Sure! Let's create a test case generator for the given problem. The generator will create random convex polygons by generating random points and ensuring they form a convex shape. 

Here's the code for the test case generator:

```python
import random
import math

def generate_random_convex_polygon(n):
    """ Generates a random convex polygon with n vertices. """
    points = []
    for _ in range(n):
        x = random.randint(0, 10000)
        y = random.randint(0, 10000)
        points.append((x, y))
    
    # Sort points to ensure the polygon is convex and counterclockwise
    points.sort()
    points.sort(key=lambda point: math.atan2(point[1], point[0]))
    
    return points

def tcgen():
    test_cases = []
    num_datasets = random.randint(1, 10)  # You can adjust the number of datasets for more tests

    for _ in range(num_datasets):
        n = random.randint(3, 100)
        points = generate_random_convex_polygon(n)
        
        dataset = f"{n}\n"
        for x, y in points:
            dataset += f"{x} {y}\n"
        
        test_cases.append(dataset.strip())
    
    # Add the terminating zero line
    test_cases.append("0")
    
    return "\n".join(test_cases)

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

### Explanation:
- `generate_random_convex_polygon(n)`: This function generates `n` random points and sorts them to form a convex polygon. Sorting by angles ensures that the points are arranged in a counterclockwise order.
- `tcgen()`: This function generates multiple datasets by calling `generate_random_convex_polygon` and formats them according to the problem's input specifications. It also appends a terminating zero line to indicate the end of input.

### Usage:
This generator will output a string that represents the entire input for the problem, including multiple datasets followed by a terminating zero. You can adjust the ranges and numbers to generate different sets of test cases for thorough testing.