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Fat curves in two‐dimensional Euclidean space are discussed. Previous work on fat curves is reviewed and a new definition is given for a fat curve having a smooth axis. The joining of two fat curves is discussed and a technique for scan‐converting fat curves is presented.

This paper is motivated by a special linear interpolation problem encountered in scan‐line algorithms for scan‐conversion of filled polygons. rounding‐up integral linear interpolation is defined and its efficient computation is discussed. The paper then incorporates rounding‐up integral linear interpolation into a scan‐line algorithm for filled polygons, and it discusses the implementation of the algorithm. This approach has the advantage of only requiring integer arithmetic in the calculations. Furthermore, the approach provides a unified treatment for calculating span extrema for left and right edges of the polygon that guarantees the mutual exclusiveness of the ownership of boundary pixels of two filled polygons sharing an edge.