diff --git a/src/lib.rs b/src/lib.rs
index 2d69bd5..293fd51 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -66,11 +66,11 @@ struct Ship {
 fn point_to_cga(x: f64, y: f64) -> CGA {
     let x_vec = CGA::e1();
     let y_vec = CGA::e2();
-    let _z_vec =CGA::e3();
+    let _z_vec =CGA::e3(); //This game assumes everything takes place in the plane.
     let e_vec = CGA::e4();
     let e_bar = CGA::e5();
-    let n_vec = &e_vec + &e_bar;
-    let n_bar = &e_vec - &e_bar;
+    let n_vec = &e_vec + &e_bar; //Null vector for the point at infinity.
+    let n_bar = &e_vec - &e_bar; //Null vector for the origin.
 
     let mut ux = x;
     let mut uy = y;
@@ -81,7 +81,7 @@ fn point_to_cga(x: f64, y: f64) -> CGA {
         mag_sqr = 1.;
     }
 
-    0.5*mag_sqr*n_vec + ux*x_vec + uy*y_vec - 0.5*n_bar
+    0.5*mag_sqr*n_vec + ux*x_vec + uy*y_vec - 0.5*n_bar //F(x) = 1/2(x^2 n + 2x - nbar) = -1/2(x-e)n(x-e)
 }
 
 fn point_to_screen_space(x: f64, y: f64) -> (f64, f64) {
@@ -145,11 +145,8 @@ fn draw_line(context: &CanvasRenderingContext2d, line: &CGA) {
 
         //draw_point(context, &point_to_cga(c_x, c_y));
 
-        //Convert into Canvas Space
         let (canvas_x, canvas_y) = point_to_screen_space(c_x, c_y);
         let canvas_r = r*RADIUS;
-
-        //Draw
         context.arc(canvas_x, canvas_y, canvas_r, 0., TWO_PI).unwrap();
     }
     context.stroke();
@@ -185,6 +182,7 @@ pub fn start() -> Result<(), JsValue> {
     context.arc(CENTER_X, CENTER_Y, RADIUS, 0., TWO_PI).unwrap();
     context.stroke();
 
+    //Testing example lines and circles.
     let point = point_to_cga(0.,0.);
     draw_point(&context, &point);
 
@@ -194,7 +192,7 @@ pub fn start() -> Result<(), JsValue> {
     draw_point(&context, &p2);
     let p3 = point_to_cga(0.7, 0.6);
     draw_point(&context, &p3);
-    let circle = &p1 ^ &p2 ^ &p3 ^ &CGA::e3();
+    let circle = &p1 ^ &p2 ^ &p3 ^ &CGA::e3(); //wedge e3 to force into the plane
     draw_line(&context, &circle);
 
     let p1 = point_to_cga(0.9, 0.2);
@@ -215,5 +213,19 @@ pub fn start() -> Result<(), JsValue> {
     let circle = &p1 ^ &p2 ^ &p3 ^ &CGA::e3();
     draw_line(&context, &circle);
 
+    let p1 = point_to_cga(0.9, 0.);
+    draw_point(&context, &p1);
+    let p2 = point_to_cga(0.9, -0.1);
+    draw_point(&context, &p2);
+    let circle = &p1 ^ &p2 ^ &CGA::e4() ^ &CGA::e3(); //Wedge e4 to create a circle through p1 and p1 that is tangent to the unit circle.
+    draw_line(&context, &circle);
+
+    let p1 = point_to_cga(0.9, 0.);
+    draw_point(&context, &p1);
+    let p2 = point_to_cga(0.9, -0.1);
+    draw_point(&context, &p2);
+    let circle = &p1 ^ &p2 ^ &CGA::e5() ^ &CGA::e3(); //Orthogonal to the line at infinity
+    draw_line(&context, &circle);
+
     Ok(())
 }