Optimal Reliable Point-in-Polygon Test and Differential Coding Boolean Operations on Polygons

Abstract

This paper provides a full theoretical and experimental analysis of a serial algorithm for the point-in-polygon test, which requires less running time than previous algorithms and can handle all degenerate cases. The serial algorithm can quickly determine whether a point is inside or outside a polygon and accurately determine the contours of input polygon. It describes all degenerate cases and simultaneously provides a corresponding solution to each degenerate case to ensure the stability and reliability. This also creates the prerequisites and basis for our novel boolean operations algorithm that inherits all the benefits of the serial algorithm. Using geometric probability and straight-line equation, it optimizes our two algorithms that avoid the division operation and do not need to compute any intersection points. Our algorithms are applicable to any polygon that may be self-intersecting or with holes nested to any level of depth. They do not have to sort the vertices clockwise or counterclockwise beforehand. Consequently, they process all edges one by one in any order for input polygons. This allows a parallel implementation of each algorithm to be made very easily. We also prove several theorems guaranteeing the correctness of algorithms. To speed up the operations, we assign each vector a number code and derive two iterative formulas using differential calculus. However, the experimental results as well as the theoretical proof show that our serial algorithm for the point-in-polygon test is optimal and the time complexities of all algorithms are linear. Our methods can be extended to three-dimensional space, in particular, they can be applied to 3D printing to improve its performance.

Development of Multilayer-Based Map Matching to Enhance Performance in Large Truck Fleet Dispatching

“…This study evaluates our proposed multilayer-based map matching algorithm under both spatial data structures, vector and raster (Step 3), in order to compare performance (Step 4). The point-in-polygon algorithm described in [40,41] was applied to verify performance efficiency using the puncture (traditional) method to determine whether the point falls within the polygon. In this scenario, the puncture method can be used with vector data to process the mapping between coordinates and map features and can be applied to map matching algorithms [39].…”

Robust Lane Detection and Tracking Algorithm for Steering Assist Systems

“…The purpose is to find only a simple condition that will tell us if a pixel lies in the parallelogram area without creating an actual mask. There are many proposed methods [19], but we are interested in a solution that requires as few computations as possible.…”

“…The purpose is to find only a simple condition that will tell us if a pixel lies in the parallelogram area without creating an actual mask. There are many proposed methods [19], but we are interested in a solution that requires as few computations as possible. However, creating a parallelogram region of interest image and then appl and bitwise operator is not the most optimal approach.…”

Efficient Construction of Voxel Models for Ore Bodies Using an Improved Winding Number Algorithm and CUDA Parallel Computing

“…The problem of point in polygon has its roots in the early days of geometric graphics [31]. Today, as computer graphics have become essential in many fields, many scholars continue to discuss this problem [32,33]. With the application of three-dimensional geometry, the problem has expanded to include discussions of methods, improvements, and efficiency.…”