When your cat is purring, you probably assume that she's happy. But do you really know all of the things that make cats happy — or unhappy, for that matter?

In her new book, "Purr: The Science of Making Your Cat Happy" (Greystone Books), author Zazie Todd — a psychologist and creator of the website Companion Animal Psychology — takes readers on a tour of cat behaviors and desires, sharing the science behind feline play, greetings, communication, socialization and more.

In 14 chapters — plus checklists, appendices and training plans — she uncovers the evidence on why cats need hiding places, what they look for in terms of resources — from food dishes to litter boxes to toys — and how and why they interact with humans and each other. Chapters cover getting a cat; setting up a home that's attractive to a cat; addressing behavior problems, care and lifestyle; and the needs of cats at every life stage. I spoke to Todd about what people should know when it comes to keeping cats happy.

Take scratching. It's a normal behavior for cats — important not only for grooming but also for communication and exercise. But not all cats scratch alike. They have individual preferences on exactly how they want to scratch, preferences that aren't always recognized by their people.

"Many people have scratching posts that are not very sturdy or not tall enough or they're made of a surface the cat doesn't like," Todd says. "And some will prefer a horizontal surface rather than a vertical one. It's up to us to provide cats with surfaces which they can scratch and encourage and reward them for using those rather than trying to punish them for scratching in what we think is the wrong place."

Petting is another aspect of feline happiness that can leave people scratching their heads. New cat owners, especially those more accustomed to dogs, can get a sharp-clawed reprimand if they try to pet a cat's belly, even if the cat has rolled over to expose it. While some cats allow it — briefly — most prefer to be petted elsewhere. And they like it if you ask permission first.

That's right, you should give cats a chance to come to you and request petting, as well as the chance to move away when they've had enough. Knowing where they do and don't like to be petted is important, too.

"Most cats do not like to be petted around the base of the tail or on the tail, and most cats really don't like to be petted on the tummy," Todd says. "There will be some exceptions, especially if you have a really good relationship with your cat, but most cats prefer to be petted around the head and face, which is where their scent glands are."

What does Todd hope readers take away from the book?

One wish is that pet parents toss away spray bottles, shake cans and other forms of punishment.

"Punishment isn't good for cats," she says. "It can make them stressed, and it risks affecting their relationship with us."

But she also believes many feline lovers will find that they're already doing a good job.

"I have a checklist for a happy cat at the end, and I think people will find things that they're already doing," she says. "They can give themselves a big pat on the back for that, but they probably will also find some things they're not doing. They can think about whether or not that would work for them and their cats in their home."