source, cg);
-    assert(ok);
-    return cg.ops;
-}
-
-Graph eval(const std::vector<Op> &ops) {
-    std::vector<std::stack<size_t>> stacks(1);
-
-    Graph g;
-    stacks.back().emplace(g.rank++);
-
-    for (const auto &op: ops) {
-        switch (op.code) {
-            case Op::FREE:
-            case Op::LINK: {
-                tc::Mult order = tc::FREE;
-
-                if (op.code == Op::LINK) {
-                    order = op.value;
-                }
-
-                auto top = stacks.back().top();
-                auto curr = g.rank++;
-
-                stacks.back().emplace(curr);
-                g.edges.emplace_back(top, curr, order);
-
-                break;
-            }
-            case Op::PUSH: {
-                stacks.emplace_back();
-
-                auto ptop = stacks[stacks.size() - 2].top();
-                stacks.back().emplace(ptop);
-
-                break;
-            }
-            case Op::POP: {
-                stacks.pop_back();
-
-                break;
-            }
-            case Op::LOOP: {
-                g.rank--;
-
-                auto ptop = stacks[stacks.size() - 2].top();
-                auto &[top, _, order] = g.edges.back();
-
-                stacks.back().pop();
-                g.edges.pop_back();
-
-                g.edges.emplace_back(top, ptop, order);
-
-                break;
-            }
-            default:
-                throw std::runtime_error("Invalid opcode");
-        }
-    }
-
-    return g;
-}
-
-namespace tc {
-    Group coxeter(const std::string &symbol) {
-        auto ops = compile(symbol);
-        auto diagram = eval(ops);
-        Group res(diagram.rank);
-        for (const auto &[i, j, m]: diagram.edges) {
-            res.set(i, j, m);
-        }
-        return res;
-    }
-}

tc/src/solve.cpp

@@ -1,211 +0,0 @@
-#include <algorithm>
-#include <queue>
-#include <utility>
-#include <vector>
-
-#include <tc/core.hpp>
-
-namespace tc {
-    /**
-     * Each coset is associated a row in each table.
-     * Rows document the "loops" formed by 
-     */
-    struct Row {
-        bool free: 1;
-        bool idem: 1;
-        unsigned int gnr: 14;  // progress through the loop
-        unsigned int lst_idx: 32;  // the coset that would complete the loop
-
-        Row() : free(true), idem(false), gnr(0), lst_idx(0) {}
-    };
-
-    struct Tables {
-        std::vector<Group::Rel> rels;
-        std::vector<std::vector<Row>> rows;
-
-        explicit Tables(std::vector<Group::Rel> rels)
-            : rels(std::move(rels)), rows() {
-        }
-
-        [[nodiscard]] size_t size() const {
-            return rels.size();
-        }
-
-        void add_row() {
-            rows.emplace_back(rels.size());
-        }
-    };
-
-    [[nodiscard]] Cosets Group::solve(std::vector<size_t> const &idxs, size_t bound) const {
-        // region Initialize Cosets Table
-        Cosets cosets(rank());
-        cosets.add_row();
-
-        if (rank() == 0) {
-            cosets._complete = true;
-            return cosets;
-        }
-
-        for (size_t g: idxs) {
-            if (g < rank())
-                cosets.set(0, g, 0);
-        }
-        // endregion
-
-        // region Initialize Relation Tables
-        std::vector<Group::Rel> rels;
-        for (int i = 0; i < rank(); ++i) {
-            for (int j = i + 1; j < rank(); ++j) {
-                // The algorithm only works for Coxeter groups; multiplicities m_ii=1 are assumed. Relation tables
-                // _may_ be added for them, but they are redundant and hurt performance so are skipped.
-                if (i == j) continue;
-
-                // Coxeter groups admit infinite multiplicities, represented by contexpr tc::FREE. Relation tables
-                // for these should be skipped.
-                auto m = get(i, j);
-
-                if (m == FREE) {
-                    continue;
-                }
-
-                rels.emplace_back(i, j, m);
-            }
-        }
-
-        Tables rel_tables(rels);
-        std::vector<std::vector<size_t>> tables_for(rank());
-        int rel_idx = 0;
-        for (const auto &[i, j, m]: rels) {
-            tables_for[i].push_back(rel_idx);
-            tables_for[j].push_back(rel_idx);
-            rel_idx++;
-        }
-
-        std::vector<size_t> lst_vals;
-        rel_tables.add_row();
-        for (int table_idx = 0; table_idx < rel_tables.size(); ++table_idx) {
-            const auto &[i, j, m] = rel_tables.rels[table_idx];
-            Row &row = rel_tables.rows[0][table_idx];
-
-            if (!cosets.isset(0, i) && !cosets.isset(0, j)) {
-                row.lst_idx = lst_vals.size();
-                lst_vals.push_back(0);
-                row.free = false;
-                row.gnr = 0;
-            } else {
-                row.free = false;
-                row.gnr = 1;
-                row.idem = true;
-            }
-        }
-        // endregion
-
-        size_t idx = 0;
-        size_t fact_idx;
-        size_t coset, gen, target, lst;
-
-        while (true) {
-            // find next unknown product
-            while (idx < cosets.size() and cosets.isset(idx))
-                idx++;
-
-            if (cosets.order() >= bound) {
-                return cosets;
-            }
-
-            // if there are none, then return
-            if (idx == cosets.size()) {
-                // todo unrolled linked list interval
-//                rel_tables.del_rows_to(idx / ngens);  
-                break;
-            }
-
-            // the unknown product must be a new coset, so add it
-            target = cosets.order();
-            cosets.add_row();
-            rel_tables.add_row();
-
-            // queue of products that equal target
-            std::queue<size_t> facts;
-            facts.push(idx);  // new product should be recorded and propagated
-
-            // todo unrolled linked list interval
-//            rel_tables.del_rows_to(coset);
-
-            // find all products which also lead to target
-            while (!facts.empty()) {
-                fact_idx = facts.front();
-                facts.pop();
-
-                // skip if this product was already learned
-                if (cosets.get(fact_idx) != -1) continue;
-
-                cosets.set(fact_idx, target);
-
-                coset = fact_idx / rank();
-                gen = fact_idx % rank();
-
-                // If the product stays within the coset todo
-                for (size_t table_idx: tables_for[gen]) {
-                    auto &[i, j, m] = rel_tables.rels[table_idx];
-                    auto &trow = rel_tables.rows[target][table_idx];
-                    auto &crow = rel_tables.rows[coset][table_idx];
-
-                    size_t other_gen = (i == gen) ? j : i;
-
-                    // Test if loop is closed
-                    if (trow.free) {
-                        trow = crow;
-                        trow.gnr++;
-
-                        if (target == coset) {
-                            trow.idem = true;
-                        }
-
-                        if (trow.idem) {
-                            if (trow.gnr == m) {
-                                // loop is closed, but idempotent, so the target links to itself via the other generator.
-                                // todo might be able to move this logic up into the (target == coset) block and avoid those computations.
-                                facts.push(target * rank() + other_gen);
-                            }
-                        } else {
-                            if (trow.gnr == m - 1) {
-                                // loop is almost closed. record that the target closes this loop.
-                                lst_vals[trow.lst_idx] = target;
-                            } else if (trow.gnr == m) {
-                                // loop is closed. We know the last element in the loop must link with this one. 
-                                lst = lst_vals[trow.lst_idx];
-//                            delete trow.lst_ptr;
-                                facts.push(lst * rank() + other_gen);
-                            }
-                        }
-                    }
-                }
-            }
-
-            // If any target row wasn't identified with a loop,
-            // then assign it a new loop.
-            for (size_t table_idx = 0; table_idx < rel_tables.size(); table_idx++) {
-                auto &[i, j, m] = rel_tables.rels[table_idx];
-                auto &trow = rel_tables.rows[target][table_idx];
-
-                if (trow.free) {
-                    if ((cosets.get(target, i) != target) and
-                        (cosets.get(target, j) != target)) {
-                        trow.lst_idx = lst_vals.size();
-                        trow.free = false;
-                        lst_vals.push_back(0);
-                        trow.gnr = 0;
-                    } else {
-                        trow.free = false;
-                        trow.gnr = 1;
-                        trow.idem = true;
-                    }
-                }
-            }
-        }
-
-        cosets._complete = true;
-        return cosets;
-    }
-}

tc/test/CMakeLists.txt

@@ -1,18 +0,0 @@
-include(GoogleTest)
-
-add_executable(test_solve test_solve.cpp)
-target_link_libraries(test_solve tc GTest::gtest_main)
-
-add_executable(test_lang test_lang.cpp)
-target_link_libraries(test_lang PUBLIC tc::tc GTest::gtest_main)
-
-set(MIN_DEBUG_CPS 200000)
-set(MIN_RELEASE_CPS 1000000)
-
-target_compile_definitions(
-    test_solve PUBLIC
-    MIN_COS_PER_SEC=$<IF:$<CONFIG:Debug>,${MIN_DEBUG_CPS},${MIN_RELEASE_CPS}>
-)
-
-gtest_discover_tests(test_solve)
-gtest_discover_tests(test_lang)

tc/test/test_lang.cpp

@@ -1,54 +0,0 @@
-#include <tc/core.hpp>
-#include <tc/groups.hpp>
-
-#include <gtest/gtest.h>
-
-// "5 3 3"
-// "5 (3 3)"
-// "[5 3 3]"
-// "[4 3 [3 5] 3]"
-// "{3 4 5 6 7 8 9}"
-// "3 {3 3 [4] 3} 5"
-// "5 * 3"
-// "5 * [3]"
-// "5 * {2 3}"
-// "5 * [3 2]"
-// "(5 2) * [3 2]"
-// "4 [3 * [2 3]] 5"
-// "{3 * 3} [4] [5]"
-
-TEST(coxeter, simple) {
-    auto g = tc::coxeter("5 3 3");
-
-    ASSERT_EQ(g.rank(), 4);
-
-    EXPECT_EQ(g.get(0, 0), 1);
-    EXPECT_EQ(g.get(0, 1), 5);
-    EXPECT_EQ(g.get(0, 2), 2);
-    EXPECT_EQ(g.get(0, 3), 2);
-    
-    EXPECT_EQ(g.get(1, 0), 5);
-    EXPECT_EQ(g.get(1, 1), 1);
-    EXPECT_EQ(g.get(1, 2), 3);
-    EXPECT_EQ(g.get(1, 3), 2);
-    
-    EXPECT_EQ(g.get(2, 0), 2);
-    EXPECT_EQ(g.get(2, 1), 3);
-    EXPECT_EQ(g.get(2, 2), 1);
-    EXPECT_EQ(g.get(2, 3), 3);
-    
-    EXPECT_EQ(g.get(3, 0), 2);
-    EXPECT_EQ(g.get(3, 1), 2);
-    EXPECT_EQ(g.get(3, 2), 3);
-    EXPECT_EQ(g.get(3, 3), 1);
-}
-
-TEST(coxeter, looping) {
-    auto g = tc::coxeter("{5 3 4}");
-
-    ASSERT_EQ(g.rank(), 3);
-
-    EXPECT_EQ(g.get(0, 1), 5);
-    EXPECT_EQ(g.get(1, 2), 3);
-    EXPECT_EQ(g.get(2, 0), 4);
-}

