toddcox-faster/include/tc/complex.hpp

#pragma once

#include <tc/group.hpp>
#include <tc/solver.hpp>
#include <cmath>
#include <optional>
#include <numeric>
#include <iostream>
#include <utility>

namespace tc {
    std::vector<Symbol> combinations(const Symbol &symbol, size_t srank) {
        size_t rank = symbol.size();

        std::vector<bool> mask(rank, false);
        std::fill_n(mask.begin(), srank, true);

        std::vector<Symbol> combos;
        combos.reserve(choose(rank, srank));

        Symbol row(srank);
        do {
            for (int j = 0, k = 0; j < rank; ++j) {
                if (mask[j]) {
                    row(k++) = symbol(j);
                }
            }
            combos.emplace_back(row);
        } while (std::prev_permutation(mask.begin(), mask.end()));

        return combos;
    }

    // todo remove
    ArrayXui fan(const ArrayXui &prims, int root) {
        ArrayXui res(prims.rows() + 1, prims.cols());
        res.topRows(prims.rows()) << prims;
        res.bottomRows(1).fill(root);
        return res;
    }

    // todo visitor
    void apply(const tc::Cosets &table, unsigned int gen, ArrayXui &prims) {
        for (Eigen::Index i = 0; i < prims.size(); ++i) {
            prims(i) = table.get(prims(i), gen);
        }
    }

/**
 * 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.
 */
    void recontext(
        ArrayXui &prims,
        const tc::Group &context,
        const Symbol &g_gens,
        const Symbol &sg_gens
    ) {
        const auto proper_sg_gens = recontext_gens(context.rank(), g_gens, sg_gens);

        const auto table = solve(context, g_gens, Symbol(0));
        const auto path = solve(context, sg_gens, Symbol(0)).path();

        auto map = path.walk(0U, proper_sg_gens, [&table](auto coset, auto gen) {
            return table.get(coset, gen);
        });

        // todo visitor
        for (Eigen::Index i = 0; i < prims.size(); ++i) {
            prims(i) = map[prims(i)];
        }
    }

    // todo remove
    ArrayXui merge(const std::vector<ArrayXui> &meshes) {
        Eigen::Index cols = 0;
        for (const auto &mesh: meshes) {
            cols += mesh.cols();
        }

        ArrayXui res(meshes[0].rows(), cols);
        Eigen::Index offset = 0;
        for (const auto &mesh: meshes) {
            res.middleCols(offset, mesh.cols()) << mesh;
            offset += mesh.cols();
        }

        return res;
    }

    std::vector<ArrayXui> each_tile(
        ArrayXui base,
        const tc::Group &context,
        const Symbol &g_gens,
        const Symbol &sg_gens
    ) {
        recontext(base, context, g_gens, sg_gens);

        const auto table = solve(context, g_gens, Symbol(0));
        const auto path = solve(context, g_gens, sg_gens).path();

        auto _gens = context.gens;

        auto res = path.walk(base, _gens, [&table](auto from, auto &gen) {
            apply(table, gen, from);
            return from;
        });

        return res;
    }

    /**
 * Produce a mesh of primitives that fill out the volume of the subgroup generated by generators g_gens within the group context
 */
    ArrayXui triangulate(
        const tc::Group &context,
        const Symbol &g_gens
    ) {
        if (g_gens.size() == 0) {
            return ArrayXui::Zero(1, 1);
        }

        const auto &combos = combinations(g_gens, g_gens.size() - 1);

        std::vector<ArrayXui> meshes;

        // todo inline logic
        //  erase, merge, and fan can be inlined
        //  for 1..#tiles
        //   cols += cols
        //   parts.append(cols)
        //  result(rows, cols)
        //  for 1..#parts
        //   result.middlecols << part
        //  result.bottomrow.fill(0)

        // todo subgroup/coset metadata
        //  would be good to also output which coset of which subgroup each primitive is a part of.
        //  this could be used in shaders etc to make rendering things easier

        for (const auto &sg_gens: combos) {
            auto base = triangulate(context, sg_gens);
            auto tiles = each_tile(base, context, g_gens, sg_gens);
            tiles.erase(tiles.begin(), tiles.begin() + 1);
            auto raised = merge(tiles);
            auto fanned = fan(raised, 0);
            meshes.push_back(fanned);
        }

        const ArrayXui &result = merge(meshes);
        return result;
    }

    template<class T>
    auto hull(const tc::Group &group, T all_sg_gens) {
        std::vector<ArrayXui> parts;
        auto g_gens = group.gens;

        // todo inline logic
        //  should be able to inline in a similar way as is possible in triangulate

        for (const Symbol &sg_gens: all_sg_gens) {
            const auto &base = triangulate(group, sg_gens);
            const auto &tiles = each_tile(base, group, g_gens, sg_gens);
            for (const auto &tile: tiles) {
                parts.push_back(tile);
            }
        }
        return parts;
    }
}