Sure, I can write a test case generator for the "Area Folding" problem. Given the constraints and requirements, the generator will create valid input polygons with random vertices. Here's the code for the test case generator:

```python
import random

def generate_random_points(n):
    points = []
    for _ in range(n):
        x = random.randint(-105, 105)
        y = random.randint(-105, 105)
        points.append((x, y))
    return points

def tcgen():
    # Number of segments (vertices)
    N = random.randint(2, 100)
    
    # Generate N random points ensuring no two consecutive points are the same
    while True:
        points = generate_random_points(N)
        valid = True
        for i in range(1, N):
            if points[i] == points[i - 1]:
                valid = False
                break
        if valid:
            break
    
    # Convert points to the required format
    result = f"{N}\n"
    for x, y in points:
        result += f"{x} {y}\n"
    
    return result.strip()

# Example of generating a test case
print(tcgen())
```

This generator ensures that:

1. The number of vertices \( N \) is within the specified range \([2, 100]\).
2. Each point \((X_i, Y_i)\) is within the range \([-105, 105]\).
3. No two consecutive points are the same.

The generator outputs the test case in the format required by the problem statement. You can run this function multiple times to generate different test cases for your problem.