tc/test/test_solve.cpp

@@ -1,225 +0,0 @@
-#include <ctime>
-#include <vector>
-
-#include <tc/groups.hpp>
-#include <tc/core.hpp>
-
-#include <gtest/gtest.h>
-
-/// helper for testing solve and testing speed
-testing::AssertionResult AssertSolveOrder(
-    const char *group_expr,
-    const char *sub_gens_expr,
-    const char *expected_order_expr,
-    const tc::Group &group,
-    const std::vector<size_t> &sub_gens,
-    size_t expected_order
-) {
-    auto start = std::clock();
-    auto cosets = group.solve(sub_gens);
-    auto end = std::clock();
-
-    size_t actual_order = cosets.order();
-
-    auto total_sec = (double) (end - start) / CLOCKS_PER_SEC;
-    auto cosets_per_sec = (double) actual_order / total_sec;
-
-    bool order_good = actual_order == expected_order;
-    bool speed_good = cosets_per_sec >= MIN_COS_PER_SEC || total_sec < 0.0001;
-    // extremely short times cause false negatives. ex. A2 can be solved in only 3 clocks.
-
-    if (order_good && speed_good) {
-        return testing::AssertionSuccess();
-    }
-
-    testing::AssertionResult res = testing::AssertionFailure();
-    res << group_expr << " / " << sub_gens_expr << " :";
-    if (!order_good) {
-        res << " Gave order " << actual_order << " but expected order " << expected_order << ".";
-    }
-    if (!speed_good) {
-        res << " Solution too slow (" << cosets_per_sec
-            << " cos/s < " << MIN_COS_PER_SEC << ")."
-            << " " << std::fixed << total_sec << " s.";
-    }
-
-    return res;
-}
-
-#define EXPECT_SOLVE_ORDER(group, sub_gens, expected_order) EXPECT_PRED_FORMAT3(AssertSolveOrder, group, sub_gens, expected_order);
-
-using v = std::vector<size_t>;
-
-tc::Group A(unsigned int n) {
-    return tc::vcoxeter("3 * {}", {n - 1});
-}
-
-tc::Group B(unsigned int n) {
-    return tc::vcoxeter("4 3 * {}", {n - 2});
-}
-
-tc::Group D(unsigned int n) {
-    return tc::vcoxeter("3 * [1 1 {}]", {n - 3});
-}
-
-tc::Group E(unsigned int n) {
-    return tc::vcoxeter("3 * [1 2 {}]", {n - 4});
-}
-
-tc::Group F4() {
-    return tc::coxeter("3 4 3");
-}
-
-tc::Group G2() {
-    return tc::coxeter("6");
-}
-
-tc::Group H(unsigned int n) {
-    return tc::vcoxeter("5 3 * {}", {n - 2});
-}
-
-tc::Group I2(unsigned int n) {
-    return tc::vcoxeter("{}", {n});
-}
-
-tc::Group T(unsigned int m, unsigned int n) {
-    return tc::vcoxeter("{} 2 {}", {m, n});
-}
-
-tc::Group T(unsigned int n) {
-    return T(n, n);
-}
-
-// See the group orders here https://en.wikipedia.org/wiki/Coxeter_group#Properties
-
-TEST(solve, A) {
-    EXPECT_SOLVE_ORDER(A(1), v({}), 2);
-    EXPECT_SOLVE_ORDER(A(2), v({}), 6);
-    EXPECT_SOLVE_ORDER(A(3), v({}), 24);
-    EXPECT_SOLVE_ORDER(A(3), v({0}), 12);
-    EXPECT_SOLVE_ORDER(A(3), v({0, 1}), 4);
-    EXPECT_SOLVE_ORDER(A(3), v({0, 2}), 6);
-    EXPECT_SOLVE_ORDER(A(3), v({2}), 12);
-    EXPECT_SOLVE_ORDER(A(4), v({}), 120);
-    EXPECT_SOLVE_ORDER(A(4), v({0}), 60);
-    EXPECT_SOLVE_ORDER(A(4), v({0, 1}), 20);
-    EXPECT_SOLVE_ORDER(A(4), v({2}), 60);
-    EXPECT_SOLVE_ORDER(A(4), v({0, 2}), 30);
-}
-
-TEST(solve, B) {
-    EXPECT_SOLVE_ORDER(B(2), v({}), 8);
-    EXPECT_SOLVE_ORDER(B(3), v({}), 48);
-    EXPECT_SOLVE_ORDER(B(3), v({0}), 24);
-    EXPECT_SOLVE_ORDER(B(3), v({0, 2}), 12);
-    EXPECT_SOLVE_ORDER(B(4), v({}), 384);
-    EXPECT_SOLVE_ORDER(B(4), v({0}), 192);
-    EXPECT_SOLVE_ORDER(B(4), v({0, 2}), 96);
-    EXPECT_SOLVE_ORDER(B(5), v({}), 3840);
-    EXPECT_SOLVE_ORDER(B(5), v({0}), 1920);
-    EXPECT_SOLVE_ORDER(B(5), v({0, 2}), 960);
-    EXPECT_SOLVE_ORDER(B(5), v({0, 2, 3}), 320);
-    EXPECT_SOLVE_ORDER(B(6), v({}), 46080);
-    EXPECT_SOLVE_ORDER(B(6), v({0}), 23040);
-    EXPECT_SOLVE_ORDER(B(6), v({0, 2}), 11520);
-    EXPECT_SOLVE_ORDER(B(6), v({0, 2, 3}), 3840);
-    EXPECT_SOLVE_ORDER(B(6), v({0, 2, 3, 5}), 1920);
-}
-
-TEST(solve, D) {
-    EXPECT_SOLVE_ORDER(D(3), v({}), 24);
-    EXPECT_SOLVE_ORDER(D(4), v({}), 192);
-    EXPECT_SOLVE_ORDER(D(4), v({0, 1}), 32);
-    EXPECT_SOLVE_ORDER(D(4), v({0, 1, 3}), 8);
-    EXPECT_SOLVE_ORDER(D(5), v({}), 1920);
-    EXPECT_SOLVE_ORDER(D(5), v({0, 1}), 320);
-    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3}), 80);
-    EXPECT_SOLVE_ORDER(D(5), v({0, 1, 3, 4}), 16);
-    EXPECT_SOLVE_ORDER(D(6), v({}), 23040);
-    EXPECT_SOLVE_ORDER(D(6), v({0, 1}), 3840);
-    EXPECT_SOLVE_ORDER(D(6), v({0, 1, 3}), 960);
-    EXPECT_SOLVE_ORDER(D(6), v({0, 1, 3, 5}), 480);
-}
-
-TEST(solve, E) {
-    EXPECT_SOLVE_ORDER(E(4), v({}), 120);
-    EXPECT_SOLVE_ORDER(E(4), v({2}), 60);
-    EXPECT_SOLVE_ORDER(E(4), v({2, 1}), 30);
-    EXPECT_SOLVE_ORDER(E(4), v({2, 1, 3}), 10);
-    EXPECT_SOLVE_ORDER(E(5), v({}), 1920);
-    EXPECT_SOLVE_ORDER(E(5), v({2}), 960);
-    EXPECT_SOLVE_ORDER(E(5), v({2, 1}), 480);
-    EXPECT_SOLVE_ORDER(E(5), v({2, 1, 3}), 160);
-    EXPECT_SOLVE_ORDER(E(6), v({}), 51840);
-    EXPECT_SOLVE_ORDER(E(6), v({2}), 25920);
-    EXPECT_SOLVE_ORDER(E(6), v({2, 1}), 12960);
-    EXPECT_SOLVE_ORDER(E(6), v({2, 1, 3}), 4320);
-}
-
-TEST(solve, F) {
-    EXPECT_SOLVE_ORDER(F4(), v({}), 1152);
-    EXPECT_SOLVE_ORDER(F4(), v({0}), 576);
-    EXPECT_SOLVE_ORDER(F4(), v({0, 2}), 288);
-    EXPECT_SOLVE_ORDER(F4(), v({1, 3}), 288);
-    EXPECT_SOLVE_ORDER(F4(), v({1, 2, 3}), 24);
-}
-
-TEST(solve, G) {
-    EXPECT_SOLVE_ORDER(G2(), v({}), 12);
-    EXPECT_SOLVE_ORDER(G2(), v({0}), 6);
-    EXPECT_SOLVE_ORDER(G2(), v({1}), 6);
-}
-
-TEST(solve, H) {
-    EXPECT_SOLVE_ORDER(H(2), v({}), 10);
-    EXPECT_SOLVE_ORDER(H(2), v({0}), 5);
-    EXPECT_SOLVE_ORDER(H(2), v({1}), 5);
-    EXPECT_SOLVE_ORDER(H(3), v({}), 120);
-    EXPECT_SOLVE_ORDER(H(3), v({0}), 60);
-    EXPECT_SOLVE_ORDER(H(3), v({0, 1}), 12);
-    EXPECT_SOLVE_ORDER(H(3), v({0, 2}), 30);
-    EXPECT_SOLVE_ORDER(H(3), v({1, 2}), 20);
-    EXPECT_SOLVE_ORDER(H(4), v({}), 14400);
-    EXPECT_SOLVE_ORDER(H(4), v({0}), 7200);
-    EXPECT_SOLVE_ORDER(H(4), v({1}), 7200);
-    EXPECT_SOLVE_ORDER(H(4), v({1, 3}), 3600);
-}
-
-TEST(solve, I) {
-    EXPECT_SOLVE_ORDER(I2(2), v({}), 4);
-    EXPECT_SOLVE_ORDER(I2(3), v({}), 6);
-    EXPECT_SOLVE_ORDER(I2(3), v({0}), 3);
-    EXPECT_SOLVE_ORDER(I2(3), v({1}), 3);
-    EXPECT_SOLVE_ORDER(I2(4), v({}), 8);
-    EXPECT_SOLVE_ORDER(I2(4), v({0}), 4);
-    EXPECT_SOLVE_ORDER(I2(4), v({1}), 4);
-    EXPECT_SOLVE_ORDER(I2(5), v({}), 10);
-    EXPECT_SOLVE_ORDER(I2(5), v({0}), 5);
-    EXPECT_SOLVE_ORDER(I2(5), v({1}), 5);
-}
-
-TEST(solve, T) {
-    EXPECT_SOLVE_ORDER(T(3), v({}), 36);
-    EXPECT_SOLVE_ORDER(T(4), v({}), 64);
-    EXPECT_SOLVE_ORDER(T(400), v({}), 640000);
-    EXPECT_SOLVE_ORDER(T(400), v({0}), 320000);
-    EXPECT_SOLVE_ORDER(T(400), v({0, 2}), 160000);
-    EXPECT_SOLVE_ORDER(T(400, 300), v({}), 480000);
-    EXPECT_SOLVE_ORDER(T(400, 300), v({0}), 240000);
-    EXPECT_SOLVE_ORDER(T(400, 300), v({0, 2}), 120000);
-}
-
-TEST(solve_large, B) {
-    EXPECT_SOLVE_ORDER(B(7), v({}), 645120);
-    EXPECT_SOLVE_ORDER(B(8), v({}), 10321920);
-}
-
-TEST(solve_large, E) {
-    EXPECT_SOLVE_ORDER(E(6), v({}), 51840);
-    EXPECT_SOLVE_ORDER(E(7), v({}), 2903040);
-}
-
-TEST(solve_large, T) {
-    EXPECT_SOLVE_ORDER(T(500), v({}), 1000000);
-    EXPECT_SOLVE_ORDER(T(1000), v({}), 4000000);
-}

vis/CMakeLists.txt

@@ -1,4 +1,9 @@
-add_subdirectory(shaders)
+add_custom_target(shaders ALL DEPENDS shader_output)
+add_custom_command(
+        OUTPUT shader_output
+        COMMAND ${CMAKE_COMMAND} -E copy_directory ${CMAKE_CURRENT_SOURCE_DIR}/shaders ${CMAKE_CURRENT_BINARY_DIR}/shaders
+        COMMENT "copied shaders"
+)
 
 add_custom_target(presets ALL DEPENDS preset_output)
 add_custom_command(
@@ -7,13 +12,10 @@ add_custom_command(
         COMMENT "copied preses"
 )
 
