Sure! Here is a Python test case generator for the "Shy Polygons" problem:

```python
import random

def generate_polygon():
    n = random.randint(3, 14)
    vertices = []
    for _ in range(n):
        x = random.randint(0, 499)
        y = random.randint(0, 499)
        vertices.append((x, y))
    return n, vertices

def format_polygon(n, vertices):
    result = f"{n}\n"
    for x, y in vertices:
        result += f"{x} {y}\n"
    return result

def tcgen():
    test_cases = []
    while True:
        L = round(random.uniform(0.1, 50.0), 4)
        n1, vertices1 = generate_polygon()
        n2, vertices2 = generate_polygon()
        
        polygon1 = format_polygon(n1, vertices1)
        polygon2 = format_polygon(n2, vertices2)
        
        test_case = f"{L}\n{polygon1}{polygon2}"
        test_cases.append(test_case)
        
        # Decide randomly when to stop adding test cases
        if random.random() < 0.2:
            break
    
    test_cases.append("0")  # End of input indicator
    return "\n".join(test_cases)

# Example usage
print(tcgen())
```

This generator creates a series of test cases for the "Shy Polygons" problem. The generator includes:
- Randomly generating the minimum distance \( L \) between polygons from \( 0.1 \) to \( 50.0 \).
- Generating two polygons with a random number of vertices (between 3 and 14).
- Ensuring that each vertex has x and y coordinates within the range \( 0 \) to \( 499 \).
- Randomly decides when to stop adding more test cases, ensuring the end of input is indicated by a single "0".

The `format_polygon` function formats the polygon data to match the required input format. 

You can adjust the probabilities or ranges as needed for more specific test cases.