“Leave No Trace” leaves its traces everywhere: in your mind, in your heart, in your soul.

Fiercely involving in a way we’re not used to, made with sensitivity and honesty by director/co-writer Debra Granik, it tells its emotional story of a father and daughter living dangerously off the grid in a way that is unnerving and uncompromising yet completely satisfying.

In this it resembles Granik’s last dramatic feature, the Oscar-nominated Sundance hit “Winter’s Bone,” a tense quest drama co-written, as this one is, by Anne Rosellini.

Just as that film launched Jennifer Lawrence’s career, “Leave No Trace” depends on spectacular acting, in this case by the exceptional Ben Foster, who leaves his mark on every film he does, and an incandescent 17-year-old Thomasin Harcourt McKenzie, a quiet knockout from New Zealand.

Though no one is aware of it, the film’s opening scenes that introduce father and daughter are an apogee of happiness for Will (Foster), an Army veteran, and his teenage offspring Tom (McKenzie).

The setting is Forest Park, a 5,000-plus-acre urban woodland just outside of Portland, Ore. Sheltered by enormous trees, unseen by other humans, Will and Tom are presented in perfect harmony with each other and the woods as they go about a remarkable variety of tasks, from picking herbs to gathering moss for a fire to patching the tarp that keeps them dry.

Not initially in any kind of hurry, “Leave No Trace” spends enough time with these two, as compatible as they are self-sufficient, to see that they are everything to each other. Totally rejecting the term “homeless,” they understandably consider the forest, and each other, to be their home.

From time to time Will and Tom do walk across St. John’s Bridge into Portland proper, where Will collects medications from a veterans hospital that he sells to get money for supermarket trips for essentials like propane.

“Want or need,” Will asks when Tom holds up a possible purchase, a choice that almost defines their existence. All these two really want in the entire world is to be left alone, but it is in the nature of that world to impinge on outsiders like them.

Despite their best efforts, Will and Tom are discovered by chance, which puts them in the hands of well-meaning social services personnel whose attempts to normalize the situation fill these two, and us, with dread.

The situation is complicated because, though Will and Tom are devoted to each other, they are very different people, something the actors impeccably convey.

As a teenager full of curiosity for the world, Tom is more open than she expects to be to experiencing new things, to give new plans and places a chance.

Preternaturally poised with a pre-Raphaelite presence joined to palpable strength, actress McKenzie conveys all this quiet assurance with a minimum of fuss.

Her father, however, is a different story, and how much he can be normalized is more of an open question.

We never learn the exact nature of Will’s condition or his background. As Foster explains, “we did not overly articulate what Will is struggling with; his scars are internal.”

But he is unmistakably a veteran with PTSD, someone whose uneasiness gets more pronounced the more he has to deal with society’s conventional expectations.

Foster, memorable in a string of roles including “3:10 to Yuma,” “Lone Survivor,” “The Messenger” and “Hostiles,” is an actor who always brings edgy uncertainty and menace with him, and he makes strong use of it here.

Though “Leave No Trace” is based on Peter Rock’s novel “My Abandonment,” which in turn was inspired by a true story, Granik and Rosellini, who worked on the script for four years, have made shrewd revisions to the second half that enhance the story’s draw without falling into obvious narrative traps.

Because father and daughter deserve better than what society is able to provide — because the dangers to them individually and as a family are so real — we have our hearts in our mouths as we watch their journey play out.

When Tom worries at a certain point that “everything is different now,” her father reassures her by saying “we can still think our own thoughts.” Whether that will be enough is just one of the threads this exceptional film follows to the end.