import numpy as np
from PIL import Image, ImageDraw

# Parameters
R = 9.0          # mm
H = 20.0         # mm
fov_half = np.radians(75)  # 75 degrees half-angle
pixels_per_mm = 100

# Texture dimensions
width = int(np.pi * 2 * R * pixels_per_mm)   # circumference
height = int(H * pixels_per_mm)

# Desired dot pattern in image space (normalized)
delta_theta = np.radians(10)      # 10° azimuth spacing
delta_r = 0.1                     # radial spacing in normalized units
rho = 0.08                        # normalized dot radius (from reference)

# Generate dot centers in image space
r_vals = np.arange(R/H, np.tan(fov_half), delta_r)
theta_vals = np.arange(0, 2*np.pi, delta_theta)

# Create empty texture (white background)
img = Image.new('L', (width, height), color=255)
draw = ImageDraw.Draw(img)

for r_img in r_vals:
    z = R / r_img
    v = z / H
    # Ellipse axes in texture coordinates
    a_u = (rho * z) / (2 * np.pi * R)
    a_v = (rho * z**2) / (R * H)
    # Convert to pixels
    a_u_px = a_u * width
    a_v_px = a_v * height
    for theta in theta_vals:
        u = theta / (2 * np.pi)
        cx = u * width
        cy = v * height
        # Draw ellipse (bounding box)
        bbox = [cx - a_u_px, cy - a_v_px, cx + a_u_px, cy + a_v_px]
        draw.ellipse(bbox, fill=0)   # black dot

img.save('cylinder_marker_texture.png')