1. A method, comprising: sweeping a scan line over line segments from different ones of first polygonal objects; identifying an event point via the scan line; evaluating the line segments in response to identifying the event point to identify an intersection of at least two of the line segments from different ones of the first polygonal objects; determining relationships between the line segments based on the intersection, wherein determining the relationships between the line segments comprises determining segment pairs of the line segments, and wherein each segment pair comprises two segments located on different edges of a region and which intersect the scan line; removing a redundancy between the at least two of the line segments; generating, using a computer, second polygonal objects based on the intersection and the at least two line segments; and outputting, from the computer, embroidery data representative of the second polygonal objects.