Canada’s Cassie Sharpe celebrates a gold medal thanks to the influence of the late Sarah Burke. (Loic Venance/Agence France-Presse/Getty Images)

If it were not for Sarah Burke, there might have been no women’s freestyle skiing halfpipe competition in the Olympics and possibly no Cassie Sharpe, who won gold for Canada.

In an emotional competition, Sharpe edged Marie Martinod of France for the gold and it was hard not to think of Burke, a pioneer in the sport who campaigned hard for its addition to Olympic competition. Burke, who died in a training accident in Utah in 2012, was a four-time champion in X Games superpipe and was expected to be a gold medal contender when the sport was added to the 2014 Games in Sochi. Instead, her coach scattered her ashes in the mountains of Russia that year.

On Tuesday, Burke’s husband, Rory Bushfield, watched proudly from Canada as Sharpe won gold.

“Sarah gave her life for that,” he told the Associated Press from his home in Whistler, B.C. “It’s cool to sit back and enjoy it. It’s super-emotional for me.”

Just as it was for Burke’s coach, Trennon Paynter, who happens to coach the halfpipe team. He took Burke to the competition, too, posting an Instagram photo of a backpack with her name and writing, “As always, she is with us every step of the way. We wouldn’t be here without you Sarah! #werestokedonit #sarahisstokedonit#celebratesarah #teamcanada #weloveyou.”

Burke, 29, suffered a fatal injury while trying to land a trick during training in Park City, Utah. She crashed and struck her head, rupturing her vertebral artery and suffering a severe intracranial hemorrhage. She was placed on life support and died nine days later, according to a family statement at the time.

Burke’s campaign for the sport included grass-roots work, which paid off in Sharpe’s gold and in the bronze won by Brita Sigourney of the United States. In Sharpe, Paynter sees potential.

“She’s the first girl in quite some time to really push the sport to new levels. It’s really cool to see where she’s taking it . . .” he told the Toronto Star earlier this month. “On one hand, it would be nice to see her get way out front and make it easy [to win], but for the sport as a whole, what she’s done over the last little bit has forced all the other girls to really elevate their game.

“It reminds me in a sense of Sarah back in the day, breaking new ground for women’s skiing.”

A new generation is carrying on, thanks to Burke.

“It almost becomes a Sarah mythology,” Roz Groenewoud, a friend of Burke’s, said. Groenewoud finished 10th for Canada and told the Associated Press of how moved she was to see South Korean halfpipe skier Yujin Jang carrying the flag with the Olympic rings at the Opening Ceremonies.

“I thought, ‘Wow, that’s really cool,’ ” she said as she began to cry. “It made me think of Sarah a lot.”

Read more Olympic coverage from The Post:

How a skier managed to compete in the Olympics despite not being very good

French ski team boots Mikaela Shiffrin’s boyfriend from Olympics over salty comments

American Brita Sigourney earns bronze on final run of freestyle skiing halfpipe

For Team USA, it’s not quite a medal drought, but it’s certainly no Olympic reign