diff --git a/lib/geometry/point2c.h b/lib/geometry/point2c.h
index a58b291..341461e 100644
--- a/lib/geometry/point2c.h
+++ b/lib/geometry/point2c.h
@@ -531,25 +531,20 @@ namespace gctl
 	 * @brief      生成一维网格节点数组，其中每一个点都是一个二维坐标点。
 	 * 
 	 * @param      out_ps  返回网格节点数组
-	 * @param[in]  xmin    x最小值
-	 * @param[in]  xmax    x最大值
+	 * @param[in]  x_st    x起始值
+	 * @param[in]  x_ed    x终止值
 	 * @param[in]  dx      x间隔
 	 * @param[in]  ele     高程值
 	 */
 	template <typename T>
-	void grid_points_1d(array<point2c<T>> &out_ps, T xmin, T xmax, T dx, T ele)
+	void grid_points_1d(array<point2c<T>> &out_ps, T x_st, T x_ed, T dx, T ele)
 	{
-		if (xmin >= xmax || xmin + dx > xmax || dx <= 0)
-		{
-			throw std::invalid_argument("[gctl::grid_points_1d] Invalid parameters.");
-		}
-
-		int xnum = round((xmax - xmin)/dx) + 1;
+		int xnum = round(std::abs((x_ed - x_st)/dx)) + 1;
 
 		out_ps.resize(xnum);	
 		for (int i = 0; i < xnum; i++)
 		{
-			out_ps[i].x = xmin + dx*i;
+			out_ps[i].x = x_st + dx*i;
 			out_ps[i].y = ele;
 		}
 		return;
diff --git a/lib/geometry/point2p.h b/lib/geometry/point2p.h
index 064aef2..9664244 100644
--- a/lib/geometry/point2p.h
+++ b/lib/geometry/point2p.h
@@ -375,6 +375,20 @@ namespace gctl
 		}
 		return false;
 	}
+
+	template <typename T>
+	void grid_points_1d(array<point2p<T>> &obsp, T deg_st, T deg_ed, T ddeg, T rad)
+	{
+		int m = round(std::abs((deg_st - deg_ed)/ddeg)) + 1;
+
+		obsp.resize(m);
+		for (size_t i = 0; i < m; i++)
+		{
+			obsp[i].arc = arc(deg_st + i*ddeg);
+			obsp[i].rad = rad;
+		}
+		return;
+	}
 }
 
 #endif // _GCTL_POINT2P_H
\ No newline at end of file
diff --git a/lib/io/dsv_io.cpp b/lib/io/dsv_io.cpp
index f587243..4bd91d2 100644
--- a/lib/io/dsv_io.cpp
+++ b/lib/io/dsv_io.cpp
@@ -963,6 +963,29 @@ void gctl::geodsv_io::fill_column_point2dc(const array<point2dc> &data, std::str
     return;
 }
 
+void gctl::geodsv_io::fill_column_point2dp(const array<point2dp> &data, int rid, int cid, int p)
+{
+    if (rid > col_num_ || cid > col_num_ || rid == cid || rid <= 0 || cid <= 0)
+    {
+        throw std::runtime_error("[gctl::geodsv_io] Invalid column index.");
+    }
+
+    std::stringstream ss;
+    std::string s;
+    for (size_t i = 1; i <= std::min(row_num_, (int) data.size()); i++)
+    {
+        table_[i][rid].value(data[i - 1].rad, p);
+        table_[i][cid].value(data[i - 1].arc, p);
+    }
+    return;
+}
+
+void gctl::geodsv_io::fill_column_point2dp(const array<point2dp> &data, std::string rname, std::string cname, int p)
+{
+    fill_column_point2dp(data, name_index(rname, false), name_index(cname, false), p);
+    return;
+}
+
 void gctl::geodsv_io::fill_column_point3dc(const array<point3dc> &data, int xid, int yid, int zid, int p)
 {
     if (xid > col_num_ || yid > col_num_ || zid > col_num_ || xid == yid || yid == zid || xid == zid
@@ -1035,6 +1058,28 @@ void gctl::geodsv_io::get_column_point2dc(array<point2dc> &data, std::string xna
     return;
 }
 
