loose_quadtree.h

#pragma once
 
#include <cstdint>
#include "../../math/aabb.h"
#include "../../frustum.h"
#include "../../generic/check_signature.h"
 
namespace smlt {
 
static constexpr int64_t ipow(int64_t base, int exp, int64_t result = 1) {
  return exp < 1 ? result : ipow(base*base, exp/2, (exp % 2) ? result*base : result);
}
 
/*
 * Fast loose-Quadtree implementation with O(1) insertions, built on a linear
 * array for good cache locality.
 *
 * TreeData is a structure which contains data needed across the whole tree,
 * this may usually contain the vertex data for the mesh being inserted.
 *
 * NodeData is a structure for storing data on the individual nodes, this is usually
 * index data for the mesh.
 */
 
typedef uint8_t Level;
typedef uint16_t GridCoord;
 
template<typename TreeData, typename NodeData>
class Quadtree {
public:
    struct Node {
        Level level = 0;
        GridCoord grid[2] = {0, 0};
        NodeData* data = nullptr;
        uint32_t child_indexes[4];
 
        Vec3 centre;
        float size;
    };
 
    using TraverseCallback = void(Quadtree::Node*);
 
    typedef TreeData tree_data_type;
    typedef NodeData node_data_type;
 
    Quadtree(const AABB& bounds, uint8_t max_level_count=4, std::shared_ptr<TreeData> tree_data=std::shared_ptr<TreeData>()):
        tree_data_(tree_data),
        root_width_(bounds.max_dimension()),
        bounds_(bounds),
        centre_(bounds_.centre()) {
 
        /* Make sure the bounds are square */
        float maxd = root_width_;
        auto halfd = maxd / 2.0f;
 
        auto half = Vec3(halfd, 0, halfd);
        bounds_.set_min(centre_ - half);
        bounds_.set_max(centre_ + half);
 
        /* Grow the tree to whatever size we passed in */
        grow(max_level_count);
    }
 
    virtual ~Quadtree() {
        /* Make sure we delete the node data */
        for(auto& node: nodes_) {
            delete node.data;
            node.data = nullptr;
        }
    }
 
    bool is_leaf(Node& node) const {
        return node.level == (levels_ - 1);
    }
 
    Quadtree::Node* find_destination_for_sphere(const Vec3& centre, float radius) {
        auto diameter = radius * 2.0f;
        auto level_and_node_width = level_for_width(diameter);
 
        /* Calculate the cell index to insert the sphere */
        auto half_width = root_width_ * 0.5f;
 
        assert(centre.x <= bounds_.max().x && centre.x >= bounds_.min().x);
        assert(centre.z <= bounds_.max().z && centre.z >= bounds_.min().z);
 
        auto x = (GridCoord) ((centre.x + half_width - centre_.x) / level_and_node_width.second);
        auto z = (GridCoord) ((centre.z + half_width - centre_.z) / level_and_node_width.second);
 
        assert(x >= 0);
        assert(z >= 0);
 
        auto level_width = ipow(2, level_and_node_width.first);
        assert(x <= level_width);
        assert(z <= level_width);
 
        /* This handles the case that the center was on the cusp of the cell
         * in which case the above calculation will result in an out of range
         * index */
        x = std::min<GridCoord>(x, level_width - 1);
        z = std::min<GridCoord>(z, level_width - 1);
 
        auto idx = calc_index(level_and_node_width.first, x, z);
        assert(idx < nodes_.size());
 
        return &nodes_[idx];
    }
 
    Quadtree::Node* find_destination_for_triangle(const Vec3* vertices) {
        /*
         * Return the node that this triangle should be
         * inserted into (the actual insertion won't happen as that's implementation specific
         * depending on the NodeData).
         */
 
