Sure! Here is the test case generator for the "Convex Hull" problem.

```python
import random

def tcgen():
    # Number of points in P
    n = random.randint(3, 100000) 
    
    # Generating n unique points with coordinates in the range [-10000, 10000]
    points_set = set()
    while len(points_set) < n:
        x = random.randint(-10000, 10000)
        y = random.randint(-10000, 10000)
        points_set.add((x, y))
    
    points_list = list(points_set)
    
    # Formatting the output similar to the input structure
    input_str = f"{n}\n"
    for (x, y) in points_list:
        input_str += f"{x} {y}\n"
    
    return input_str

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

This Python function `tcgen` generates a random test case for the "Convex Hull" problem. It ensures that the points are unique and within the constraint bounds. The output is formatted as a string to match the input format of the problem statement.