import pygame
from kingdon import Algebra
import math

ERROR = 0.00001

alg = Algebra(2,1,0)
locals().update(alg.blades)
b = 2*e12
print(b)

def motor(generator):
    bivector = generator.grade(2)
    sqr = (bivector*bivector).grade(0).e
    mag = bivector.norm().e
    generator = bivector.normalized()
    if mag < ERROR:
            #Zero Norm
            return 1+bivector
    elif sqr < 0:
        return math.cos(mag) + math.sin(mag)*generator
    else:
        return math.cosh(mag) + math.sinh(mag)*generator

motor(1*e12)
motor(1*e13)
motor(1*e23)







'''
# Initialize Pygame
pygame.init()

# Set up the screen
WIDTH, HEIGHT = 800, 600
screen = pygame.display.set_mode((WIDTH, HEIGHT))
pygame.display.set_caption("Clifford and Pygame Example")

# Colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
RED = (255, 0, 0)

# Initial point in GA (e.g., a vector representing a point)
# We'll represent it as a multivector with a vector component
initial_point_ga = 100 * e1 + 50 * e2

# Create a rotor for rotation (e.g., 45 degrees counter-clockwise)
angle = math.pi / 4 # 45 degrees
rotor = math.e**(angle * e12)

# Game loop
running = True
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # Clear the screen
    screen.fill(BLACK)

    # Apply the rotation to the point
    rotated_point_ga = rotor * initial_point_ga * ~rotor

    # Extract the vector components for Pygame display
    # We assume the point is a vector, so we access its e1 and e2 components
    x_coord = rotated_point_ga.value[e1.index] + WIDTH // 2  # Adjust for screen center
    y_coord = -rotated_point_ga.value[e2.index] + HEIGHT // 2 # Invert y for Pygame coordinates

    # Draw the point
    pygame.draw.circle(screen, RED, (int(x_coord), int(y_coord)), 5)

    # Update the display
    pygame.display.flip()

# Quit Pygame
pygame.quit()
'''