This article is part of our latest special report on Design, which is about getting personal with customization.

When Wid Chapman and Shachi Shah purchased their Fifth Avenue apartment overlooking Central Park in 2016, they knew they had a lot of work to do. Their goal was to create a personal sanctuary, visually connected to the park — a space that could be both intimate, for their own five-person family, and expansive, to host their many relatives and friends.

But the unit, which had last been renovated decades ago, was a tight warren of small, inefficient rooms. The first thing you saw upon entering was a wall. The floor plan looked like a long tic-tac-toe board.

“There was no sense of place, no hierarchy,” Mr. Chapman said. “Everything just looked the same.”

So Mr. Chapman, 60, an architect with his own practice, and Ms. Shah, 52, the chief financial officer at a venture capital firm, rolled up their sleeves. Together with their contractor, NYC Builders Group, they began removing walls, shaping rooms and creating something altogether different. Mr. Chapman was the project’s architect.

Now, the first view you get is the expanse of Central Park, 14 floors down, spread across the five large windows of the open kitchen, living and dining areas. Each of the apartment’s spaces — including the adjacent master bedroom and the widened hall extending around the corner — is, in some way, connected to that green vista. On the far side of the hall, a media room with large sliding doors has an explicit link to the home’s heart — you can see the park from some angles — but the guest and children’s rooms farther down feel like part of the action, too.

This sense of connection is accentuated by the apartment’s spatial informality. There are very few corners or barriers. Instead, the couple created wide vistas and custom sculpted surfaces — columns, counters, ceilings and walls — encouraging you to move freely from each space to the next. The marble-topped kitchen island resembles a faceted iceberg; some ceilings contain artful crevices, continuing from room to room. A grayed European oak floor further knits the spaces together.

“You’re navigating, you’re not opening and closing,” noted Mr. Chapman of this informal progression. The master bedroom is entered via an oblique, fractured jut in the hall, whose other end finishes at an angle, not a dead end, encouraging you to keep moving into the bedrooms. “There’s a sense of mystery to it. That it’s yours to discover.”

The apartment is perfect for hosting, something the family does a lot. Last Christmas, they entertained close to a dozen members of both families — as many as eight people were cooking at one time in the kitchen — and over New Year’s about 45 guests mingled in the living room alone. Ms. Shah recalled that when she was growing up in London with strikingly convivial parents, hosting 50 people was the norm.

At the same time, the home was designed for nuclear family members to gather on their own. The same faceted surfaces that encourage people to cluster also support privacy. You can have your own space, or you can share it. In the living room, the wall behind the sofa folds and bends around you, creating a snug sense of enclosure. But you still have a clear view to the kitchen, or down the hall. The faceted columns in the living room hug you, and you want to lean on them, but they won’t block your view of the park, or anyone nearby. Brilliant turquoise window seats are perfect for solitary park gazing. But during a party, that is where guests congregate and chatter.

“It embraces you, but you still feel connected,” Ms. Shah said of surroundings that were carved out for her and Mr. Chapman. A little while later, as if proving her point, she gestured to Mr. Chapman, who was on the other side of the apartment. He looked up immediately.

The home feels customized to an extent that few do — a deft accomplishment considering the couple’s different upbringings. Mr. Chapman was raised outside Boston by an architect and designer who met while working for the Bauhaus founder Walter Gropius’s firm The Architects Collaborative. Ms. Shah grew up in London, to parents who emigrated from Gujarat, India. Her father was a diamond dealer, jewelry designer and avid gardener, and her mother a schoolteacher and prolific cook. These backgrounds leave traces throughout the home, smoothly and vibrantly merged in a palette that also draws from the natural cues of the park outside.

From Mr. Chapman, you find a small color-field silk-screen from the series “Homage to the Square,” by Josef Albers, with whom Mr. Chapman’s mother, Amy Chapman, studied at Yale. The artwork is hung between two of the living room windows, above a lovely abstract piece by Ms. Chapman herself. Take a few steps and you will come across an exquisitely crafted wood Hans Wegner chair, an Eero Aarnio Bubble chair suspended from the ceiling, and an Eero Saarinen dining room table. A 200-year-old grandfather clock — a Chapman family heirloom — is ensconced in the wall leading to the couple’s bedroom.

To Ms. Shah is owed the living room’s plush, satiny couch, which was made to fit into the folded wall. It is crystal blue, pulling in the tones of the sky over Central Park, and revealing her early immersion in gemlike patterns and rich colors. The couch pillows have faceted and floral patterns. Three rooms are decked entirely in solid color, and throughout the home are patterned screens, variegated tiles and vibrant fabrics. Across from Mr. Chapman’s clock, a bright magenta shrine in a recess is filled with Hindu deities. (Another niche contains a Buddha.)

But over all, the apartment speaks to Ms. Shah and Mr. Chapman as a collective. Both share a love of art and a desire to create a refuge. Despite its layered, complex components and deft functionality, the home is, at the end of the day, just that.

“When I walk in, I feel grounded, renewed,” Ms. Shah said. “It’s a place of sanctuary, harmony, quiet and joy.”