-add_executable(vis
-    src/main.cpp
-    src/components.hpp
-    )
+add_definitions(${NANOGUI_EXTRA_DEFS})
+include_directories(${NANOGUI_EXTRA_INCS})
+
+add_executable(vis src/main.cpp)
 target_include_directories(vis PRIVATE include)
-target_link_libraries(vis PRIVATE
-    tc shaders
-    glad eigen glfw yaml-cpp fmt EnTT imgui
-    )
-add_dependencies(vis presets)
+target_link_libraries(vis PRIVATE tc nanogui yaml-cpp ${NANOGUI_EXTRA_LIBS})
+add_dependencies(vis shaders presets)

vis/include/cgl/buffer.hpp

@@ -2,22 +2,29 @@
 
 #include <memory>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 namespace cgl {
     template<class T>
     class Buffer {
         GLuint id{};
-        size_t _count = 0;
 
     public:
-        using Element = T;
-
         Buffer() {
             glCreateBuffers(1, &id);
         }
 
-        Buffer(Buffer &) = delete;
+        Buffer(const T &data, GLenum usage = GL_STATIC_DRAW)
+            : Buffer() {
+            put(data, usage);
+        }
+
+        Buffer(const std::vector<T> &data, GLenum usage = GL_STATIC_DRAW)
+            : Buffer() {
+            put(data, usage);
+        }
+
+        Buffer(const Buffer &) = delete;
 
         Buffer(Buffer &&o) noexcept {
             id = std::exchange(o.id, 0);
@@ -33,26 +40,44 @@ namespace cgl {
         }
 
         [[nodiscard]] size_t size() const {
-            return _count * sizeof(T);
+            GLint res;
+            glGetNamedBufferParameteriv(id, GL_BUFFER_SIZE, &res);
+            return (size_t) res;
         }
 
         [[nodiscard]] size_t count() const {
-            return _count;
-        }
-
-        template<typename It>
-        void put(It begin, It end, GLenum usage = GL_STATIC_DRAW) {
-            _count = end - begin;
-
-            glNamedBufferData(id, sizeof(T) * _count, nullptr, usage);
-            void* ptr = glMapNamedBuffer(id, GL_WRITE_ONLY);
-            std::copy(begin, end, (T*) ptr);
-            glUnmapNamedBuffer(id);
+            return size() / sizeof(T);
         }
 
         void put(const T &data, GLenum usage = GL_STATIC_DRAW) {
-            T const* ptr = &data;
-            put(ptr, ptr + 1, usage);
+            glNamedBufferData(id, sizeof(T), &data, usage);
+        }
+
+        void put(const T *data, const size_t &size, GLenum usage = GL_STATIC_DRAW) {
+            glNamedBufferData(id, sizeof(T) * size, data, usage);
+        }
+
+        template<class E>
+        void put(const E &data, GLenum usage = GL_STATIC_DRAW) {
+            put(data.data(), data.size(), usage);
+        }
+
+        void bound(GLenum target, const std::function<void()> &action) const {
+            glBindBuffer(target, id);
+            action();
+            glBindBuffer(target, 0);
+        }
+
+        std::vector<T> getSubData(size_t offset, size_t count) const {
+            GLintptr glOffset = offset * sizeof(T);
+            GLsizeiptr glSize = count * sizeof(T);
+
+            std::vector<T> data(count);
+
+            glad_glGetNamedBufferSubData(id, glOffset, glSize, data.data());
+
+            return data;
         }
     };
+
 }

vis/include/cgl/debug.hpp

@@ -1,85 +0,0 @@
-#pragma once
-
-#include <glad/glad.h>
-#include <fmt/core.h>
-
-#include <string>
-
-#ifndef NDEBUG
-
-void GLAPIENTRY log_gl_debug_callback(
-    GLenum source,
-    GLenum type,
-    GLuint id,
-    GLenum severity,
-    GLsizei length,
-    const GLchar *message,
-    const void *userParam
-) {
-    std::string s_source;
-    switch (type) {
-        case GL_DEBUG_SOURCE_API:
-            s_source = "API:";
-        case GL_DEBUG_SOURCE_WINDOW_SYSTEM:
-            s_source = "WINDOW:";
-        case GL_DEBUG_SOURCE_SHADER_COMPILER:
-            s_source = "SHADER:";
-        case GL_DEBUG_SOURCE_THIRD_PARTY:
-            s_source = "3P:";
-        case GL_DEBUG_SOURCE_APPLICATION:
-            s_source = "APP:";
-        default:
-            s_source = "";
-    }
-
-    std::string s_type;
-    switch (type) {
-        case GL_DEBUG_TYPE_ERROR:
-            s_type = "ERROR:";
-            break;
-        case GL_DEBUG_TYPE_DEPRECATED_BEHAVIOR:
-            s_type = "DEPRECATED:";
-            break;
-        case GL_DEBUG_TYPE_UNDEFINED_BEHAVIOR:
-            s_type = "UNDEFINED:";
-            break;
-        case GL_DEBUG_TYPE_PORTABILITY:
-            s_type = "PORTABILITY:";
-            break;
-        case GL_DEBUG_TYPE_PERFORMANCE:
-            s_type = "PERFORMANCE:";
-            break;
-        case GL_DEBUG_TYPE_MARKER:
-            s_type = "MARKER:";
-            break;
-        case GL_DEBUG_TYPE_PUSH_GROUP:
-            s_type = "PUSH_GROUP:";
-            break;
-        case GL_DEBUG_TYPE_POP_GROUP:
-            s_type = "POP_GROUP:";
-            break;
-        default:
-            s_type = "";
-            break;
-    }
-
-    std::string s_severity;
-    switch (severity) {
-        case GL_DEBUG_SEVERITY_HIGH:
-            s_severity = "HIGH:";
-            break;
-        case GL_DEBUG_SEVERITY_MEDIUM:
-            s_severity = "MED:";
-            break;
-        case GL_DEBUG_SEVERITY_LOW:
-            s_severity = "LOW:";
-            break;
-        default:
-            s_severity = "INFO:";
-            break;
-    }
-
-    fmt::print(stderr, "GL:{}{}{} {}\n", s_source, s_type, s_severity, message);
-}
-
-#endif

vis/include/cgl/error.hpp

@@ -2,7 +2,7 @@
 
 #include <stdexcept>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 namespace cgl {
     class GlError : public std::domain_error {

vis/include/cgl/pipeline.hpp

@@ -4,7 +4,7 @@
 #include <string>
 #include <utility>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 #include <cgl/error.hpp>
 #include <cgl/shaderprogram.hpp>
@@ -83,5 +83,11 @@ namespace cgl {
             glUseProgramStages(id, GL_COMPUTE_SHADER_BIT, pgm);
             return *this;
         }
+
+        void bound(const std::function<void()> &action) const {
+            glBindProgramPipeline(id);
+            action();
+            glBindProgramPipeline(0);
+        }
     };
 }

vis/include/cgl/program.hpp

@@ -3,7 +3,7 @@
 #include <string>
 #include <utility>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 #include <cgl/error.hpp>
 #include <cgl/shader.hpp>

vis/include/cgl/shader.hpp

@@ -3,7 +3,7 @@
 #include <string>
 #include <utility>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 #include <cgl/error.hpp>
 

vis/include/cgl/shaderprogram.hpp

@@ -3,7 +3,7 @@
 #include <string>
 #include <utility>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 #include <cgl/error.hpp>
 #include <cgl/shader.hpp>
@@ -19,9 +19,7 @@ namespace cgl{
             glProgramParameteri(id, GL_PROGRAM_SEPARABLE, GL_TRUE);
         }
 
-        explicit ShaderProgram(const std::string_view &src) : ShaderProgram(std::string(src)) {}
-
-        explicit ShaderProgram(const std::string &src) : ShaderProgram() {
+        ShaderProgram(const std::string &src) : ShaderProgram() {
             Shader<mode> sh(src);
 
             attach(sh);

vis/include/cgl/vertexarray.hpp

@@ -4,7 +4,7 @@
 #include <string>
 #include <utility>
 
-#include <glad/glad.h>
+#include <nanogui/opengl.h>
 
 #include <cgl/error.hpp>
 #include <cgl/buffer.hpp>
@@ -33,34 +33,43 @@ namespace cgl {
             return id;
         }
 
-        void format(
+        void bound(const std::function<void()> &action) const {
+            glBindVertexArray(id);
+            action();
+            glBindVertexArray(0);
+        }
+
+        template<class T>
+        void pointer(
             GLuint index,
+            const Buffer<T> &buf,
             unsigned size,
             GLenum type,
             bool normalized = false,
             unsigned stride = 0
-        ) {
-            glEnableVertexArrayAttrib(id, index);
-            glVertexArrayAttribFormat(id, index, size, type, normalized, stride);
+        ) const {
+            bound([&]() {
+                glEnableVertexAttribArray(index);
+                buf.bound(GL_ARRAY_BUFFER, [&]() {
+                    glVertexAttribPointer(index, size, type, normalized, stride, nullptr);
+                });
+            });
         }
 
-        void iformat(
+        template<class T>
+        void ipointer(
             GLuint index,
+            const Buffer<T> &buf,
             unsigned size,
             GLenum type,
             unsigned stride = 0
-        ) {
-            glEnableVertexArrayAttrib(id, index);
-            glVertexArrayAttribIFormat(id, index, size, type, stride);
-        }
-
-        template<class Buf>
-        void vertexBuffer(
-            GLuint index,
-            Buf &buf,
-            unsigned offset = 0
-        ) {
-            glVertexArrayVertexBuffer(id, index, buf, offset, sizeof(typename Buf::Element));
+        ) const {
+            bound([&]() {
+                glEnableVertexAttribArray(index);
+                buf.bound(GL_ARRAY_BUFFER, [&]() {
+                    glVertexAttribIPointer(index, size, type, stride, nullptr);
+                });
+            });
         }
     };
 }

vis/include/combinations.hpp

@@ -0,0 +1,53 @@
+#pragma once
+
+#include <vector>
+#include <set>
+#include <algorithm>
+
+template<class V>
+V select(const V &options, const std::vector<bool> &mask, size_t count) {
+    V result;
+    result.reserve(count);
+
+    for (int i = 0; i < mask.size(); ++i) {
+        if (mask[i]) result.push_back(options[i]);
+    }
+
+    return result;
+}
+
+template<class V>
+std::set<V> combinations(const V &options, size_t count) {
+    std::set<V> result;
+
+    std::vector<bool> mask(options.size(), false);
+    std::fill(mask.begin(), mask.begin() + count, true);
+
+    do {
+        result.insert(select(options, mask, count));
+    } while (std::next_permutation(mask.begin(), mask.end(), std::greater<>()));
+
+    return result;
+}
+
+template<class V>
+std::set<V> set_difference(const std::set<V> &a, const std::set<V> &b) {
+    std::set<V> result;
+    std::set_difference(
+        a.begin(), a.end(),
+        b.begin(), b.end(),
+        std::inserter(result, result.end())
+    );
+    return result;
+}
+
+template<class V>
+std::set<V> set_union(const std::set<V> &a, const std::set<V> &b) {
+    std::set<V> result;
+    std::set_union(
+        a.begin(), a.end(),
+        b.begin(), b.end(),
+        std::inserter(result, result.end())
+        );
+    return result;
+}

vis/include/geometry.hpp

@@ -6,10 +6,8 @@
 #include <numeric>
 #include <iostream>
 
-#include <Eigen/Eigen>
-
 template<unsigned N>
-using Indices = Eigen::Array<unsigned, N, Eigen::Dynamic>;
+using Prims = Eigen::Matrix<unsigned, N, Eigen::Dynamic>;
 
 template<int N>
 using vec = Eigen::Matrix<float, N, 1>;

vis/include/mirror.hpp

@@ -6,87 +6,115 @@
 #include <vector>
 #include <algorithm>
 
+#include <nanogui/glutil.h>
+
 #include <geometry.hpp>
 
-template<unsigned int N>
-Eigen::Matrix<float, N, N> mirror(const tc::Group &group) {
-    Eigen::Matrix<float, N, N> res;
-    res.setZero();
+template<class V>
+float dot(int n, const V &a, const V &b) {
+    float sum = 0;
+    for (int i = 0; i < n; ++i) {
+        sum += a[i] * b[i];
+    }
+    return sum;
+}
 
