为什么在下列代码中如何表示与*v_it与prev_vh表示的是同一个点：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; }

在这段代码中，*v_it是当前点的句柄，prev_vh是prev_p所在的点的句柄。如果要表示它们是同一个点，可以使用prev_vh.idx() == v_it->idx()这个条件来判断，因为prev_vh.idx()返回的是prev_vh所在的点的索引，v_it->idx()返回的是当前点的索引，如果它们相等，那么*v_it和prev_vh就表示同一个点。所以可以在代码中添加一个判断条件if (prev_vh.idx() == v_it->idx()) { prev_p = mesh.point(*v_it); }来表示它们是同一个点。

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为什么在下列代码中如何表示与curr_pi与prev_p表示的是同一个点：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; }

在这段代码中，curr_pi是当前点的位置，prev_p是它的前一个点的位置。如果要表示它们是同一个点，可以使用prev_vh == *v_it这个条件来判断，因为prev_vh是prev_p所在的点的句柄，*v_it是当前点的句柄，如果它们相等，那么prev_p和curr_pi就表示同一个点。所以可以在代码中添加一个判断条件if (prev_vh == *v_it) { prev_p = mesh.point(*v_it); }来表示它们是同一个点。

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。