diff --git a/stim/visualization/gl_network.h b/stim/visualization/gl_network.h
index 3107256..438708f 100644
--- a/stim/visualization/gl_network.h
+++ b/stim/visualization/gl_network.h
@@ -55,7 +55,7 @@ public:
 		//glFlush();
 	}
 
-	///render the vertex as sphere
+	///render the vertex as sphere based on glut build-in function
 	///@param x, y, z are the three coordinates of the center point
 	///@param radius is the radius of the sphere
 	///@param subdivisions is the slice/stride along/around z-axis
@@ -66,6 +66,53 @@ public:
 		glPopMatrix();
 	}
 
+	///render the vertex as sphere based on transformation
+	///@param x, y, z are the three coordinates of the center point
+	///@param radius is the radius of the sphere
+	///@param slice is the number of subdivisions around the z-axis
+	///@param stack is the number of subdivisions along the z-axis
+	void renderBall(T x, T y, T z, T radius, T slice, T stack) {
+		T step_z = stim::PI / slice;					// step angle along z-axis
+		T step_xy = 2 * stim::PI / stack;				// step angle in xy-plane
+		T xx[4], yy[4], zz[4];							// store coordinates
+
+		T angle_z = 0.0;								// start angle
+		T angle_xy = 0.0;
+
+		glBegin(GL_QUADS);
+		for (unsigned i = 0; i < slice; i++)			// around the z-axis
+		{
+			angle_z = i * step_z;						// step step_z each time
+
+			for (unsigned j = 0; j < stack; j++)		// along the z-axis
+			{
+				angle_xy = j * step_xy;					// step step_xy each time, draw floor by floor
+
+				xx[0] = radius * std::sin(angle_z) * std::cos(angle_xy);	// four vertices
+				yy[0] = radius * std::sin(angle_z) * std::sin(angle_xy);
+				zz[0] = radius * std::cos(angle_z);
+
+				xx[1] = radius * std::sin(angle_z + step_z) * std::cos(angle_xy);
+				yy[1] = radius * std::sin(angle_z + step_z) * std::sin(angle_xy);
+				zz[1] = radius * std::cos(angle_z + step_z);
+
+				xx[2] = radius * std::sin(angle_z + step_z) * std::cos(angle_xy + step_xy);
+				yy[2] = radius * std::sin(angle_z + step_z) * std::sin(angle_xy + step_xy);
+				zz[2] = radius * std::cos(angle_z + step_z);
+
+				xx[3] = radius * std::sin(angle_z) * std::cos(angle_xy + step_xy);
+				yy[3] = radius * std::sin(angle_z) * std::sin(angle_xy + step_xy);
+				zz[3] = radius * std::cos(angle_z);
+
+				for (unsigned k = 0; k < 4; k++)
+				{
+					glVertex3f(x + xx[k], y + yy[k], z + zz[k]);			// draw the floor plane
+				}
+			}
+		}
+		glEnd();
+	}
+
 	/// Render the network centerline as a series of line strips.
 	/// glCenterline0 is for only one input
 	void glCenterline0(){
@@ -145,7 +192,7 @@ public:
 					unsigned idx = V[n].e[1][0];				// find the index of first incoming edge of that vertex
 					glTexCoord1f(E[idx].r(E[idx].size() - 1));	// bind the texture as metric of last point on that edge
 				}
-				renderBall(V[n][0], V[n][1], V[n][2], 2*radius, 20);
+				renderBall(V[n][0], V[n][1], V[n][2], 2*radius, 20, 20);
 			}
 			glEndList();						// end the display list
 		}
@@ -183,7 +230,7 @@ public:
 				else {
 					unsigned idx = V[n].e[1][0];				// find the index of first incoming edge of that vertex
 				}
-				renderBall(V[n][0], V[n][1], V[n][2], 2 * radius, 20);
+				renderBall(V[n][0], V[n][1], V[n][2], 2 * radius, 20, 20);
 			}
 			glEndList();
 		}
@@ -236,11 +283,11 @@ public:
 				size_t num_edge = V[v].e[0].size() + V[v].e[1].size();
 				if (num_edge > 1) {					// if it is the joint vertex
 					glColor3f(0.3, 0.3, 0.3);		// gray color 
-					renderBall(V[v][0], V[v][1], V[v][2], 3*radius, 20);
+					renderBall(V[v][0], V[v][1], V[v][2], 3*radius, 20, 20);
 				}
 				else {								// if it is the terminal vertex
 					glColor3f(0.6, 0.6, 0.6);		// more white gray
-					renderBall(V[v][0], V[v][1], V[v][2], 3*radius, 20);
+					renderBall(V[v][0], V[v][1], V[v][2], 3*radius, 20, 20);
 				}
 			}
 			glEndList();
--
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