import pygame
from kingdon import Algebra
import math

ERROR = 0.00001
DISK_RADIUS = 250
WIDTH, HEIGHT = 800, 600
CENTER_X, CENTER_Y = 400, 300

alg = Algebra(2,1,0)
locals().update(alg.blades)

def point(x,y):
    #Construct a point.
    #Hyperbolic space is modeled as a hyperboloid embedded in 3D Minkowski space.
    #Find w such that x,y,w is a point on the hyperboloid.
    w_sqr = x*x + y*y + 1
    w = math.sqrt(w_sqr)
    return x*e23 -y*e13 + w*e12

def draw_point(point):
    #Normalize the 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)
    x_0 = x_0/norm
    x_1 = x_1/norm
    x_2 = x_2/norm
    #Transform it into the Poincare Space
    u = x_1/(1+x_0)
    v = x_2/(1+x_0)

    pygame.draw.circle(screen, RED, (int(u*DISK_RADIUS+CENTER_X), int(v*DISK_RADIUS+CENTER_Y)), 5)

def draw_line(line):
    delta = line.e3
    if abs(delta) < ERROR:
        # The geodesic is a line through the origin.
        if abs(line.e2) < ERROR:
            pygame.draw.line(screen, BLUE, (CENTER_X, CENTER_Y+DISK_RADIUS), (CENTER_X, CENTER_Y-DISK_RADIUS), 1)
        else:
            slope = line.e1/line.e2
            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)
    else:
        #The geodesic is a circle
        a = line.e1
        b = line.e2
        sqr = a*a + b*b
        norm = math.sqrt(sqr)
        x_c = a/delta
        y_c = b/delta
        r = math.sqrt(x_c*x_c+y_c*y_c - 1)
        c_x = int(CENTER_X + x_c*DISK_RADIUS)
        c_y = int(CENTER_Y + y_c*DISK_RADIUS)
        pygame.draw.circle(screen, BLUE, (c_x, c_y), int(r*DISK_RADIUS), 1)




y_axis = e1 #x = 0 line
x_axis = e2 #y = 0 line

tx_generator = e13 #A translation in the x direction
ty_generator = e23 #A translation in the y direction
origin = e12 #The origin, and a rotation about the origin


# Initialize Pygame
pygame.init()

screen = pygame.display.set_mode((WIDTH, HEIGHT))
pygame.display.set_caption("Pygame Example")

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


# Game loop
running = True
t = 0

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
    transform = math.sin(t)*tx_generator + math.sin(math.sqrt(2)*t)*ty_generator + math.sin(math.sqrt(3)*t)*origin
    transform = transform
    motor = transform.exp()

    #Apply the transformation
    y_tick = motor*y_axis*motor.reverse()
    x_tick = motor*x_axis*motor.reverse()

    #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()