pisteintersect

pisteintersect is a computational geometry algorithm designed to determine the intersection points between two line segments, often referred to as pistes in certain contexts. This algorithm is fundamental in various applications, including computer graphics, geographic information systems (GIS), and robotics, where accurate collision detection or path analysis is required.

The core principle of pisteintersect involves solving a system of linear equations derived from the parametric representations of the two line segments. Each line segment can be described by its start and end points. By expressing any point on a segment as a linear combination of its endpoints, an equation can be formulated that equates the coordinates of a potential intersection point on both segments.

The algorithm typically proceeds by first checking if the line segments are collinear. If they are, it then determines if they overlap. If the segments are not collinear, the algorithm calculates the parameters that define the intersection point. These parameters indicate the position of the intersection along each segment. If these parameters fall within the range of 0 to 1 (inclusive) for both segments, it signifies that the segments intersect within their defined lengths. Otherwise, the lines containing the segments intersect, but the segments themselves do not. Edge cases, such as parallel segments or segments sharing an endpoint, are also handled by the algorithm.