The Gift Wrapping procedure, also known as the Jarvis March, is a fundamental procedure in computational geometry that calculates the convex hull of a set of points. Convex hulls are useful in a variety of applications, including pattern recognition, image processing, and computational geometry. The Gift Wrapping Algorithm is simple and intuitive, like wrapping a gift with a ribbon around a group of points. It works by starting at the leftmost point and iteratively finding the point that makes the least left turn before returning to the starting point, resulting in the convex hull.

One of technic is applied VIF, Variance Inflation Factor for determine collinear points. In R Software Programming is in library(faraway).

The Gift Wrapping algorithm works by wrapping a "string" around points in counterclockwise direction, starting from the leftmost point. At each step, it selects the point that forms the smallest angle with the previous segment of the string and adds it to the convex hull. The algorithm stops when it returns to the starting point. However, it may encounter issues when dealing with collinear points, i.e., points that lie on a straight line. These points can lead to incorrect or incomplete convex hulls. Handling collinear points is crucial to ensure the accuracy and completeness of the convex hull.

Collinear points are points that lie on the same straight line or in a single line. 3 points are collinear if the slope of any 2 pairs of points are the same. Pseudocode - 1) Empty code to store convex full points, find leftmost point in the input set, Add this to the list, Set th current point as left most point ASSUMPTION - 1) There are no 3 points in P that are on the same straight line 2) If there are collinear points then the implemented algorithm will produce inconsistent results In 2 dimensional space this is called Jarvis algorithm PS :This answer has information understood from other soiurces

In a real-world scenario, consider a city planner tasked with designing a road network. The planner uses the Gift Wrapping algorithm to determine the convex hull of existing buildings in the downtown area to understand the outer boundary for road construction. However, some buildings along the main street are aligned in a perfectly straight line due to historical zoning regulations. These collinear buildings pose a challenge for the algorithm because selecting different starting points may lead to different interpretations of the outer boundary.

To handle collinear points in the Gift Wrapping algorithm, we can choose the point farthest away in the same direction instead of the one making the smallest angle. This helps us skip unnecessary points and get a better convex shape. It's like picking the point that sticks out the most to draw the shape. This makes the algorithm work better, even if there are points lined up in a straight line.

Imagine you're a farmer planning to fence off a piece of land for a new crop field. You want to use the Gift Wrapping algorithm to determine the most efficient shape for your fence, minimizing costs while maximizing the usable area. However, part of your land contains a row of tall trees planted in a perfectly straight line. These collinear trees can complicate the boundary determination process, potentially resulting in an irregular or inefficient fence shape. By applying the modified Gift Wrapping algorithm, which selects the point farthest away in the same direction when encountering collinear points, you can ensure that your fence follows the natural contours of the land while avoiding unnecessary detours around the trees.

The complexity of handling collinear points arises when using algorithms like the Gift Wrapping algorithm. These points, which lie in a straight line, can lead to ambiguity and inconsistency in determining the convex hull. By modifying the algorithm to account for collinear points, such as by selecting the farthest point in the same direction, we can ensure a more robust and accurate solution.

When working with collinear points, it's recommended to modify algorithms to handle them effectively. One approach is to select the farthest point along the same direction to ensure a more robust and accurate solution. This helps avoid ambiguity and inconsistency in determining geometric properties such as convex hulls.