基于可见性的图割算法：C++网格切割实现技术问询

Alright, let's walk through exactly how to implement visibility-based Graph Cut for your 3D Delaunay mesh cutting task, building on the graph setup you already have. I’ll tie in the octree optimization ideas from the example you referenced too.

First, you need to tag every Delaunay vertex as either visible or occluded from your camera position—this forms the basis of your S-T graph's source/sink assignments:

• For each vertex v, cast a ray from the camera position directly to v
• Check if this ray intersects any other faces in the Delaunay triangulation (make sure to exclude faces that include v itself, to avoid false positives)
• If the ray reaches v without hitting any other faces, mark it as visible; otherwise, mark it as occluded

Graph Cut relies on a binary segmentation: vertices either stay (source side) or get cut (sink side). Use your visibility labels to set up these connections:

• For visible vertices: Add an edge from the source (S) to the vertex with a very high weight (like 1e9). This tells the algorithm we strongly prefer keeping these vertices.
• For occluded vertices: Add an edge from the vertex to the sink (T) with the same high weight. This means we strongly prefer cutting these vertices.
• For ambiguous vertices (e.g., near the visibility boundary), you can assign small weights to both S and T to let the algorithm decide based on neighboring edges.

Now handle the internal edges of your Delaunay graph—these weights represent the cost of cutting that edge, tied to your energy function E=L (triangle intersection count):

• For each Delaunay edge connecting vertices u and v:
  • If u and v have different visibility labels (one visible, one occluded): This edge is a potential cut boundary. Calculate its weight using your E=L function—for example, sum the intersection counts of all triangles connected to this edge (higher intersection count = higher cut cost, since we want to avoid cutting through high-intersection regions).
  • If u and v have the same visibility label: Assign a very low weight (like 1e-9), since cutting this edge serves no purpose and should be avoided.
• Add undirected edges by adding two directed edges (one from u to v, one from v to u) with the same weight—this matches the directed graph structure your library expects.

With the graph fully built, execute the max-flow computation (thanks to the max-flow min-cut theorem, this gives us the minimal energy cut):

• Call your library's maxflow() method on the graph object
• For each vertex, use what_segment() (or the equivalent method in your library) to check if it belongs to the source side (keep) or sink side (cut)

Finally, turn the segmentation result into a usable surface mesh:

• Iterate through all Delaunay triangles
• Identify triangles that cross the cut boundary (i.e., have a mix of source-side and sink-side vertices)
• For these crossing triangles, extract the edges that lie between source and sink vertices—connect these edges to form your new surface mesh

To speed this up for large meshes, use octree partitioning like the example you mentioned:

• Split your 3D space into octree nodes
• Only process nodes that contain both visible and occluded vertices—these are the only regions where cuts can occur
• Prune nodes that are entirely visible or entirely occluded to reduce the number of vertices/edges you need to process

Here’s how this might look in code, tailored to your graph library setup:

// Step 1: Classify vertex visibility
std::vector<bool> isVisible(nodeCount, false);
for (int i = 0; i < nodeCount; ++i) {
    Vertex v = delaunayVertices[i];
    Ray ray(cameraPosition, v - cameraPosition);
    bool occluded = false;
    // Check intersection with non-adjacent Delaunay faces
    for (const auto& face : delaunayFaces) {
        if (face.containsVertex(i)) continue;
        if (ray.intersectsFace(face)) {
            occluded = true;
            break;
        }
    }
    isVisible[i] = !occluded;
}

// Step 2: Add S-T connections
const GraphCost HIGH_PRIORITY = 1e9;
const GraphCost LOW_PRIORITY = 1e-9;
for (int i = 0; i < nodeCount; ++i) {
    if (isVisible[i]) {
        // Source to visible vertex: high cost to cut (keep it)
        graph->add_tweights(i, HIGH_PRIORITY, 0);
    } else {
        // Occluded vertex to sink: high cost to keep (cut it)
        graph->add_tweights(i, 0, HIGH_PRIORITY);
    }
}

// Step 3: Add Delaunay edge weights
for (const auto& edge : delaunayEdges) {
    int u = edge.uId;
    int v = edge.vId;
    GraphCost edgeCost;

    if (isVisible[u] != isVisible[v]) {
        // Calculate cost based on your E=L (triangle intersection count)
        edgeCost = calculateCutCost(u, v); // Implement this with your L value
    } else {
        edgeCost = LOW_PRIORITY;
    }

    // Add undirected edge as two directed edges
    graph->add_edge(u, v, edgeCost, edgeCost);
}

// Step 4: Compute min cut
GraphCost totalFlow = graph->maxflow();
std::vector<int> vertexSegment(nodeCount);
for (int i = 0; i < nodeCount; ++i) {
    vertexSegment[i] = graph->what_segment(i); // 0 = source side, 1 = sink side
}

// Step 5: Extract cut surface
std::vector<Face> cutSurfaceFaces;
for (const auto& face : delaunayFaces) {
    int sourceCount = 0;
    for (int vid : face.vertexIds) {
        if (vertexSegment[vid] == GraphType::SOURCE) sourceCount++;
    }
    // Process faces that cross the cut boundary
    if (sourceCount > 0 && sourceCount < 3) {
        cutSurfaceFaces.push_back(extractBoundaryFace(face, vertexSegment)); // Implement this
    }
}

内容的提问来源于stack exchange，提问作者andre