kdtree/kdtree.h

#include <algorithm>
#include <glm/glm.hpp>
#include <vector>

// Forward declarations
struct Node;
struct Point;
struct Triangle;

struct Node {
    Node(int axis, Point *point, Node *left, Node *right)
        : axis(axis), point(point), left(left), right(right) {}

    int axis;

    Point *point;

    Node *left;
    Node *right;
};

struct Triangle {
    Triangle(Point *p1, Point *p2, Point *p3) : p1(p1), p2(p2), p3(p3) {}

    Point *p1;
    Point *p2;
    Point *p3;
};

struct Point {
    Point(float coordinates[3], Triangle *triangle)
        : coordinates(coordinates), triangle(triangle) {}

    float *coordinates;

    Triangle *triangle;
};

class KDTree {
  public:
    KDTree(std::vector<Point *> points) { root = build(points, 0); }

    ~KDTree() = default;

  private:
    Node *root;

    int MAX_DEPTH = 500;

    // Returns a comparator lambda for assessing which of the two points has a
    // greater coordinate in the given axis.
    auto get_point_comparator(int axis) {
        return [axis](Point *p1, Point *p2) {
            return p1->coordinates[axis] < p2->coordinates[axis];
        };
    }

    Node *build(std::vector<Point *> points, int depth) {
        // Exit conditions
        if (points.empty() || depth > MAX_DEPTH) { return nullptr; }

        // Select axis by choosing the one with maximal extent
        float max_extent = 0;
        int axis = 0;

        for (int it_axis = 0; it_axis < 3; it_axis++) {
            // Get extent along this axis
            auto comparator = get_point_comparator(it_axis);

            Point *min = *std::max_element(points.begin(), points.end(), comparator);
            Point *max = *std::max_element(points.begin(), points.end(), comparator);

            float extent = max->coordinates[it_axis] - min->coordinates[it_axis];

            // Is it greater than max_extent?
            if (extent > max_extent) {
                // If so, make this the splitting axis
                max_extent = extent;
                axis = it_axis;
            }
        }

        // Choose the median as the pivot and sort the points into
        // left-of-median and right-of-median using nth_element
        int middle = points.size() / 2;

        std::nth_element(points.begin(), points.begin() + middle, points.end(),
                         get_point_comparator(axis));

        Point *median;
        float pivot;

        // TODO: This copies. Can we split the vector into two without copying?
        std::vector<Point *> left_of_median(points.begin(), points.begin() + middle);
        std::vector<Point *> right_of_median(points.begin() + middle, points.end());

        // Create node, recursively call to construct subtree
        return new Node(axis, median, build(left_of_median, depth + 1),
                        build(right_of_median, depth + 1));
    }
};