squares on wafers

squares_with_coordinates.py

import math

def squares_with_coordinates(d, b, w):
    """
    Compute the coordinates of the center of each square inside a circular wafer.

    Parameters:
    d (float): Wafer diameter in mm
    b (float): Border width in mm
    w (float): Square size in mm

    Returns:
    list of tuples: Each tuple represents (x, y) coordinates of a square center.
    """
    # Compute the effective radius after removing the border
    effective_radius = (d - 2 * b) / 2

    # Find the number of full squares that fit along the diameter
    max_rows = math.floor(effective_radius / w)

    square_centers = []

    # Iterate through each row from top to bottom
    for i in range(-max_rows, max_rows + 1):
        y_center = i * w  # Compute y-coordinate of row center
        row_width = math.floor(math.sqrt(effective_radius**2 - (y_center) ** 2) / w)
        
        for j in range(-row_width, row_width + 1):
            x_center = j * w  # Compute x-coordinate of column center
            square_centers.append((x_center, y_center))

    return square_centers

# Example usage
wafer_diameter = 4 * 25.4  # Convert inches to mm
border = 2  # in mm
square_width = 3  # in mm

# Compute and store square center coordinates
square_coordinates = squares_with_coordinates(wafer_diameter, border, square_width)

# Print results
print(f"Total squares: {len(square_coordinates)}")
print("Sample coordinates:", square_coordinates[:10])  # Print first 10 coordinates