how to use morton code to build octree on a obj format mesh C++

To use Morton code to build an octree on a .obj format mesh in C++, you can follow these steps:

1. Load the .obj file into your program and extract the vertex positions and face indices.
2. Calculate the bounding box of the mesh using the vertex positions.
3. Divide the bounding box into eight equal sub-boxes to create the root nodes of the octree.
4. For each vertex in the mesh, calculate its Morton code based on its position relative to the bounding box.
5. Traverse the octree from the root nodes and insert each vertex into the appropriate leaf node based on its Morton code.
6. For each face in the mesh, calculate its bounding box and traverse the octree to find the nodes that intersect with the box.
7. For each intersecting node, add the face to the list of faces stored in that node.
8. If a leaf node contains more than a certain number of vertices or faces, subdivide it into eight child nodes and redistribute the vertices and faces among them.
9. Repeat steps 4-8 until all vertices and faces have been inserted into the octree.

Here is some sample code that demonstrates how to use Morton code to build an octree:

#include <vector>
#include <Eigen/Dense>

using namespace Eigen;

// Node structure for octree
struct OctreeNode {
    Vector3d minCorner;
    Vector3d maxCorner;
    std::vector<Vector3d> vertices;
    std::vector<int> faces;
    OctreeNode* children[8];
};

// Calculate Morton code for a point
uint64_t mortonCode(Vector3d point, Vector3d minCorner, Vector3d maxCorner) {
    uint64_t code = 0;
    for (int i = 0; i < 3; i++) {
        double normalizedCoord = (point[i] - minCorner[i]) / (maxCorner[i] - minCorner[i]);
        normalizedCoord = std::min(std::max(normalizedCoord, 0.0), 1.0);
        uint64_t mortonCoord = normalizedCoord * 1023;
        code |= (mortonCoord << (i * 10));
    }
    return code;
}

// Insert a vertex into the octree
void insertVertex(OctreeNode* node, Vector3d vertex, Vector3d minCorner, Vector3d maxCorner) {
    uint64_t code = mortonCode(vertex, minCorner, maxCorner);
    for (int i = 0; i < 8; i++) {
        Vector3d childMin = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d(i & 1, (i >> 1) & 1, (i >> 2) & 1));
        Vector3d childMax = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d((i & 1) + 1, ((i >> 1) & 1) + 1, ((i >> 2) & 1) + 1));
        if (code >= mortonCode(childMin, minCorner, maxCorner) && code <= mortonCode(childMax, minCorner, maxCorner)) {
            if (node->children[i] == nullptr) {
                node->children[i] = new OctreeNode;
                node->children[i]->minCorner = childMin;
                node->children[i]->maxCorner = childMax;
            }
            insertVertex(node->children[i], vertex, minCorner, maxCorner);
            break;
        }
    }
    node->vertices.push_back(vertex);
}

// Insert a face into the octree
void insertFace(OctreeNode* node, MatrixXd vertices, Vector3i face, Vector3d minCorner, Vector3d maxCorner) {
    Vector3d faceMin = vertices.row(face.minCoeff()).transpose().cwiseMin(vertices.row(face.maxCoeff()).transpose()).cwiseMin(vertices.row(face(1)).transpose());
    Vector3d faceMax = vertices.row(face.maxCoeff()).transpose().cwiseMax(vertices.row(face.minCoeff()).transpose()).cwiseMax(vertices.row(face(1)).transpose());
    for (int i = 0; i < 8; i++) {
        Vector3d childMin = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d(i & 1, (i >> 1) & 1, (i >> 2) & 1));
        Vector3d childMax = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d((i & 1) + 1, ((i >> 1) & 1) + 1, ((i >> 2) & 1) + 1));
        if (faceMin[0] <= childMax[0] && faceMax[0] >= childMin[0] &&
            faceMin[1] <= childMax[1] && faceMax[1] >= childMin[1] &&
            faceMin[2] <= childMax[2] && faceMax[2] >= childMin[2]) {
            if (node->children[i] != nullptr) {
                insertFace(node->children[i], vertices, face, minCorner, maxCorner);
            } else {
                node->faces.push_back(face);
            }
        }
    }
}

// Subdivide a node into eight child nodes
void subdivideNode(OctreeNode* node, Vector3d minCorner, Vector3d maxCorner) {
    Vector3d center = 0.5 * (node->minCorner + node->maxCorner);
    for (int i = 0; i < 8; i++) {
        Vector3d childMin = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d(i & 1, (i >> 1) & 1, (i >> 2) & 1));
        Vector3d childMax = node->minCorner + 0.5 * (node->maxCorner - node->minCorner).cwiseProduct(Vector3d((i & 1) + 1, ((i >> 1) & 1) + 1, ((i >> 2) & 1) + 1));
        node->children[i] = new OctreeNode;
        node->children[i]->minCorner = childMin;
        node->children[i]->maxCorner = childMax;
        for (Vector3d vertex : node->vertices) {
            insertVertex(node->children[i], vertex, minCorner, maxCorner);
        }
        for (int faceIdx : node->faces) {
            insertFace(node->children[i], vertices, faces.row(faceIdx), minCorner, maxCorner);
        }
    }
    node->vertices.clear();
    node->faces.clear();
}

// Build an octree from a mesh
OctreeNode* buildOctree(MatrixXd vertices, MatrixXi faces, int maxVerticesPerNode, int maxFacesPerNode) {
    Vector3d minCorner = vertices.colwise().minCoeff();
    Vector3d maxCorner = vertices.colwise().maxCoeff();
    OctreeNode* root = new OctreeNode;
    root->minCorner = minCorner;
    root->maxCorner = maxCorner;
    for (int i = 0; i < vertices.rows(); i++) {
        insertVertex(root, vertices.row(i).transpose(), minCorner, maxCorner);
    }
    for (int i = 0; i < faces.rows(); i++) {
        insertFace(root, vertices, faces.row(i), minCorner, maxCorner);
    }
    std::vector<OctreeNode*> nodesToSubdivide = {root};
    while (!nodesToSubdivide.empty()) {
        OctreeNode* node = nodesToSubdivide.back();
        nodesToSubdivide.pop_back();
        if (node->vertices.size() > maxVerticesPerNode || node->faces.size() > maxFacesPerNode) {
            subdivideNode(node, minCorner, maxCorner);
            for (int i = 0; i < 8; i++) {
                nodesToSubdivide.push_back(node->children[i]);
            }
        }
    }
    return root;
}