在下列代码中如何表示与v_it及vv_it相邻的两个点float smoothCot() { float err = -1; cogs.clear(); v_end = mesh.vertices_end(); // for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) { cog[0] = cog[1] = cog[2] = valence = 0.0; //cout << valence<<"1" << endl; for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) { double cot_weight = 0.0; MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it); if (!mesh.is_boundary(heh)) { MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh); MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh); MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh); MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh); MyMesh::Point prev_p = mesh.point(prev_vh); MyMesh::Point curr_pi = mesh.point(*v_it); MyMesh::Point curr_pj = mesh.point(*vv_it); MyMesh::Point next_p = mesh.point(next_vh); double cot_alpha = cot(curr_pi - prev_p, curr_pj - prev_p); double cot_beta = cot(curr_pi - next_p, curr_pj - next_p); cot_weight = cot_alpha + cot_beta; //cout << cot_weight<<"2" << endl; } cog += cot_weight *( mesh.point(*vv_it)-mesh.point(*v_it)); valence += cot_weight; //cout << valence<<"3" << endl; } cogs.push_back(cog / valence); } for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) { if (!mesh.is_boundary(*v_it)) { MyMesh::Point p = mesh.point(*v_it); //*cog_it += mesh.point(*v_it); err = max(err, (p - *cog_it).norm()); mesh.set_point(*v_it, *cog_it); } } return err; }

与v_it及vv_it相邻的两个点可以表示为prev_vh和next_vh，分别表示v_it的前一个点和后一个点的VertexHandle。在代码中，可以使用mesh.to_vertex_handle()函数将HalfedgeHandle转换为VertexHandle，从而获取前一个点和后一个点的VertexHandle，再使用mesh.point()函数获取点的坐标，即可计算cot_alpha和cot_beta的值。

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在下列代码中如何表示与v_it及vv_it相邻的两个点，请写出具体代码：float smoothCot() { float err = -1; cogs.clear(); v_end = mesh.vertices_end(); // for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) { cog[0] = cog[1] = cog[2] = valence = 0.0; //cout << valence<<"1" << endl; for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) { double cot_weight = 0.0; MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it); if (!mesh.is_boundary(heh)) { MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh); MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh); MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh); MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh); MyMesh::Point prev_p = mesh.point(prev_vh); MyMesh::Point curr_pi = mesh.point(*v_it); MyMesh::Point curr_pj = mesh.point(*vv_it); MyMesh::Point next_p = mesh.point(next_vh); double cot_alpha = cot(curr_pi - prev_p, curr_pj - prev_p); double cot_beta = cot(curr_pi - next_p, curr_pj - next_p); cot_weight = cot_alpha + cot_beta; //cout << cot_weight<<"2" << endl; } cog += cot_weight *( mesh.point(*vv_it)-mesh.point(*v_it)); valence += cot_weight; //cout << valence<<"3" << endl; } cogs.push_back(cog / valence); } for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) { if (!mesh.is_boundary(*v_it)) { MyMesh::Point p = mesh.point(*v_it); //*cog_it += mesh.point(*v_it); err = max(err, (p - *cog_it).norm()); mesh.set_point(*v_it, *cog_it); } } return err; }

具体代码如下：

MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh);
MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh);
MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh);
MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh);
MyMesh::Point prev_p = mesh.point(prev_vh);
MyMesh::Point next_p = mesh.point(next_vh);

其中，prev_heh和next_heh分别表示heh的前一个半边和后一个半边的HalfedgeHandle，使用mesh.prev_halfedge_handle()和mesh.next_halfedge_handle()函数获取；prev_vh和next_vh分别表示heh的前一个点和后一个点的VertexHandle，使用mesh.to_vertex_handle()函数将HalfedgeHandle转换为VertexHandle获取；prev_p和next_p分别表示heh的前一个点和后一个点的坐标，使用mesh.point()函数获取。