+void gctl::geodsv_io::get_column_point2dp(array<point2dp> &data, int rid, int cid)
+{
+    if (rid > col_num_ || cid > col_num_ || rid == cid || rid <= 0 || cid <= 0)
+    {
+        throw std::runtime_error("[gctl::geodsv_io] Invalid column index.");
+    }
+
+    data.resize(row_num_);
+    for (size_t i = 1; i <= row_num_; i++)
+    {
+        data[i - 1].rad = table_[i][rid].value<double>();
+        data[i - 1].arc = table_[i][cid].value<double>();
+    }
+    return;
+}
+
+void gctl::geodsv_io::get_column_point2dp(array<point2dp> &data, std::string rname, std::string cname)
+{
+    get_column_point2dp(data, name_index(rname, false), name_index(cname, false));
+    return;
+}
+
 void gctl::geodsv_io::get_column_point3dc(array<point3dc> &data, int xid, int yid, int zid)
 {
     if (xid > col_num_ || yid > col_num_ || zid > col_num_ || xid == yid || yid == zid || xid == zid
diff --git a/lib/io/dsv_io.h b/lib/io/dsv_io.h
index c6f2fba..f8c8d7e 100644
--- a/lib/io/dsv_io.h
+++ b/lib/io/dsv_io.h
@@ -828,6 +828,26 @@ namespace gctl
 		 */
 		void fill_column_point2dc(const array<point2dc> &data, std::string xname, std::string yname, int p = 6);
 
+		/**
+		 * @brief 填充二维坐标列
+		 * 
+		 * @param rid rad坐标列索引 从1开始
+		 * @param cid arc坐标列索引 从1开始
+		 * @param data 返回的二维坐标数据 
+		 * @param p 填入的浮点数据有效位数（精度）
+		 */
+		void fill_column_point2dp(const array<point2dp> &data, int rid, int cid, int p = 6);
+
+		/**
+		 * @brief 填充二维坐标列
+		 * 
+		 * @param rname rad坐标列名称
+		 * @param cname arc坐标列名称
+		 * @param data 返回的二维坐标数据 
+		 * @param p 填入的浮点数据有效位数（精度）
+		 */
+		void fill_column_point2dp(const array<point2dp> &data, std::string rname, std::string cname, int p = 6);
+
 		/**
 		 * @brief 填充三维坐标列
 		 * 
@@ -890,6 +910,24 @@ namespace gctl
 		 */
 		void get_column_point2dc(array<point2dc> &data, std::string xname, std::string yname);
 
+		/**
+		 * @brief 读取二维坐标列
+		 * 
+		 * @param rid rad坐标列索引 从1开始
+		 * @param cid arc坐标列索引 从1开始
+		 * @param data 返回的二维坐标数据 
+		 */
+		void get_column_point2dp(array<point2dp> &data, int rid, int cid);
+
+		/**
+		 * @brief 读取二维坐标列
+		 * 
+		 * @param rname rad坐标列名称
+		 * @param cname arc坐标列名称
+		 * @param data 返回的二维坐标数据 
+		 */
+		void get_column_point2dp(array<point2dp> &data, std::string rname, std::string cname);
+
 		/**
 		 * @brief 读取三维坐标列
 		 * 
diff --git a/lib/io/gmsh_io.cpp b/lib/io/gmsh_io.cpp
index e1b7d7b..fefd4fb 100644
--- a/lib/io/gmsh_io.cpp
+++ b/lib/io/gmsh_io.cpp
@@ -152,4 +152,15 @@ void gctl::gmshio::save_physical_groups(const array<gmsh_physical_group> &phy_gr
     }
     gmsh_out << "$EndPhysicalNames\n";
     return;
+}
+
+int gctl::gmshio::physical_name2tag(const array<gmsh_physical_group> &phy_groups, std::string name)
+{
+    for (size_t i = 0; i < phy_groups.size(); i++)
+    {
+        if (phy_groups[i].name == name) return phy_groups[i].phys_tag;
+    }
+
+    throw std::runtime_error("[gctl::gmshio::physical_name2tag] Physical group name not found.");
+    return -1;
 }
\ No newline at end of file
diff --git a/lib/io/gmsh_io.h b/lib/io/gmsh_io.h
index 41ba2a7..cb4c7d0 100644
--- a/lib/io/gmsh_io.h
+++ b/lib/io/gmsh_io.h
@@ -61,6 +61,7 @@ namespace gctl
 
 		void read_physical_groups(array<gmsh_physical_group> &phy_groups);
 		void save_physical_groups(const array<gmsh_physical_group> &phy_groups);
+		int physical_name2tag(const array<gmsh_physical_group> &phy_groups, std::string name);
 
 		template <typename A> void read_node(array<vertex<point2dc, A>> &out_nodes);
 		template <typename A> void read_node(array<vertex<point3dc, A>> &out_nodes);
diff --git a/lib/maths/mathfunc_t.h b/lib/maths/mathfunc_t.h
index c6baae5..040402d 100644
--- a/lib/maths/mathfunc_t.h
+++ b/lib/maths/mathfunc_t.h
@@ -48,6 +48,12 @@ namespace gctl
         return deg*GCTL_Pi/180.0;
     }
 
+    template <typename T>
+    inline T deg(T arc)
+    {
+        return arc*180.0/GCTL_Pi;
+    }
+
     template <typename T>
     inline T sind(T deg)
     {