以递归遍历的方式搜索四叉树quadtree的每个节点，获取区域范围与射线相交的叶子节点中存储的三角面索引，并且根据索引得到三角面的顶点坐标和法向量，最后用射线与三角面进行求交运算，最后遍历完整棵四叉树，得到射线与所有三角面的交点，返回交点坐标和索引信息。请编写一段完整的matlab代码。

以下是一个简单的Matlab代码，用于搜索四叉树quadtree的每个节点，获取区域范围与射线相交的叶子节点中存储的三角面索引，并且根据索引得到三角面的顶点坐标和法向量，最后用射线与三角面进行求交运算，最后遍历完整棵四叉树，得到射线与所有三角面的交点，返回交点坐标和索引信息。

function [vertices, normals, indices] = quadtree_ray_tracing(root, ray_origin, ray_direction)
    % Recursive function to traverse the quadtree and find intersections
    % with ray
    
    % Check if current node is a leaf node
    if isempty(root.children)
        % Check if ray intersects with leaf node's bounding box
        intersection = ray_box_intersection(root.box, ray_origin, ray_direction);
        if intersection
            % Get triangle indices from leaf node
            indices = root.indices;
            % Get vertices and normals from indices
            [vertices, normals] = get_vertices_normals(indices);
            % Find ray-triangle intersections
            [intersections, ~] = TriangleRayIntersection(ray_origin, ray_direction, vertices);
            % Return intersection information
            if ~isempty(intersections)
                % Find closest intersection
                [~, index] = min(intersections);
                intersection_point = vertices(index, :);
                intersection_normal = normals(index, :);
                return
            end
        end
    else
        % Recursively traverse child nodes
        for i = 1:length(root.children)
            child = root.children(i);
            intersection = ray_box_intersection(child.box, ray_origin, ray_direction);
            if intersection
                [vertices, normals, indices] = quadtree_ray_tracing(child, ray_origin, ray_direction);
                if ~isempty(indices)
                    return
                end
            end
        end
    end
    
    % No intersection found
    vertices = [];
    normals = [];
    indices = [];
end

function [vertices, normals] = get_vertices_normals(indices)
    % Get vertices and normals from triangle indices
    
    % Load mesh data
    mesh_data = load('mesh_data.mat');
    vertices = mesh_data.vertices;
    normals = mesh_data.normals;
    
    % Get vertices and normals for each triangle
    vertices = vertices(indices, :);
    normals = normals(indices, :);
end

function intersection = ray_box_intersection(box, ray_origin, ray_direction)
    % Check if ray intersects with bounding box
    
    % Check for intersection with each face of bounding box
    tmin = (box([1 2 3]) - ray_origin) ./ ray_direction;
    tmax = (box([4 5 6]) - ray_origin) ./ ray_direction;
    
    tmin = max(min(tmin, tmax), 0);
    tmax = min(max(tmin, tmax), 1);
    
    intersection = all(tmax >= tmin);
end

function [t, u, v] = TriangleRayIntersection(Orig, Dir, Verts)
    % Calculate ray-triangle intersection
    
    % Triangle vertices
    v1 = Verts(1,:);
    v2 = Verts(2,:);
    v3 = Verts(3,:);
    
    % Edge vectors
    e1 = v2 - v1;
    e2 = v3 - v1;
    
    % Normal vector
    n = cross(e1, e2);
    
    % Check if ray is parallel to triangle
    ndotd = dot(n, Dir);
    if abs(ndotd) < eps
        t = Inf;
        u = 0;
        v = 0;
        return
    end
    
    % Calculate intersection point
    w = Orig - v1;
    ndotw = dot(n, w);
    t = -ndotw / ndotd;
    
    % Check if intersection is behind ray origin
    if t < 0
        t = Inf;
        u = 0;
        v = 0;
        return
    end
    
    % Calculate barycentric coordinates
    q = cross(Dir, e2);
    u = dot(w, q) / dot(n, q);
    p = cross(w, e1);
    v = dot(Dir, p) / dot(n, p);
    
    % Check if point is inside triangle
    if u < 0 || v < 0 || u + v > 1
        t = Inf;
        u = 0;
        v = 0;
        return
    end
end

请注意，上面的代码只是一个简单的示例，需要根据具体的应用场景和数据格式进行修改和调整。同时，代码中还需要加载存储三角面数据的文件，这里假设该数据以matlab格式存储，文件名为`mesh_data.mat`，包含`vertices`和`normals`两个变量，分别存储所有三角面的顶点坐标和法向量。