-    for (int c = 0; c < group.rank(); ++c) {
-        for (int r = 0; r < c; ++r) {
-            auto angle = M_PI / group.get(c, r);
-            auto dot = res.col(c).dot(res.col(r));
+template<unsigned N>
+std::vector<vec<N>> mirror(const tc::Group &group) {
+    std::vector<std::vector<float>> mirrors;
 
-            res(r, c) = (dot - cos(angle)) / res(r, r);
+    for (int p = 0; p < group.ngens; ++p) {
+        std::vector<float> vp;
+        for (int m = 0; m < p; ++m) {
+            auto &vq = mirrors[m];
+            vp.push_back((cos(M_PI / group.get(p, m)) - dot(m, vp, vq)) / vq[m]);
+        }
+        vp.push_back(std::sqrt(1 - dot(p, vp, vp)));
+
+        for (const auto &v : mirrors) {
+            if (dot(p, vp, vp) > 0) {
+                for (auto &e : vp) {
+                    e *= -1;
+                }
+                break;
+            }
         }
 
-        res(c, c) = sqrt(1 - res.col(c).squaredNorm());
+        mirrors.push_back(vp);
     }
 
+    std::vector<vec<N>> res;
+    for (const auto &v : mirrors) {
+        vec<N> rv = vec<N>::Zero();
+
+        // ortho proj
+        for (int i = 0; i < std::min(v.size(), (size_t) N); ++i) {
+            rv[i] = v[i];
+        }
+
+        res.push_back(rv);
+    }
     return res;
 }
 
-struct Stereo {
-    template<class U>
-    auto operator()(U &&mat) const {
-        const auto Rows = std::remove_reference<U>::type::RowsAtCompileTime;
-        return std::forward<U>(mat).template topRows<Rows - 1>().rowwise() / (1 - mat.template bottomRows<1>());
+template<unsigned N>
+vec<N> stereo(const vec<N + 1> &v) {
+    vec<N> r;
+    for (int i = 0; i < N; ++i) {
+        r[i] = v[i] / (1 - v[N]);
     }
-};
-
-struct Ortho {
-    template<class U>
-    auto operator()(U &&mat) const {
-        const auto Rows = std::remove_reference<U>::type::RowsAtCompileTime;
-        return std::forward<U>(mat).template topRows<Rows - 1>();
-    }
-};
-
-struct Project {
-    template<class U, class V>
-    auto operator()(U &&point, V &&axis) const {
-        return point.dot(axis) / axis.dot(axis) * std::forward<V>(axis);
-    }
-};
-
-struct Reflect {
-    template<class U, class V>
-    auto operator()(U &&point, V &&axis) const {
-        return std::forward<U>(point) - 2 * Project()(point, axis);
-    }
-};
-
-template<class Mat>
-Mat gram_schmidt(Mat mat) {
-    for (int i = 0; i < mat.cols(); ++i) {
-        for (int j = i + 1; j < mat.cols(); ++j) {
-            mat.col(j) -= Project()(mat.col(j), mat.col(i));
-        }
-    }
-    return mat;
+    return r;
 }
 
-template<class Mat>
-Mat plane_intersections(Mat normals) {
-    auto last = normals.cols() - 1;
+template<unsigned N>
+vec<N> ortho(const vec<N + 1> &v) {
+    vec<N> r;
+    for (int i = 0; i < N; ++i) {
+        r[i] = v[i];
+    }
+    return r;
+}
 
-    Mat results(normals.rows(), normals.cols());
-    results.setZero();
+template<class V>
+V project(const V &vec, const V &target) {
+    return vec.dot(target) / target.dot(target) * target;
+}
 
-    Eigen::Matrix<int, Mat::ColsAtCompileTime, 1> indices(normals.cols());
-    std::iota(indices.begin(), indices.end(), 0);
+template<class V>
+V reflect(const V &a, const V &axis) {
+    return a - 2.f * project(a, axis);
+}
 
-    for (int i = 0; i < normals.cols(); ++i) {
-        std::rotate(indices.begin(), indices.begin() + 1, indices.end());
-
-        Mat cur = normals * Eigen::PermutationMatrix<Mat::ColsAtCompileTime>(indices);
-        Mat res = gram_schmidt(cur);
-
-        results.col(i) = res.col(last);
+template<class V>
+V gram_schmidt_last(std::vector<V> vecs) {
+    for (int i = 0; i < vecs.size(); ++i) {
+        for (int j = 0; j < i; ++j) {
+            vecs[i] -= project(vecs[i], vecs[j]);
+        }
     }
 
-    results.colwise().normalize();
+    return vecs[vecs.size() - 1].normalized();
+}
+
+template<class V, class C>
+V barycentric(const std::vector<V> &basis, const C &coords) {
+    V res = V::Zero();
+
+    int N = std::min((int) basis.size(), (int) coords.rows());
+    for (int i = 0; i < N; ++i) {
+        res += basis[i] * coords[i];
+    }
+    return res;
+}
+
+template<class V>
+std::vector<V> plane_intersections(std::vector<V> normals) {
+    std::vector<V> results(normals.size());
+
+    for (int i = 0; i < normals.size(); ++i) {
+        std::rotate(normals.begin(), normals.begin() + 1, normals.end());
+        results[i] = gram_schmidt_last(normals);
+    }
 
     return results;
 }
@@ -100,21 +128,3 @@ mat<N> rot(int u, int v, float theta) {
     res(v, v) = std::cos(theta);
     return res;
 }
-
-template<class U, class V>
-auto rotor(U const &u, V const &v) {
-    using Rotor = Eigen::Matrix<
-        typename U::Scalar,
-        std::min(U::RowsAtCompileTime, V::RowsAtCompileTime),
-        std::min(U::RowsAtCompileTime, V::RowsAtCompileTime),
-        U::Options,
-        std::max(U::MaxRowsAtCompileTime, V::MaxRowsAtCompileTime),
-        std::max(U::MaxRowsAtCompileTime, V::MaxRowsAtCompileTime)
-    >;
-
-    const auto &ident = Rotor::Identity(u.rows(), v.rows());
-    const auto &inner = (u + v) / (1 + u.dot(v)) * (u + v).transpose();
-    const auto &outer = v * u.transpose();
-
-    return ident - inner + 2 * outer;
-}

vis/include/rendering.hpp

@@ -0,0 +1,112 @@
+# pragma once
+
+#include <cgl/vertexarray.hpp>
+#include <cgl/buffer.hpp>
+#include <cgl/pipeline.hpp>
+
+#include <geometry.hpp>
+#include <mirror.hpp>
+#include <combinations.hpp>
+
+struct Matrices {
+    mat4 proj = mat4::Identity();
+    mat4 view = mat4::Identity();
+
+    Matrices() = default;
+
+    Matrices(mat4 proj, mat4 view) : proj(std::move(proj)), view(std::move(view)) {}
+
+    static Matrices build(const nanogui::Screen &screen) {
+        auto aspect = (float) screen.width() / (float) screen.height();
+        auto pheight = 1.4f;
+        auto pwidth = aspect * pheight;
+//        auto proj = orthographic(-pwidth, pwidth, -pheight, pheight, -10.0f, 10.0f);
+//        auto proj = perspective(-pwidth, pwidth, pheight, -pheight, 10.0f, 0.01f);
+        auto proj = perspective(0.4, aspect, 0.1, 10.0);
+
+        auto view = translation(0, 0, -4);
+
+        return Matrices(proj, view);
+    }
+};
+
+template<class T>
+class Renderer {
+public:
+    virtual void draw(const T &prop) const = 0;
+};
+
+template<unsigned N>
+class Slice {
+private:
+    const tc::Group group;
+
+public:
+    cgl::Buffer<unsigned> ibo;
+    cgl::Buffer<vec4> vbo;
+    cgl::VertexArray vao;
+
+    vec5 root = vec5::Ones().normalized();
+    vec5 center = vec5::Zero();
+    mat5 transform = mat5::Identity();
+
+    vec3 color = vec3::Ones();
+
+    explicit Slice(const tc::Group &g) : group(g) {
+        vao.ipointer(0, ibo, 4, GL_UNSIGNED_INT);
+    }
+
+    void setMesh(const Mesh<N> &mesh) {
+        ibo.put(mesh);
+    }
+
+    void setPoints() {
+        auto cosets = group.solve();
+        auto mirrors = mirror<5>(group);
+
+        auto corners = plane_intersections(mirrors);
+        auto start = barycentric(corners, root);
+
+        auto higher = cosets.path.walk<vec5, vec5>(start, mirrors, reflect<vec5>);
+
+        std::transform(
+                higher.begin(), higher.end(), higher.begin(),
+                [&](const vec5& v) { return center + transform * v; }
+        );
+
+        std::vector<vec4> lower(higher.size());
+        std::transform(higher.begin(), higher.end(), lower.begin(), stereo<4>);
+
+        vbo.put(lower);
+    }
+};
+
+template<unsigned N>
+class SliceRenderer : public Renderer<Slice<N>> {
+private:
+    cgl::pgm::vert defer = cgl::pgm::vert::file(
+            "shaders/slice/deferred.vs.glsl");
+    cgl::pgm::geom slice = cgl::pgm::geom::file(
+            "shaders/slice/slice.gm.glsl");
+    cgl::pgm::frag solid = cgl::pgm::frag::file(
+            "shaders/solid.fs.glsl");
+
+    cgl::pipeline pipe;
+
+    cgl::Buffer<Matrices> ubo;
+
+public:
+    SliceRenderer() {
+        pipe.stage(defer);
+        pipe.stage(slice);
+        pipe.stage(solid);
+    }
+
+    void draw(const Slice<N> &prop) const {
+        glBindProgramPipeline(pipe);
+        glBindBufferBase(GL_SHADER_STORAGE_BUFFER, 1, prop.vbo);
+        glProgramUniform3fv(solid, 2, 1, prop.color.data());
+        glBindVertexArray(prop.vao);
+        glDrawArrays(GL_POINTS, 0, prop.ibo.count() * N);
+    }
+};

vis/include/solver.hpp

@@ -7,186 +7,250 @@
 #include <iostream>
 
 #include <geometry.hpp>
+#include <utility>
+
+#include <combinations.hpp>
 
 /**
- * Convert the indexes of this mesh to those of a different context, using g_gens to build the parent context and sg_gens to build this context.
+ * Produce a list of all generators for the group context. The range [0..group.ngens).
  */
-template<int N>
-[[nodiscard]]
-Indices<N> recontext(
-    Indices<N> prims,
-    const tc::Group &G,
-    const tc::Group &H
-) {
-    const auto table = G.solve({});
-    const auto cosets = H.solve({});
+std::vector<int> generators(const tc::Group &context) {
+    std::vector<int> g_gens(context.ngens);
+    std::iota(g_gens.begin(), g_gens.end(), 0);
+    return g_gens;
+}
 
