The would-be assassin who opened fire at Donald J. Trump’s campaign rally in Butler, Pa., on July 13 was able to get a clear shot at the former president, as countersniper teams nearby failed to see him in time to thwart the shooting.

The New York Times used drone photography to build a 3-D model and recreate the lines of sight for both the gunman, Thomas Matthew Crooks, and three teams of countersnipers — two federal and one local. The analysis shows that Mr. Crooks, 20, who appears to have flown a drone to survey the site the morning of the rally, exploited one of the few blind spots within a rifle’s range of Mr. Trump, raising questions about serious lapses in security planning for the event.

At a contentious hearing on Capitol Hill on Monday, Kimberly A. Cheatle, the Secret Service director, offered few specifics to lawmakers’ repeated questions about sightlines and security breakdowns.

What Secret Service Countersnipers on the North Barn Saw

This is the line of sight that one of two Secret Service teams most likely had just minutes before Mr. Crooks opened fire.

The gunman was largely concealed by two trees and the slope of a warehouse building roof, which he used as his perch. The warehouse complex, owned by AGR International, was outside the Secret Service’s designated security perimeter, the agency later said.

Stationed on the northernmost barn behind Mr. Trump, one of the Secret Service teams had been facing the gunman’s direction for 30 minutes before violence erupted, according to videos posted on social media and verified by The Times. At one point, team members can be seen standing up and looking in the gunman’s direction with binoculars.

The Times captured its own drone footage three days after the shooting. This footage provides a glimpse into how much the trees might have impaired the countersnipers’ view of the gunman.

The Times used a spatial technique called viewshed analysis to calculate what areas would have been visible from the northern countersniper team’s position, taking into account obstructions like trees and buildings. The analysis confirmed that Mr. Crooks chose a prime spot that allowed him to stay largely out of sight — even from a countersniper team that had been facing his direction for a length of time — as he prepared for the first shot.

What Secret Service Countersnipers on the South Barn Saw

A second Secret Service countersniper team was positioned on the roof of a barn farther to the south and west. It had been monitoring a different area — initially facing away from the gunman, videos posted to social media show.

Video footage shows the countersnipers later turning toward the gunman’s direction one minute and 35 seconds before the first shot was fired. This is the view they would have had when they turned around.

But the slope of the warehouse roof that the gunman had chosen would have also made it difficult for the south countersniper team to see him as he crawled upward, a Times analysis shows. Only the very top of Mr. Crooks’s head would have been visible in either Secret Service countersniper team’s line of sight, and only while the gunman was hunkered behind the highest point on the roof.

Forty-two seconds after the shooting began, Secret Service agents can be heard saying “Shooter down” in video footage. Mr. Crooks was fatally shot by a Secret Service countersniper, the agency later confirmed. It’s likely the shot came from the countersnipers on the south barn, who would have been one of the best positioned.

What Local Law Enforcement Countersnipers Saw

A third group of three law enforcement countersnipers was stationed in the same warehouse complex as the gunman, but in an adjacent building, according to a local law enforcement official, who was not authorized to comment.

The building that the countersnipers were in did have windows facing the side of the roof of the building that Mr. Crooks climbed up. But it is not known whether they were assigned to any of those windows that day.

The law enforcement official said the countersnipers, who were tasked with watching over the crowds, were positioned on the other side of the building, at the second-floor windows further from the gunman. Here is what the view of one countersniper — facing those attending the rally — might have looked like.

From this view inside the building, the gunman would have been out of the countersnipers’ lines of sight.

Videos and photos reviewed by The Times show what was most likely a fourth countersniper team from a local law enforcement agency roughly 1,000 feet from Mr. Crooks’s position on the roof. The team was visible several times in the hours and minutes before Mr. Trump began his speech. The Times could not confirm whether the team fired at any point during the shooting.

What the Gunman Saw

The gunman’s spot on a warehouse roof — less than 500 feet from Mr. Trump — provided him with a clear, elevated line of sight.

As he crawled up toward the peak of the roof, its slight slope would have concealed him from the Secret Service countersnipers for a majority of the time. And, once he reached the top, the two trees would have provided some cover from the north countersniper team.

Investigators said that Mr. Crooks appears to have used a drone to survey the rally site before the shooting. The Secret Service did not seek to use drones to provide agents with aerial views of the rally, Ms. Cheatle testified on Monday.

Mr. Crooks was able to fire multiple shots — unimpeded — in Mr. Trump’s direction, injuring Mr. Trump’s right ear. A rally attendee sitting in the bleachers closest to the gunman was fatally shot in the head. Two others in the top row of bleachers to the south were also struck, though they survived.

Other Security Missteps

Two rows of chain-link fencing divide the Butler Farm Show property from the warehouse complex. It’s unclear if the Secret Service used the fencing to delineate the security perimeters, but the agency later acknowledged that the AGR warehouses were excluded from the secure zone.

The warehouse complex, which sits next to a state highway and a major road, is accessible to the public. In a video taken an hour before the shooting, Mr. Crooks can be seen in front of the warehouse building he would later use as his perch.

On the ground, dozens of officers from multiple agencies were also present on the Butler Farm Show grounds, where the rally took place. Ms. Cheatle, the Secret Service director, said on Monday that the AGR building complex was being monitored at the time of shooting, but she did not specify by whom.

An F.B.I. investigation had found that a local SWAT team spotted Mr. Crooks on the roof of a warehouse approximately 18 minutes before Mr. Trump took the stage, Ms. Cheatle also said at Monday’s hearing. The Secret Service had been informed of a potential “suspicious” person through radio communication, but it did not stop Mr. Trump from taking the stage.