        AABB bounds(vertices, 3);
        auto centre = bounds.centre();
        auto radius = bounds.max_dimension() / 2.0f;
        return find_destination_for_sphere(centre, radius);
    }
 
    void traverse(std::function<void (Quadtree::Node*)> cb) {
        if(nodes_.empty()) {
            return;
        }
 
        std::function<void (Quadtree::Node&)> visitor = [&](Quadtree::Node& node) {
            cb(&node);
 
            if(!is_leaf(node)) {
                for(auto child: node.child_indexes) {
                    assert(child < nodes_.size());
                    visitor(nodes_[child]);
                }
            }
        };
 
        visitor(nodes_[0]);
    }
 
    template<typename Callback>
    void traverse_visible(const Frustum& frustum, const Callback& cb) {
        check_signature<Callback, TraverseCallback>();
 
        if(nodes_.empty()) {
            return;
        }
 
        _visible_visitor(frustum, cb, nodes_[0]);
    }
 
    AABB bounds() const { return bounds_; }
 
    TreeData* data() const { return tree_data_.get(); }
private:
    template<typename Callback>
    void _visible_visitor(const Frustum& frustum, const Callback& callback, Quadtree::Node& node) {
        if(frustum.intersects_cube(node.centre, node.size * 2.0f)) {
            callback(&node);
 
            if(!is_leaf(node)) {
                for(auto child: node.child_indexes) {
                    assert(child < nodes_.size());
                    _visible_visitor(frustum, callback, nodes_[child]);
                }
            }
        }
    }
 
    std::pair<Level, float> level_for_width(float obj_width) {
        /*
         * Given the diameter of the object
         * this returns the level the object will fit, and the node width at that level
         *
         * I *know* there's a non-iterative way to calculate this, so if you know, let me know!
         */
 
        assert(obj_width <= root_width_);
 
        if(obj_width > root_width_) {
            // Should never happen, but this is the safest thing to do if it does
            return std::make_pair(0, root_width_);
        }
 
        auto node_width = root_width_;
        Level depth = 0;
 
        while(node_width >= obj_width) {
            ++depth;
            node_width *= 0.5f;
 
            if(depth == levels_) {
                break;
            }
        }
 
        assert(depth >= 1);
 
        // Off-by-one
        return std::make_pair(depth - 1, node_width * 2);
    }
 
    void calc_bounds(Quadtree::Node& node) const {
        auto grid_width = ipow(2, node.level);
        auto cell_width = bounds_.max_dimension() / grid_width;
 
        Vec3 min(node.grid[0] * cell_width, 0, node.grid[1] * cell_width);
        min += bounds_.min();
 
        float hw = cell_width * 0.5f;
        node.centre = min + Vec3(hw, hw, hw);
        node.size = cell_width;
    }
 
    static uint32_t calc_base(uint8_t level) {
        if(level == 0) return 0;
        if(level == 1) return 1;
        return calc_base(level - 1) + ipow(ipow(2, level - 1), 2);
    }
 
    static uint32_t calc_index(Level k, GridCoord x, GridCoord z) {
        auto level_base = calc_base(k);
        auto level_width = ipow(2, k);
 
        assert(x < level_width);
        assert(z < level_width);
 
        auto idx = x + level_width * z;
        return level_base + idx;
    }
 
    static void calc_child_indexes(Quadtree::Node& node) {
        uint8_t count = 0;
        for(uint32_t z = 0; z <= 1; ++z) {
            for(uint32_t x = 0; x <= 1; ++x) {
                node.child_indexes[count++] = calc_index(
                    node.level + 1,
                    2 * node.grid[0] + x,
                    2 * node.grid[1] + z
                );
            }
        }
    }
 
    void grow(uint8_t required_levels) {
 
        auto required_nodes = 0;
        for(uint8_t i = 0; i < required_levels; ++i) {
            auto nodes_across = ipow(2, i);
            required_nodes += ipow(nodes_across, 2);
        }
 
        levels_ = required_levels;
        nodes_.resize(required_nodes, Quadtree::Node());
 
        for(auto k = 0; k < levels_; ++k) {
            auto nodes_across = ipow(2, k);
 
            for(GridCoord z = 0; z < nodes_across; ++z) {
                for(GridCoord x = 0; x < nodes_across; ++x) {
                    auto idx = calc_index(k, x, z);
                    assert(idx < nodes_.size());
                    auto& new_node = nodes_[idx];
 
                    assert(!new_node.data);
 
                    new_node.grid[0] = x;
                    new_node.grid[1] = z;
                    new_node.level = k;
                    new_node.data = new NodeData();
 
                    calc_child_indexes(new_node);
                    calc_bounds(new_node);
                }
            }
        }
    }
 
    std::shared_ptr<TreeData> tree_data_;
 
    float root_width_;
    AABB bounds_;
    Vec3 centre_;
 
    Level levels_ = 0;
    std::vector<Quadtree::Node> nodes_;
 
    friend class LooseQuadtreeTests;
};
 
}