-    tc::Path<size_t> path(cosets, H.gens());
+namespace {
+    /**
+     * Determine which of g_gens are the correct names for sg_gens within the current context
+     */
+    std::vector<int> recontext_gens(
+        const tc::Group &context,
+        std::vector<int> g_gens,
+        std::vector<int> sg_gens) {
 
-    std::vector<size_t> map(path.order());
-    path.walk(0, [&table](size_t coset, size_t gen) {
+        std::sort(g_gens.begin(), g_gens.end());
+
+        int inv_gen_map[context.ngens];
+        for (size_t i = 0; i < g_gens.size(); i++) {
+            inv_gen_map[g_gens[i]] = i;
+        }
+
+        std::vector<int> s_sg_gens;
+        s_sg_gens.reserve(sg_gens.size());
+        for (const auto gen : sg_gens) {
+            s_sg_gens.push_back(inv_gen_map[gen]);
+        }
+        std::sort(s_sg_gens.begin(), s_sg_gens.end());
+
+        return s_sg_gens;
+    }
+
+    /**
+     * Solve the cosets generated by sg_gens within the subgroup generated by g_gens of the group context
+     */
+    tc::Cosets solve(
+        const tc::Group &context,
+        const std::vector<int> &g_gens,
+        const std::vector<int> &sg_gens
+    ) {
+        const auto proper_sg_gens = recontext_gens(context, g_gens, sg_gens);
+        return context.subgroup(g_gens).solve(proper_sg_gens);
+    }
+
+    /**
+     * Apply some context transformation to all primitives of this mesh.
+     */
+    template<unsigned N>
+    void apply(const tc::Cosets &table, int gen, Prims<N> &mat) {
+        auto data = mat.data();
+        for (int i = 0; i < mat.size(); ++i) {
+            data[i] = table.get(data[i], gen);
+        }
+    }
+}
+
+template<unsigned N>
+class Mesh {
+public:
+    const tc::Group *g;  // todo this needs to be handled more consistently
+    std::vector<int> ctx;
+    Prims<N> prims;
+
+    Mesh(const tc::Group &g_, std::vector<int> ctx_, size_t cols);
+
+    static Mesh<N> fill(const tc::Group &g, const std::vector<int> &ctx);
+
+//    template<class SC>
+//    static Mesh<N> hull(const tc::Group &g, const std::vector<int> &ctx, const SC &sub_ctxs);
+
+    Mesh<N> recontext(std::vector<int> ctx_);
+
+    Mesh<N> tile(const std::vector<int> &ctx_);
+
+    std::vector<Mesh<N>> each_tile(const std::vector<int> &ctx_);
+
+    Mesh<N + 1> fan(unsigned root);
+
+    [[nodiscard]] size_t size() const { return prims.size(); }
+
+    [[nodiscard]] size_t rows() const { return prims.rows(); }
+
+    [[nodiscard]] size_t cols() const { return prims.cols(); }
+
+    [[nodiscard]] unsigned *data() { return prims.data(); }
+
+    [[nodiscard]] const unsigned *data() const { return prims.data(); }
+};
+
+template<class M>
+M merge(const std::vector<M> &meshes) {
+    if (meshes.empty()) throw std::logic_error("cannot merge an empty list of meshes");
+
+    auto g = meshes[0].g;
+    auto ctx = meshes[0].ctx;
+
+    size_t cols = 0;
+    for (const auto &mesh : meshes) {
+        cols += mesh.prims.cols();
+    }
+
+    M res(*g, ctx, cols);
+
+    size_t offset = 0;
+    for (const auto &mesh : meshes) {
+        res.prims.middleCols(offset, mesh.prims.cols()) = mesh.prims;
+        offset += mesh.prims.cols();
+    }
+
+    return res;
+}
+
+template<unsigned N>
+Mesh<N> Mesh<N>::recontext(std::vector<int> ctx_) {
+    Mesh<N> res = *this;
+    res.ctx = ctx_;
+
+    const auto proper_sg_gens = recontext_gens(*g, res.ctx, ctx);
+    const auto table = solve(*g, res.ctx, {});
+    const auto path = solve(*g, ctx, {}).path;
+
+    auto map = path.template walk<int, int>(0, proper_sg_gens, [table](int coset, int gen) {
         return table.get(coset, gen);
-    }, map.begin());
+    });
 
-    Indices<N> res(prims);
-    auto data = res.data();
-    for (int i = 0; i < prims.size(); ++i) {
+    auto data = res.prims.data();
+    for (int i = 0; i < res.prims.size(); ++i) {
         data[i] = map[data[i]];
     }
 
     return res;
 }
 
-/**
- * Union several meshes of the same dimension
- */
-template<int N>
-Indices<N> merge(
-    const std::vector<Indices<N>> &meshes
-) {
-    size_t cols = 0;
-    for (const auto &mesh: meshes) {
-        cols += mesh.cols();
-    }
-
-    Indices<N> res(N, cols);
-
-    size_t offset = 0;
-    for (const Indices<N> &mesh: meshes) {
-        res.middleCols(offset, mesh.cols()) = mesh;
-        offset += mesh.cols();
-    }
-
-    return res;
+template<unsigned N>
+Mesh<N> Mesh<N>::tile(const std::vector<int> &ctx_) {
+    return merge(each_tile(ctx_));
 }
 
-template<int N>
-[[nodiscard]]
-std::vector<Indices<N>> tile(
-    Indices<N> prims,
-    const tc::Group &G,
-    const tc::Group &H
-) {
-    const auto &table = G.solve({});
-    const auto &cosets = G.solve(H.gens());
+template<unsigned N>
+std::vector<Mesh<N>> Mesh<N>::each_tile(const std::vector<int> &ctx_) {
+    auto base = recontext(ctx_);
 
-    tc::Path<> path(cosets);
+    auto table = solve(*g, base.ctx, {});
+    auto path = solve(*g, base.ctx, ctx).path;
 
-    std::vector<Indices<N>> res(path.order());
-
-    path.walk(prims, [&](Indices<N> from, auto gen) {
-        for (int i = 0; i < from.size(); ++i) {
-            from(i) = table.get(from(i), gen);
+    std::vector<Mesh<N>> res = path.template walk<Mesh<N>, int>(
+        base, generators(*g),
+        [&](Mesh<N> mesh, int gen) {
+            apply<N>(table, gen, mesh.prims);
+            return mesh;
         }
-        return from;
-    }, res.begin());
+    );
 
     return res;
 }
 
-/**
- * Produce a mesh of higher dimension by fanning a single point to all primitives in this mesh.
- */
-template<int N>
-[[nodiscard]]
-Indices<N + 1> fan(
-    Indices<N> prims,
-    int root
-) {
-    Indices<N + 1> res(N + 1, prims.cols());
+template<unsigned N>
+Mesh<N + 1> Mesh<N>::fan(unsigned root) {
+    Mesh<N + 1> res(*g, ctx, prims.cols());
 
-    res.topRows(N) = prims;
-    res.bottomRows(1) = root;
+    res.prims.topRows(1) = Prims<1>::Constant(1, prims.cols(), root);
+    res.prims.bottomRows(N) = prims;
 
     return res;
 }
 
-/**
- * Produce a mesh of primitives that fill out the volume of the subgroup generated by generators g_gens within the group context
- */
-template<int N>
-Indices<N> cell(
-    const tc::Group &G
-) {
-    assert(G.rank() + 1 == N);  // g_gens size must be one less than N
+template<unsigned N>
+Mesh<N>::Mesh(const tc::Group &g_, std::vector<int> ctx_, size_t cols)
+    : g(&g_), ctx(std::move(ctx_)) {
+    prims.setZero(N, cols);
+}
 
-    std::vector<Indices<N - 1>> facets;
+template<unsigned N>
+Mesh<N> Mesh<N>::fill(const tc::Group &g, const std::vector<int> &ctx) {
+    if (ctx.size() + 1 != N)
+        throw std::logic_error("ctx size must be one less than N");
 
-    for (auto H: G.subs(N - 2)) {
-        auto sub_base = cell<N - 1>(H);
-        auto base = recontext(sub_base, G, H);
-        auto tiles = tile(base, G, H);
+//    const auto &combos = Combos(ctx, (int)ctx.size() - 1);
+    const auto &combos = combinations(ctx, (int) ctx.size() - 1);
 
-        facets.insert(
-            facets.end(),
-            tiles.begin() + 1, // skip "near" facet
-            tiles.end()
-        );
+    std::vector<Mesh<N>> meshes;
+
+    for (const auto &sub_ctx : combos) {
+        auto base = Mesh<N - 1>::fill(g, sub_ctx);
+        auto parts = base.each_tile(ctx);
+        parts.erase(parts.begin(), parts.begin() + 1);
+
+        if (parts.empty()) continue;
+        auto raised = merge(parts);
+
+        auto fanned = raised.fan(0);
+        meshes.push_back(fanned);
     }
 
-    return fan(merge(facets), 0);
+    return merge(meshes);
 }
 
-/**
- * Single-index primitives should not be further triangulated.
- */
 template<>
-Indices<1> cell<1>(
-    const tc::Group &G
-) {
-    assert(G.rank() == 0); // rank must be 0 for trivial Mesh
+Mesh<1> Mesh<1>::fill(const tc::Group &g, const std::vector<int> &ctx) {
+    if (not ctx.empty())
+        throw std::logic_error("ctx must be empty for a trivial Mesh.");
 
-    return Indices<1>::Zero(1, 1);
+    return Mesh<1>(g, ctx, 1);
 }
 
-template<int N>
-struct Hull {
-    struct Tiling {
-        Eigen::Index first;
-        Eigen::Index count;
-    };
+template<unsigned N, class C, class SC>
+Mesh<N> fill_each_tile_merge(const tc::Group &g, const C &ctx, const SC &sub_ctxs) {
+    std::vector<Mesh<N>> parts;
 
-    std::vector<Tiling> tilings{};
-    std::vector<std::vector<size_t>> subgroups{};
-
-    Indices<N> inds{};
-
-    explicit Hull(tc::Group const &G) {
-        std::vector<Indices<N>> parts;
-
-        Eigen::Index first = 0;
-        for (const auto &H: G.subs(N - 1)) {
-            auto sub_base = cell<N>(H);
-            auto base = recontext(sub_base, G, H);
-            auto tiles = tile(base, G, H);
-            auto tiling = merge(tiles);
-
-            subgroups.push_back(H.gens());
-            tilings.push_back({first, tiling.cols()});
-
-            parts.push_back(tiling);
-            first += tiling.cols();
-        }
-
-        inds = merge(parts);
+    for (const auto &sub_ctx : sub_ctxs) {
+        auto root = Mesh<N>::fill(g, sub_ctx);
+        auto faces = root.each_tile(ctx);
+        parts.insert(parts.end(), faces.begin(), faces.end());
     }
-};
 
