Computing a scale factor to insert a first set of shapes into a second set of shapes to form a combined image includes receiving the two sets of shapes, using a processor to convert the first set of shapes into a set of rectangles and the second set of shapes into a set of intervals and computing the scale factor for either the set of intervals or the set of rectangles to generate the combined image by iteratively inserting the set of rectangles into the set of intervals and updating the scale factor in response to a residual area or an overflow area until all the rectangles in the set of rectangles have been inserted into the set of intervals and the residual area in the set of intervals is below a threshold, and storing the combined image in memory.