Refactor some code, and draw a grid of points.

main.py

@@ -10,6 +10,9 @@ CENTER_X, CENTER_Y = 400, 300
 alg = Algebra(2,1,0)
 locals().update(alg.blades)
 
+points = []
+lines  = []
+
 def point(x,y):
     #Construct a point.
     #Hyperbolic space is modeled as a hyperboloid embedded in 3D Minkowski space.
@@ -23,7 +26,10 @@ def draw_point(point):
     x_0 = point.e12
     x_1 = -point.e23
     x_2 = point.e13
-    norm = math.sqrt(x_0*x_0 - x_1*x_1 - x_2*x_2)
+    sqr = x_0*x_0 - x_1*x_1 - x_2*x_2
+    if sqr < 0:
+        return
+    norm = math.sqrt(sqr)
     x_0 = x_0/norm
     x_1 = x_1/norm
     x_2 = x_2/norm
@@ -37,11 +43,12 @@ def draw_line(line):
     delta = line.e3
     if abs(delta) < ERROR:
         # The geodesic is a line through the origin.
-        if abs(line.e2) < ERROR:
+        theta   = math.atan2(line.e1, line.e2)
-            pygame.draw.line(screen, BLUE, (CENTER_X, CENTER_Y+DISK_RADIUS), (CENTER_X, CENTER_Y-DISK_RADIUS), 1)
+        start_x = int(CENTER_X-DISK_RADIUS*math.cos(theta))
-        else:
+        start_y = int(CENTER_Y-DISK_RADIUS*math.sin(theta))
-            slope = line.e1/line.e2
+        end_x   = int(CENTER_X+DISK_RADIUS*math.cos(theta))
-            pygame.draw.line(screen, BLUE, (CENTER_X-DISK_RADIUS, int(CENTER_Y-slope*DISK_RADIUS)), (CENTER_X+DISK_RADIUS, int(CENTER_Y+slope*DISK_RADIUS)), 1)
+        end_y   = int(CENTER_Y+DISK_RADIUS*math.sin(theta))
+        pygame.draw.line(screen, BLUE, (start_x, start_y), (end_x, end_y), 1)
     else:
         #The geodesic is a circle
         a = line.e1
@@ -55,7 +62,33 @@ def draw_line(line):
         c_y = int(CENTER_Y + y_c*DISK_RADIUS)
         pygame.draw.circle(screen, BLUE, (c_x, c_y), int(r*DISK_RADIUS), 1)
 
+def simulation(t):
+    lines.clear()
+    points.clear()
+    lines.append(y_axis)
+    lines.append(x_axis)
+    points.append(origin)
 
+    x_motor = tx_generator.exp()
+    y_motor = ty_generator.exp()
+
+    generator = math.sin(t)*tx_generator + math.sin(math.sqrt(2)*t)*ty_generator + math.sin(math.sqrt(3)*t)*origin
+    m = generator.exp()
+    y_tick = m*y_axis*m.reverse()
+    x_tick = m*x_axis*m.reverse()
+    lines.append(y_tick)
+    lines.append(x_tick)
+    points.append(y_tick^x_tick)
+
+    for i in range(13):
+        for j in range(13):
+            motor_x = ((i-6)*tx_generator/10).exp()
+            motor_y = ((j-6)*ty_generator/10).exp()
+            y_tick = m * motor_x * y_axis * motor_x.reverse() * m.reverse()
+            x_tick = m * motor_y * x_axis * motor_y.reverse() * m.reverse()
+            lines.append(y_tick)
+            lines.append(x_tick)
+            points.append(y_tick^x_tick)
 
 
 y_axis = e1 #x = 0 line
@@ -83,49 +116,28 @@ BLUE = (0, 0, 255)
 running = True
 t = 0
 
+lines.append(x_axis)
+lines.append(y_axis)
 while running:
     t += 0.0002
-    for event in pygame.event.get():
-        if event.type == pygame.QUIT:
-            running = False
-
     # Clear the screen
     screen.fill(WHITE)
 
     #Poincare Disk Boundary
     pygame.draw.circle(screen, BLACK, (CENTER_X, CENTER_Y), DISK_RADIUS, 1)
 
-    #Generate a transformation for demonstration
+    simulation(t)
-    transform = math.sin(t)*tx_generator + math.sin(math.sqrt(2)*t)*ty_generator + math.sin(math.sqrt(3)*t)*origin
+    for line in lines:
-    transform = transform
+        draw_line(line)
-    motor = transform.exp()
+    for point in points:
+        draw_point(point)
 
-    #Apply the transformation
+    for event in pygame.event.get():
-    y_tick = motor*y_axis*motor.reverse()
+        if event.type == pygame.QUIT:
-    x_tick = motor*x_axis*motor.reverse()
+            running = False
-
-    #Construct a point as the intersection of the two lines
-    point = y_tick^x_tick
-
-    #Draw everything
-    draw_line(y_tick)
-    draw_line(x_tick)
-    draw_point(point)
-
-    tx = tx_generator.exp()
-    ty = ty_generator.exp()
-    point_a = tx*ty*origin*ty.reverse()*tx.reverse()
-    point_b = ty*tx*origin*tx.reverse()*ty.reverse()
-    draw_line(x_axis)
-    draw_line(y_axis)
-    draw_point(origin)
-    draw_point(point_a)
-    draw_point(point_b)
 
     # Update the display
     pygame.display.flip()
 
-
-
 # Quit Pygame
 pygame.quit()