The first time I encountered Gregg Popovich was in 2000. He came out of the visiting locker room snarling like a dog guarding a steak bone.

Bad Pop has reprised that act during sideline interviews and NBA Finals news conferences for years, earning a reputation as a nasty piece of business. Tuesday night, his Spurs were in town to face the Timberwolves, and for a change of pace so was Good Pop.

He spoke of opening his doors to an out-of-work Tom Thibodeau, of caring for his players as humans. He was funny and thoughtful, nothing like the persona he often shows off and very much like the person he is known for being behind the scenes.

The great San Antonio columnist Buck Harvey tells of Popovich learning early in Tim Duncan’s career that Duncan loved carrot cake. NBA coaches eat a lot of restaurant meals on the road during the season, and at the end of each one, Popovich would order a ­carrot cake to go and leave it in front of Duncan’s hotel door.

And after for years ridiculing the silly on-court quarter-break TV interviews that reveal nothing other than the power of television networks, Popovich in 2015 welcomed TNT reporter Craig Sager back to work after his ­recovery from cancer.

“I can honestly tell you this is the first time I’ve enjoyed doing this ridiculous interview we’re required to do, and it’s because you’re here and back with us,” Popovich said. “Now, ask me a couple of inane questions.’’

When Thibodeau visited the Spurs last year, they did more than draw on whiteboards. “We ate well, had a little wine, relaxed,’’ Popovich said. “It was just fun to throw out anything on the table ... I guess trying to invent the light bulb.

“We weren’t really successful. It was just fun to talk basketball with somebody else. ... He’s a good man.’’

Why are NBA coaches willing to share ideas? “There’s nothing that’s that amazing,’’ Popovich said. “If I took a drill from Tommy, it’s not necessarily going to keep him from doing well. And it doesn’t mean it’s going to help us be champions. If you’re a mature, secure person in your own skin, you enjoy sharing and giving and receiving in that respect. It’s a collegial thing.’’

Popovich, whose Spurs whipped the Wolves 105-91 on Tuesday, benefited from collegial goodwill early in his career. He coached at Pomona-Pitzer, then took off the 1985-86 season to work as a volunteer assistant at Kansas under Larry Brown. Brown left Kansas to coach the Spurs in 1988 and hired Popovich as an assistant, putting him in charge of ­“training.’’

“It’s amazing,’’ Popovich said. “I remember when I first came in when Larry Brown was unwise enough to hire me as an assistant way back when. I was doing the weight program for the team. I said, ‘You guys go over and lift those weights over there. Ten times, yeah, that’s good. Do that.’ Seriously, that’s what it was like.

“Now I get on the bus and our trainer comes on handing out water, drinks. The sooner you eat, the sooner you rehydrate, the sooner you get the protein and the electrolytes back in and blah, blah, blah, the more you’re going to recover for tomorrow night’s game. None of that existed back in the day. Not a bit. People like Charles [Barkley] and Larry Bird must laugh their fannies off.’’

Popovich’s old-school act belies his thirst for innovation. His conversations with Thibodeau were not one-sided.

“We’re just coaches,’’ Popovich said. “We can’t think of anything on our own. We’ve got to steal from people, get some ideas from somebody else. It’s not necessarily a huge, new strategy. It could be a drill in training camp to get something across or the way a coach says a certain thing, and you’ve been saying it differently all this time and wondering why you’re not getting it across.

“You learn a little phrase or a little technique. There’s always something that can be learned.’’

What would sound like a cliché from a less-accomplished coach sounds, from Popovich, like wisdom.