-struct Points {
-    Eigen::Array<float, 4, Eigen::Dynamic> verts;
+    return merge(parts);
+}
 
-    explicit Points(tc::Group const &G, Eigen::Vector<float, 5> root) {
-        auto mirrors = mirror<5>(G);
-        auto corners = plane_intersections(mirrors);
+template<unsigned N, class SC>
+Mesh<N> fill_each_tile_merge(const tc::Group &g, const SC &sub_ctxs) {
+    return fill_each_tile_merge<N>(g, generators(g), sub_ctxs);
+}
 
-        auto start = corners * root;
+template<unsigned N, class C, class SC>
+Mesh<N> fill_each_recontext_merge(const tc::Group &g, const C &ctx, const SC &sub_ctxs) {
+    std::vector<Mesh<N>> parts;
 
-        tc::Cosets table = G.solve();
-        tc::Path<vec5> path(table, mirrors.colwise());
-
-        Eigen::Array<float, 5, Eigen::Dynamic> higher(5, path.order());
-        path.walk(start, Reflect(), higher.matrix().colwise().begin());
-
-        verts = Stereo()(higher);
+    for (const auto &sub_ctx : sub_ctxs) {
+        auto root = Mesh<N>::fill(g, sub_ctx);
+        auto face = root.recontext(ctx);
+        parts.insert(parts.end(), face);
     }
-};
+
+    return merge(parts);
+}
+
+template<unsigned N, class SC>
+Mesh<N> fill_each_recontext_merge(const tc::Group &g, const SC &sub_ctxs) {
+    return fill_each_recontext_merge<N>(g, generators(g), sub_ctxs);
+}

vis/include/util.hpp

@@ -1,13 +1,13 @@
 #pragma once
 
+#include <nanogui/opengl.h>
+
 #include <cerrno>
 #include <fstream>
 #include <sstream>
 #include <string>
 #include <vector>
 
-#include <glad/glad.h>
-
 std::string utilInfo() {
     std::stringstream ss;
     ss
@@ -19,6 +19,10 @@ std::string utilInfo() {
     return ss.str();
 }
 
+std::string utilGetString(GLenum name) {
+    return reinterpret_cast<char const*>(glGetString(name));
+}
+
 std::string utilReadFile(const std::string &filename) {
     std::ifstream in(filename, std::ios::in | std::ios::binary);
     if (in) {

vis/presets/b_3_ortho.yaml

@@ -2,9 +2,9 @@ dimension: 3
 groups:
   - symbol: [4, 3]
     slices:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
     wires:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: true

vis/presets/b_3_stereo.yaml

@@ -2,9 +2,9 @@ dimension: 3
 groups:
   - symbol: [4, 3]
     slices:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
     wires:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: false

vis/presets/b_4_ortho.yaml

@@ -2,9 +2,9 @@ dimension: 4
 groups:
   - symbol: [4, 3, 3]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
     wires:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: true

vis/presets/b_4_stereo.yaml

@@ -2,9 +2,9 @@ dimension: 4
 groups:
   - symbol: [4, 3, 3]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
     wires:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: false

vis/presets/b_4_stereo_exclude.yaml

@@ -2,11 +2,11 @@ dimension: 4
 groups:
   - symbol: [4, 3, 3]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
         exclude:
           - [0, 1, 2]
     wires:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: false

vis/presets/b_4_stereo_exclude_nowire.yaml

@@ -2,7 +2,7 @@ dimension: 4
 groups:
   - symbol: [4, 3, 3]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
         exclude:
           - [0, 1, 2]

vis/presets/b_4_stereo_exclude_thick.yaml

@@ -2,7 +2,7 @@ dimension: 5
 groups:
   - symbol: [4, 3, 3, 2]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.09]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.09]
         color: [0.9, 0.9, 0.9]
         exclude:
           - [0, 1, 2]

vis/presets/default.yaml

@@ -2,9 +2,9 @@ dimension: 4
 groups:
   - symbol: [4, 3, 3]
     slices:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.9, 0.9, 0.9]
     wires:
-      - root: [0.85, 0.09, 0.09, 0.09, 0.01]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
         color: [0.3, 0.3, 0.3]
         ortho: false

vis/presets/f_4_stereo.yaml

@@ -0,0 +1,12 @@
+dimension: 4
+groups:
+  - symbol: [3, 4, 3, 2]
+    slices:
+      - root: [1.00, 0.10, 0.10, 0.10, 0.05]
+        color: [1.0, 1.0, 1.0]
+        exclude:
+          - [0, 1, 2]
+    wires:
+      - root: [1.00, 0.10, 0.10, 0.10, 0.05]
+        color: [1.0, 1.0, 1.0]
+        ortho: false

vis/presets/h_4_stereo.yaml

@@ -0,0 +1,10 @@
+dimension: 4
+groups:
+  - symbol: [5, 3, 3]
+    slices:
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
+        color: [0.9, 0.9, 0.9]
+    wires:
+      - root: [0.90, 0.09, 0.09, 0.09, 0.01]
+        color: [0.3, 0.3, 0.3]
+        ortho: false

vis/presets/h_4_stereo_exclude_thick.yaml

@@ -2,7 +2,7 @@ dimension: 5
 groups:
   - symbol: [5, 3, 3, 2]
     slices:
-      - root: [0.80, 0.09, 0.09, 0.09, 0.09]
+      - root: [0.90, 0.09, 0.09, 0.09, 0.09]
         color: [0.9, 0.9, 0.9]
         exclude:
           - [0, 1, 2]

vis/shaders/CMakeLists.txt

@@ -1,5 +0,0 @@
-add_embed_library(shaders
-    solid.fs.glsl
-    deferred.vs.glsl
-    slice.gm.glsl
-    )

vis/shaders/curve-ortho.gm.glsl

@@ -0,0 +1,38 @@
+#version 430
+
+#define SUBS 20
+
+layout(lines) in;
+layout(line_strip, max_vertices = SUBS) out;
+
+layout(std430, binding=1) buffer Positions {
+    vec4 verts[];
+};
+
+layout(std140, binding=1) uniform Matrices {
+    mat4 proj;
+    mat4 view;
+};
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    float gl_PointSize;
+};
+
+in vec4 gpos[];
+
+out vec4 vpos;
+
+vec4 stereo(vec4 v) {
+    return vec4(v.xyz, 1);
+}
+
+void main() {
+    for (int i = 0; i < SUBS; i++) {
+        vpos = mix(gpos[0], gpos[1], i * 1.0f / (SUBS - 1));
+        vpos = normalize(vpos);
+        gl_Position = proj * stereo(vpos);
+        EmitVertex();
+    }
+    EndPrimitive();
+}

vis/shaders/curve-stereo.gm.glsl

@@ -0,0 +1,39 @@
+#version 430
+
+#define SUBS 20
+
+layout(lines) in;
+layout(line_strip, max_vertices = SUBS) out;
+
+layout(std430, binding=1) buffer Positions {
+    vec4 verts[];
+};
+
+layout(std140, binding=1) uniform Matrices {
+    mat4 proj;
+    mat4 view;
+};
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    float gl_PointSize;
+};
+
+in vec4 gpos[];
+
+out vec4 vpos;
+
+vec4 stereo(vec4 v) {
+    return vec4(v.xyz / (1 - v.w), 1);
+}
+
+void main() {
+    for (int i = 0; i < SUBS; i++) {
+        vpos = mix(gpos[0], gpos[1], i * 1.0f / (SUBS - 1));
+        vpos = normalize(vpos);
+
+        gl_Position = proj * stereo(vpos);
+        EmitVertex();
+    }
+    EndPrimitive();
+}

vis/shaders/diffuse.fs.glsl

@@ -0,0 +1,14 @@
+#version 430
+
+layout(location=1) in vec4 col;
+layout(location=2) in vec3 normal;
+
+out vec4 color;
+
+void main() {
+    float bright = dot(normal, normalize(vec3(-0.6, 1, 2)));
+    bright = .6 + .3 * bright;
+
+    color = col;
+    color.xyz *= bright;
+}

vis/shaders/direct-ortho.vs.glsl

@@ -0,0 +1,24 @@
+#version 430
+
+layout(std430, binding=1) buffer Positions {
+    vec4 verts[];
+};
+
+layout(std140, binding=1) uniform Matrices {
+    mat4 proj;
+    mat4 view;
+};
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    float gl_PointSize;
+};
+
+out vec4 vpos;
+
+void main() {
+    vec4 pos = verts[gl_VertexID];
+    vpos = view * pos;
+    gl_Position = proj * vec4(vpos.xyz / (1), 1);
+    gl_PointSize = 5;
+}

vis/shaders/direct-stereo.vs.glsl

@@ -0,0 +1,24 @@
+#version 430
+
+layout(std430, binding=1) buffer Positions {
+    vec4 verts[];
+};
+
+layout(std140, binding=1) uniform Matrices {
+    mat4 proj;
+    mat4 view;
+};
+
+out gl_PerVertex {
+    vec4 gl_Position;
+    float gl_PointSize;
+};
+
+out vec4 vpos;
+
+void main() {
+    vec4 pos = verts[gl_VertexID];
+    vpos = view * pos;
+    gl_Position = proj * vec4(vpos.xyz / (1 - vpos.w), 1);
+    gl_PointSize = 5;
+}

vis/shaders/slice/deferred.vs.glsl

@@ -9,16 +9,11 @@ layout(std140, binding=1) uniform Matrices {
     mat4 view;
 };
 
-layout(std140, binding=2) uniform ModelMatrices {
-    mat4 linear;
-    vec4 translation;
-};
-
 layout(location=0) in ivec4 inds;
-layout(location=1) in vec3 col;
+layout(location=1) in vec4 col;
 
 out ivec4 vInds;
-out vec3 vCol;
+out vec4 vCol;
 
 out gl_PerVertex {
     vec4 gl_Position;
@@ -29,7 +24,7 @@ void main() {
     vInds = inds;
     vCol = col;
 
-    vec4 pos = linear * verts[vInds.x] + translation;
+    vec4 pos = view * verts[vInds.x];
     gl_Position = proj * vec4(pos.xyz, 1);
     gl_PointSize = 5;
 }

vis/shaders/slice/slice.gm.glsl

@@ -12,16 +12,11 @@ layout(std140, binding=1) uniform Matrices {
     mat4 view;
 };
 
