How Can We Efficiently Assign Points to Either Side of a Line?

Efficiently Dividing Points Based on Line Position

To effectively categorize points into two groups based on their position relative to a line segment, we need a method to determine if each point falls to the left or right. While calculating the angle between line segments might seem intuitive, the limited range of ArcCos (0° to 180°) presents a challenge.

A more robust solution utilizes the cross product:

<code>isLeft(a, b, c) = (b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x) > 0</code>

Here, a, b, and c represent the points. This formula computes the cross product of vectors (b - a) and (c - a). A positive result indicates point c lies to the left of line segment a-b; a negative result signifies it's to the right; and a zero result means c is collinear with the segment.

For horizontal lines, a positive result correctly identifies points above the line. This cross-product approach offers a reliable and efficient method for classifying points relative to a given line segment.

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