Today visitors to Gettysburg can climb to the cupola of the Lutheran seminary, where Lee stationed himself on July 2, the second day of fighting; or stand on Seminary Ridge, where the next day Lee watched from behind the Confederate lines as thousands of his men advanced across the open farmland to their deaths in the notorious Pickett’s Charge. But they won’t see what the general saw because the intervening years have altered the topography. Over the decades a quarry, a reservoir, different plants and trees have been added, and elevations have changed as a result of mechanical plowing and erosion.

Geographic Information Systems, known as GIS, allowed Ms. Knowles and her colleagues to recreate a digital version of the original Gettysburg battlefield from historical maps, documented descriptions of troop positions and scenery, and renderings of historic roads, fences, buildings and vegetation. “The only way I knew how to answer the question,” about what Lee saw, Ms. Knowles said, “was to recreate the ground digitally using GIS and then ask the GIS program: What can you see from a certain position on the digital landscape, and what can you not see?”

She said her work helps “make Lee’s dilemma more vivid and personal.” Nineteenth-century military leaders relied primarily on their own eyes, and small differences in elevation were strategically important. “Lee probably could not have possibly seen the massive federal forces building up on the eastern side of the battlefield on Day 2 during the famous attack on Little Round Top,” Ms. Knowles said. “He had to make decisions with really inadequate information.”

So did Lt. Gen. James Longstreet, who was vilified in the Confederacy partly because of his decision on July 2 to take his troops on a long countermarch to avoid detection rather than attack Little Round Top directly. The march “made Longstreet the goat of Gettysburg,” Ms. Knowles said. But there was no way that Longstreet could have seen that Little Round Top was undefended at the time. “The analysis says Longstreet made the best decision he could,” added Ms. Knowles, who is currently working on a digital map of the Nazis’ territorial conquests and forced labor camps in Europe.