-layout(std140, binding=2) uniform ModelMatrices {
-    mat4 linear;
-    vec4 translation;
-};
-
 in ivec4 vInds[];
-in vec3 vCol[];
+in vec4 vCol[];
 
 layout(location=0) out vec4 pos;
-layout(location=1) out vec3 col;
+layout(location=1) out vec4 col;
 layout(location=2) out vec3 normal;
 
 out gl_PerVertex {
@@ -35,14 +30,13 @@ float unmix(float u, float v) {
 void emit(vec4 v) {
     pos = v;
     col = vCol[0];
-    gl_Position = proj * vec4(v.xyz, 1);
+    gl_Position = proj * view * vec4(v.xyz, 1);
     EmitVertex();
 }
 
 void main() {
     vec4 pos4[4];
-    for (int i = 0; i < 4; ++i)
-        pos4[i] = view * (linear * verts[vInds[0][i]] + translation);
+    for (int i = 0; i < 4; ++i) pos4[i] = view * verts[vInds[0][i]];
 
     int lo[4], L = 0;
     int hi[4], H = 0;

vis/shaders/solid.fs.glsl

@@ -1,7 +1,8 @@
 #version 430
 
-layout(location=0) in vec3 pos;
-layout(location=1) in vec3 col;
+layout(location=2) uniform vec3 col;
+
+layout(location=0) in vec4 pos;
 layout(location=2) in vec3 normal;
 
 out vec4 color;

vis/src/components.hpp

@@ -1,81 +0,0 @@
-#pragma once
-
-#include <cgl/buffer.hpp>
-#include <cgl/shaderprogram.hpp>
-#include <cgl/vertexarray.hpp>
-#include <cgl/pipeline.hpp>
-
-#include <tc/groups.hpp>
-
-#include <Eigen/Eigen>
-
-#include <entt/entt.hpp>
-
-#include "mirror.hpp"
-#include "geometry.hpp"
-#include "solver.hpp"
-
-#include <shaders.hpp>
-
-namespace vis {
-    using Color = Eigen::Vector<float, 3>;
-
-    template<int R_, int D_, int G_>
-    struct Structure {
-        static constexpr auto Rank = R_;
-        static constexpr auto Dim = D_;
-        static constexpr auto Grade = G_;
-
-        using AffineDf = Eigen::Transform<float, Dim, Eigen::Affine>;
-
-        using VectorRf = Eigen::Vector<float, Rank>;
-
-        // todo cache and recompute cells/points on frame (only if changed) in a system.
-
-        tc::Group group;
-        VectorRf root;
-
-        AffineDf transform = AffineDf::Identity();
-
-        explicit Structure(tc::Group const &group, VectorRf root) :
-            group(group), root(root), transform(AffineDf::Identity()) {
-        }
-    };
-
-    template<typename Str_>
-    struct Part {
-        using Str = Str_;
-
-        entt::entity parent;
-
-        GLuint first;
-        GLuint count;
-        Color color = Color::Ones();
-        bool enabled = true;
-    };
-
-    struct Command {
-        unsigned int count, instanceCount, first, baseInstance;
-    };
-
-    template<typename Str_>
-    struct VBOs {
-        using Str = Str_;
-
-        using VectorDf = Str::VectorDf;
-        using Color = Str::Color;
-        using ArrayGui = Str::ArrayGui;
-
-        struct Uniform {
-            Eigen::Matrix4f linear;
-            Eigen::Vector4f translation;
-        };
-
-        cgl::Buffer<VectorDf> vertices;
-        cgl::Buffer<Color> colors;
-        cgl::Buffer<ArrayGui> indices;
-        cgl::Buffer<Uniform> uniform;
-        cgl::Buffer<Command> commands;
-    };
-
-}

vis/src/main.cpp

@@ -1,306 +1,138 @@
-#include <glad/glad.h>
-#include <GLFW/glfw3.h>
+#include <nanogui/opengl.h>
+#include <nanogui/nanogui.h>
+#include <nanogui/glutil.h>
 
-#include <cmath>
 #include <iostream>
+#include <string>
 
-#include <imgui.h>
-#include <backends/imgui_impl_glfw.h>
-#include <backends/imgui_impl_opengl3.h>
-
+#include <geometry.hpp>
+#include <solver.hpp>
+#include <rendering.hpp>
+#include <mirror.hpp>
+#include <util.hpp>
 #include <tc/groups.hpp>
 
-#include "util.hpp"
-#include "mirror.hpp"
+mat5 wander(float time) {
+    mat5 r = mat5::Identity();
+    r *= rot<5>(0, 2, time * .15f);
+    r *= rot<5>(1, 2, time * .13f);
+    r *= rot<5>(0, 1, time * .20f);
 
-#include "components.hpp"
-#include "fmt/core.h"
-#include "fmt/ranges.h"
-#include "systems.hpp"
+    r *= rot<5>(0, 3, time * .17f);
+    r *= rot<5>(1, 3, time * .25f);
+    r *= rot<5>(2, 3, time * .12f);
 
-#include <shaders.hpp>
+//    r *= rot<5>(1, 4, time * .27f);
 
-#ifndef NDEBUG
-#include <cgl/debug.hpp>
-#include <utility>
-#endif
-
-#ifdef _WIN32
-extern "C" {
-__attribute__((unused)) __declspec(dllexport) int NvOptimusEnablement = 0x00000001;
+    return r;
 }
-#endif
 
-#ifndef M_PI_2f32
-#define M_PI_2f32 3.14159265358979323846f
-#endif
+class ExampleApplication : public nanogui::Screen {
+public:
+    std::unique_ptr<SliceRenderer<4>> ren;
+    std::unique_ptr<cgl::Buffer<Matrices>> ubo;
 
-struct Matrices {
-    Eigen::Matrix4f proj;
-    Eigen::Matrix4f view;
-
-    Matrices(Eigen::Matrix4f proj, Eigen::Matrix4f view)
-        : proj(std::move(proj)), view(std::move(view)) {
-    }
-};
-
-struct State {
-    int dimension;
+    std::vector<Slice<4>> slices;
 
+    float glfw_time = 0;
+    float last_frame = 0;
+    float frame_time = 0;
     float time = 0;
 
-    Eigen::Matrix4f view = Eigen::Matrix4f::Identity();
+    bool paused = false;
 
-    entt::registry registry;
-};
+    ExampleApplication() : nanogui::Screen(
+        Eigen::Vector2i(1920, 1080),
+        "Coset Visualization",
+        true, false,
+        8, 8, 24, 8,
+        4,
+        4, 5) {
+        using namespace nanogui;
 
-Matrices build(GLFWwindow* window, State &state, ImGuiContext* ctx) {
-    int width, height;
-    glfwGetFramebufferSize(window, &width, &height);
+//        auto *window = new Window(this, "Sample Window");
+//        window->setPosition(Vector2i(15, 15));
+//        window->setFixedWidth(250);
+//        window->setLayout(new BoxLayout(Orientation::Vertical));
 
-    auto aspect = (float) width / (float) height;
-    auto pheight = 1.4f;
-    auto pwidth = aspect * pheight;
-    Eigen::Matrix4f proj = orthographic(-pwidth, pwidth, -pheight, pheight, -10.0f, 10.0f);
+//        auto pause = new ToolButton(window, ENTYPO_ICON_CONTROLLER_PAUS);
+//        pause->setFlags(Button::ToggleButton);
+//        pause->setChangeCallback([&](bool value) { this->paused = value; });
 
-    auto &io = ImGui::GetIO();
+        performLayout();
 
-    if (io.MouseDown[0] && !io.WantCaptureMouse) {
-        Eigen::Vector4f src{0, 0, 1, 0};
-        Eigen::Vector4f dst{io.MouseDelta.x, -io.MouseDelta.y, 300, 0};
-        dst.normalize();
-
-        auto rotate = rotor(src, dst);
-        state.view = rotate * state.view;
-    }
-
-    return Matrices(proj, state.view);
-}
-
-void show_overlay(State &state) {
-    static std::string gl_vendor = (const char*) glGetString(GL_VENDOR);
-    static std::string gl_renderer = (const char*) glGetString(GL_RENDERER);
-    static std::string gl_version = (const char*) glGetString(GL_VERSION);
-    static std::string glsl_version = (const char*) glGetString(GL_SHADING_LANGUAGE_VERSION);
-
-    ImGuiWindowFlags window_flags =
-        ImGuiWindowFlags_AlwaysAutoResize |
-        ImGuiWindowFlags_NoSavedSettings |
-        ImGuiWindowFlags_NoFocusOnAppearing |
-        ImGuiWindowFlags_NoNav |
-        ImGuiWindowFlags_NoBringToFrontOnFocus |
-        ImGuiWindowFlags_NoMove;
-
-    ImGuiStyle &style = ImGui::GetStyle();
-    const auto PAD = style.DisplaySafeAreaPadding;
-    auto window_pos = PAD;
-
-    ImGui::SetNextWindowPos(window_pos, ImGuiCond_Always);
-    ImGui::SetNextWindowBgAlpha(0.35f * style.Alpha);
-    ImGui::SetNextWindowCollapsed(true, ImGuiCond_Appearing);
-    ImGui::Begin("Graphics Information", nullptr, window_flags);
-    ImGui::Text("GL Vendor    | %s", gl_vendor.c_str());
-    ImGui::Text("GL Renderer  | %s", gl_renderer.c_str());
-    ImGui::Text("GL Version   | %s", gl_version.c_str());
-    ImGui::Text("GLSL Version | %s", glsl_version.c_str());
-
-    auto v2 = ImGui::GetWindowSize();
-    window_pos.y += v2.y + PAD.y;
-    ImGui::End();
-}
-
-void show_options(entt::registry &registry) {
-    using Slice = vis::Structure<5, 4, 4>;
-    auto view = registry.view<Slice>();
-
-    for (auto [entity, structure]: view.each()) {
-        ImGui::Begin("Structure View Options");
-
-        for (int idx = 0; idx < structure.parts.size(); ++idx) {
-            const auto &part_entity = structure.parts[idx];
-            auto &part = registry.get<Slice::Part>(part_entity);
-
-            std::string label = fmt::format("{}", idx);
-
-            ImGui::Checkbox(label.c_str(), (bool*) (&(part.enabled)));
-            ImGui::ColorEdit3(label.c_str(), part.color.data(), ImGuiColorEditFlags_NoLabel);
-        }
-
-        ImGui::End();
-    }
-}
-
-void set_style() {
-    ImGui::StyleColorsDark();
-
-    ImGuiStyle &style = ImGui::GetStyle();
-    style.WindowRounding = 4;
-    style.FrameRounding = 2;
-    style.DisplaySafeAreaPadding.x = 10;
-    style.DisplaySafeAreaPadding.y = 10;
-}
-
-int run(GLFWwindow* window, ImGuiContext* ctx) {
-    if (glfwRawMouseMotionSupported()) {
-        glfwSetInputMode(window, GLFW_RAW_MOUSE_MOTION, GLFW_TRUE);
-    }
-
-    glEnable(GL_DEPTH_TEST);
-
-    glEnable(GL_BLEND);
-    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
-
-    using Slice = vis::Structure<5, 4, 4>;
-    vis::SliceRenderer<Slice> renderer;
-
-    State state{};
-    glfwSetWindowUserPointer(window, &state);
-
-    auto &registry = state.registry;
-    state.dimension = 4;
-
-    auto entity = registry.create();
-    registry.emplace<Slice>(
-        entity,
-        tc::schlafli({5, 3, 3, 2}),
-        vec5{0.80, 0.09, 0.09, 0.09, 0.09}
-    );
-    registry.emplace<vis::VBOs<Slice>>(entity);
-
-    vis::upload_structure<Slice>(registry);
-    registry.get<Slice::Part>(
-        registry.get<Slice>(entity).parts[0]
-    ).enabled = false;
-//    registry.get<Slice>(entity).enabled[0] = false;  // disable {0,1,2} cells
-
-    auto ubo = cgl::Buffer<Matrices>();
-    glBindBufferBase(GL_UNIFORM_BUFFER, 1, ubo);
-
-    while (!glfwWindowShouldClose(window)) {
-        glfwPollEvents();
-
-        ImGui_ImplOpenGL3_NewFrame();
-        ImGui_ImplGlfw_NewFrame();
-
-        auto io = ImGui::GetIO();
-        if (io.KeysDown[GLFW_KEY_ESCAPE]) {
-            glfwSetWindowShouldClose(window, true);
-            continue;
-        }
-
-        ImGui::NewFrame();
-        show_overlay(state);
-        show_options(registry);
-        ImGui::Render();
-
-        int width, height;
-        glfwGetFramebufferSize(window, &width, &height);
-        glViewport(0, 0, width, height);
-
-        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
-
-        ubo.put(build(window, state, ctx), GL_STREAM_DRAW);
+        std::cout << utilInfo();
 