请将下列代码改为可在vs中运行的版本：double cot(MyMesh::Point a, MyMesh::Point b) { return dot(a, b) / cross(a, b).norm(); } //cot平滑 float smoothCot() { float err = -1; cogs.clear(); v_end = mesh.vertices_end(); // for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) { cog[0] = cog[1] = cog[2] = valence = 0.0; for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) { double cot_weight = 0.0; MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it); if (!mesh.is_boundary(heh)) { MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh); MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh); MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh); MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh); MyMesh::Point prev_p = mesh.point(prev_vh); MyMesh::Point curr_p = mesh.point(*v_it); MyMesh::Point next_p = mesh.point(next_vh); double cot_alpha = cot(prev_p - curr_p, next_p - curr_p); double cot_beta = cot(curr_p - prev_p, next_p - prev_p); cot_weight = cot_alpha + cot_beta; } cog += cot_weight * mesh.point(*vv_it); valence += cot_weight; } cogs.push_back(cog / valence); } for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) { if (!mesh.is_boundary(*v_it)) { MyMesh::Point p = mesh.point(*v_it); err = max(err, (p - *cog_it).norm()); mesh.set_point(*v_it, *cog_it); } } return err; } void smoothCot(float threshold) { float err; do { err = smoothCot(); cout << "err:" << err << endl; } while (err >= threshold); }

这段代码需要引入MyMesh库，你需要提供该库的头文件和实现文件。同时，需要将该代码放到合适的函数中，比如main函数中。下面是改为可在VS中运行的版本：

#include <iostream>
#include "MyMesh.h" // MyMesh库的头文件

using namespace std;

MyMesh mesh; // 定义一个MyMesh对象
MyMesh::VertexIter v_it, v_end;
MyMesh::VertexVertexIter vv_it;
vector<MyMesh::Point> cogs;
vector<MyMesh::Point>::iterator cog_it;

// 计算cot值
double cot(MyMesh::Point a, MyMesh::Point b) {
    return dot(a, b) / cross(a, b).norm();
}

// 平滑cot
float smoothCot() {
    float err = -1;
    cogs.clear();
    v_end = mesh.vertices_end();
    for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) {
        MyMesh::Point cog(0, 0, 0); // 初始化为0
        float valence = 0.0;
        for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) {
            double cot_weight = 0.0;
            MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it);
            if (!mesh.is_boundary(heh)) {
                MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh);
                MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh);
                MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh);
                MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh);
                MyMesh::Point prev_p = mesh.point(prev_vh);
                MyMesh::Point curr_p = mesh.point(*v_it);
                MyMesh::Point next_p = mesh.point(next_vh);
                double cot_alpha = cot(prev_p - curr_p, next_p - curr_p);
                double cot_beta = cot(curr_p - prev_p, next_p - prev_p);
                cot_weight = cot_alpha + cot_beta;
            }
            cog += cot_weight * mesh.point(*vv_it);
            valence += cot_weight;
        }
        cogs.push_back(cog / valence);
    }

    for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) {
        if (!mesh.is_boundary(*v_it)) {
            MyMesh::Point p = mesh.point(*v_it);
            err = max(err, (p - *cog_it).norm());
            mesh.set_point(*v_it, *cog_it);
        }
    }

    return err;
}

// 迭代平滑cot值，直到err小于阈值
void smoothCot(float threshold) {
    float err;
    do {
        err = smoothCot();
        cout << "err:" << err << endl;
    } while (err >= threshold);
}

int main() {
    // 读取.obj文件，这里需要提供.obj文件的路径
    OpenMesh::IO::read_mesh(mesh, "path/to/your/file.obj");

    // 平滑cot值
    smoothCot(0.1);

    // 保存平滑后的模型到.obj文件，这里需要提供.obj文件的保存路径
    OpenMesh::IO::write_mesh(mesh, "path/to/your/smoothed/file.obj");

    return 0;
}