import math
import json
import sys

def get_cartesian(r_idx, c_idx, n_radii, n_circles, center, size):
    # Padding to keep it off the very edge
    max_radius = (size / 2) - 40
    
    # Radius calculation: C=0 is the innermost, n_circles-1 is outermost
    # We add 1 to c_idx to ensure we don't start exactly at the origin (0,0)
    ring_step = max_radius / n_circles
    r_pixel = (c_idx + 1) * ring_step
    
    # Angle calculation: 0 is 3 o'clock, moving counter-clockwise
    angle_rad = math.radians(r_idx * (360.0 / n_radii))
    
    x = center + r_pixel * math.cos(angle_rad)
    y = center + r_pixel * math.sin(angle_rad)
    return x, y

def render_polar(json_path, output_path):
    with open(json_path, 'r') as f:
        data = json.load(f)
    
    n_radii = data["n_radii"]
    n_circles = data["n_circles"]
    vertices = data["vertices"]
    
    center, size = 500, 1000
    
    # Initial State
    curr_r, curr_c = 0, 0
    x, y = get_cartesian(curr_r, curr_c, n_radii, n_circles, center, size)
    path_d = [f"M {x},{y}"]

    for move in vertices:
        if move == ">": curr_r = (curr_r + 1) % n_radii
        elif move == "<": curr_r = (curr_r - 1) % n_radii
        elif move == "v": curr_c = max(0, curr_c - 1)
        elif move == "^": curr_c = min(n_circles - 1, curr_c + 1)
        
        new_x, new_y = get_cartesian(curr_r, curr_c, n_radii, n_circles, center, size)
        
        if move in [">", "<"]:
            # Ring radius for the SVG Arc
            r_px = (curr_c + 1) * ((size / 2 - 40) / n_circles)
            # Sweep: 1 for clockwise (>), 0 for counter-clockwise (<)
            sweep = 1 if move == ">" else 0
            path_d.append(f"A {r_px},{r_px} 0 0 {sweep} {new_x},{new_y}")
        else:
            # Straight radial line
            path_d.append(f"L {new_x},{new_y}")

    svg = f'<svg viewBox="0 0 {size} {size}" xmlns="http://www.w3.org/2000/svg" style="background:white;">'
    # Optional: Draw the grid for reference
    svg += f'<path d="{" ".join(path_d)}" fill="none" stroke="black" stroke-width="3" stroke-linecap="round" stroke-linejoin="round"/>'
    svg += '</svg>'
    
    with open(output_path, 'w') as f:
        f.write(svg)
    print(f"✅ Path rendered using {n_radii} radii and {n_circles} circles.")

if __name__ == "__main__":
    render_polar(sys.argv[1], sys.argv[2])