         {
-            auto &tform = registry.get<Slice>(entity).transform;
-
-            if (!io.KeysDown[GLFW_KEY_SPACE]) {
-                float speed = 1.0 / 8.0;
-                if (io.KeysDown[GLFW_KEY_LEFT_SHIFT] | io.KeysDown[GLFW_KEY_RIGHT_SHIFT]) {
-                    speed /= 4;
+            std::vector<int> symbol = {3, 4, 3, 2};
+            auto group = tc::schlafli(symbol);
+            auto ctx = generators(group);
+            auto selected_ctxs = set_difference(
+                combinations(ctx, 3),
+                {
+                    {0, 1, 2},
                 }
-                state.time += io.DeltaTime * speed;
-            }
+            );
+            auto mesh = fill_each_tile_merge<4>(group, selected_ctxs);
 
-            tform.linear().setIdentity();
-
-            if (state.dimension > 1) {
-                tform.linear() *= rot<4>(0, 1, state.time * .40f);
-            }
-            if (state.dimension > 2) {
-                tform.linear() *= rot<4>(0, 2, state.time * .20f);
-                tform.linear() *= rot<4>(1, 2, state.time * .50f);
-            }
-            if (state.dimension > 3) {
-                tform.linear() *= rot<4>(0, 3, state.time * 1.30f);
-                tform.linear() *= rot<4>(1, 3, state.time * .25f);
-                tform.linear() *= rot<4>(2, 3, state.time * 1.42f);
-            }
-
-            tform.translation().w() = std::sin(state.time * 1.4) * 1.0;
+            auto &slice = slices.emplace_back(group);
+            slice.setMesh(mesh);
+            slice.root << .80, .02, .02, .02, .02;
         }
 
-        vis::upload_commands<Slice>(registry);
-        vis::upload_uniforms<Slice>(registry);
+        ren = std::make_unique<SliceRenderer<4>>();
 
-        renderer(registry);
-
-        ImGui_ImplOpenGL3_RenderDrawData(ImGui::GetDrawData());
-
-        glfwSwapInterval(2);
-        glfwSwapBuffers(window);
+        ubo = std::make_unique<cgl::Buffer<Matrices>>();
     }
 
-    return EXIT_SUCCESS;
-}
+    void drawContents() override {
+        glEnable(GL_DEPTH_TEST);
 
-int main(int argc, char* argv[]) {
-    if (!glfwInit()) {
-        std::cerr << "Failed to initialize GLFW" << std::endl;
-        return EXIT_FAILURE;
+        glEnable(GL_BLEND);
+        glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
+
+        glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
+
+        glViewport(0, 0, width(), height());
+        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+
+        glfw_time = (float) glfwGetTime();
+        frame_time = glfw_time - last_frame;
+        last_frame = glfw_time;
+        if (!paused) time += frame_time;
+
+        auto rotation = wander(time);
+        for (auto &slice : slices) {
+            slice.transform = rotation;
+            slice.setPoints();
+        }
+
+        Matrices mats = Matrices::build(*this);
+        glBindBufferBase(GL_UNIFORM_BUFFER, 1, *ubo);
+        ubo->put(mats);
+        for (const auto &slice : slices) {
+            ren->draw(slice);
+        }
     }
+};
 
-    glfwWindowHint(GLFW_VERSION_MAJOR, 4);
-    glfwWindowHint(GLFW_VERSION_MAJOR, 5);
-//    glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
-
-    glfwWindowHint(GLFW_SAMPLES, 8);
-
-//    glfwWindowHint(GLFW_DECORATED, false);
-//    glfwWindowHint(GLFW_TRANSPARENT_FRAMEBUFFER, true);
-
-    auto window = glfwCreateWindow(
-        1920, 1080,
-        "Coset Visualization",
-        nullptr, nullptr);
-
-    if (!window) {
-        std::cerr << "Failed to create window" << std::endl;
-        glfwTerminate();
-        exit(EXIT_FAILURE);
-    }
-
-    glfwMakeContextCurrent(window);
-    gladLoadGLLoader((GLADloadproc) glfwGetProcAddress);
-    glfwSwapInterval(1);
-
-#ifndef NDEBUG
-    glEnable(GL_DEBUG_OUTPUT);
-    glDebugMessageCallback(log_gl_debug_callback, nullptr);
-#endif
-
-    IMGUI_CHECKVERSION();
-    auto* context = ImGui::CreateContext();
-    ImGui_ImplGlfw_InitForOpenGL(window, true);
-    ImGui_ImplOpenGL3_Init("#version 130");
-
-    set_style();
-
-    int exit_code = EXIT_SUCCESS;
-
+int main(int argc, char **argv) {
     try {
-        exit_code = run(window, context);
-    } catch (const std::exception &e) {
-        std::cerr << e.what() << std::endl;
-        exit_code = EXIT_FAILURE;
+        nanogui::init();
+
+        /* scoped variables */ {
+            nanogui::ref<ExampleApplication> app = new ExampleApplication();
+            app->drawAll();
+            app->setVisible(true);
+            nanogui::mainloop(1);
+        }
+
+        nanogui::shutdown();
+    } catch (const std::runtime_error &e) {
+        std::string error_msg = std::string("Caught a fatal error: ") + std::string(e.what());
+        std::cerr << error_msg << std::endl;
+        return -1;
     }
 
-    ImGui_ImplOpenGL3_Shutdown();
-    ImGui_ImplGlfw_Shutdown();
-    ImGui::DestroyContext();
-
-    glfwDestroyWindow(window);
-    glfwTerminate();
-
-    return exit_code;
+    return 0;
 }

vis/src/systems.hpp

@@ -1,169 +0,0 @@
-#pragma once
-
-#include <cgl/buffer.hpp>
-#include <cgl/shaderprogram.hpp>
-#include <cgl/vertexarray.hpp>
-#include <cgl/pipeline.hpp>
-
-#include <tc/groups.hpp>
-
-#include <Eigen/Eigen>
-
-#include <entt/entt.hpp>
-
-#include "mirror.hpp"
-#include "geometry.hpp"
-#include "solver.hpp"
-#include "components.hpp"
-
-#include <shaders.hpp>
-
-namespace vis {
-    template<typename Str>
-    void upload_structure(entt::registry &registry) {
-        {
-            auto parts = registry.view<Part<Str>>();
-            registry.destroy(parts.begin(), parts.end());
-        }
-
-        auto view = registry.view<Str, VBOs<Str>>();
-
-        for (auto [entity, structure, vbos]: view.each()) {
-            Points points(structure.group, structure.root);
-            Hull<Str::Grade> hull(structure.group);
-
-            auto &&vertices = points.verts.colwise();
-            auto &&indices = hull.inds.colwise();
-
-            vbos.vertices.put(vertices.begin(), vertices.end());
-            vbos.indices.put(indices.begin(), indices.end());
-
-            for (const auto &tiling: hull.tilings) {
-                auto part_entity = registry.create();
-                registry.emplace<Part<Str>>(
-                    part_entity,
-                    entity,
-                    tiling.first,
-                    tiling.count
-                );
-            }
-        }
-    }
-
-    template<typename Str>
-    void upload_uniforms(entt::registry &registry) {
-        auto view = registry.view<Part<Str>>();
-
-        for (auto [entity, part]: view.each()) {
-            auto &vbos = registry.get<VBOs<Str>>(part.parent);
-        }
-
-        for (auto [entity, structure, vbos]: view.each()) {
-            std::vector<typename Str::Color> colors;
-            for (const auto &part_entity: structure.parts) {
-                const auto &part = registry.get<typename Str::Part>(part_entity);
-                colors.push_back(part.color);
-            }
-            vbos.colors.put(colors.begin(), colors.end());
-
-            typename VBOs<Str>::Uniform uniform{
-                structure.transform.linear(),
-                structure.transform.translation(),
-            };
-            vbos.uniform.put(uniform, GL_STREAM_DRAW);
-        }
-    }
-
-    template<typename Str>
-    void upload_commands(entt::registry &registry) {
-        auto view = registry.view<Part<Str>>();
-        for (auto [entity, part]: view.each()) {
-            Command comm(part.count, 1, part.first, )
-        }
-
-        auto view = registry.view<Str, VBOs<Str>>();
-
-        for (auto [entity, structure, vbos]: view.each()) {
-            std::vector<typename VBOs<Str>::Command> commands;
-
-            for (unsigned int idx = 0; idx < structure.parts.size(); idx++) {
-                const auto &part_entity = structure.parts[idx];
-                const auto &part = registry.get<typename Str::Part>(part_entity);
-                if (part.enabled) {
-                    commands.push_back(
-                        {
-                            part.count,
-                            1,
-                            part.first,
-                            idx
-                        }
-                    );
-                }
-            }
-
-            vbos.commands.put(commands.begin(), commands.end(), GL_STREAM_DRAW);
-        }
-    }
-
-    template<typename Str_>
-    struct SliceRenderer {
-        using Str = Str_;
-
-        cgl::pgm::vert defer = cgl::pgm::vert(shaders::deferred_vs_glsl);
-        cgl::pgm::geom slice = cgl::pgm::geom(shaders::slice_gm_glsl);
-        cgl::pgm::frag solid = cgl::pgm::frag(shaders::solid_fs_glsl);
-
-        cgl::pipeline pipe;
-
-        cgl::VertexArray vao;
-
-        SliceRenderer() {
-            pipe.stage(defer);
-            pipe.stage(slice);
-            pipe.stage(solid);
-
-            vao.iformat(0, Str::Grade, GL_UNSIGNED_INT);  // inds
-
-            vao.format(1, 3, GL_FLOAT);  // color
-            glVertexArrayBindingDivisor(vao, 1, 1);
-        }
-
-        void operator()(entt::registry &reg) {
-            auto view = reg.view<VBOs<Str>>();
-
-            for (auto [entity, vbos]: view.each()) {
-                glBindProgramPipeline(pipe);
-
-                glBindBufferBase(
-                    GL_SHADER_STORAGE_BUFFER,
-                    1,
-                    vbos.vertices
-                );
-                glBindBufferBase(
-                    GL_UNIFORM_BUFFER,
-                    2,
-                    vbos.uniform
-                );
-
-                glBindBuffer(
-                    GL_DRAW_INDIRECT_BUFFER,
-                    vbos.commands
-                );
-
-                vao.vertexBuffer(0, vbos.indices);
-                vao.vertexBuffer(1, vbos.colors);
-
-                glBindVertexArray(vao);
-                glMultiDrawArraysIndirect(
-                    GL_POINTS,
-                    nullptr,
-                    vbos.commands.count(),
-                    0
-                );
-                glBindVertexArray(0);
-
-                glBindProgramPipeline(0);
-            }
-        }
-    };
-}