THE "BEFORE" picture is almost a standard part of remodeling a house. But architect Charles Szoradi showed it to be a real tool in an analytical study of the problems with a wonderful but much-remodeled stone mansion. His technique offers a useful method for all remodelers.

When interior designer Alan Cox and his wife, Marie Louise, a once and future designer, called in Szoradi, "I realized that I had to prove myself to them since they weren't very familiar with my work."

So Szoradi went through the Cox house with a camera and photographed the two major problems and some smaller ones. Then with tape he red-lined the eyesores on the photographs. Then he sketched his solutions. The questions and answers were easy to see and understand.

A previous owner had, as the saying goes, "brought the outside in" with a large bay window at one end of the dining room. When the Coxes bought the house four years ago their concern was how to keep the outside out.

The bay window brought in light, all right, but it also framed an imposing view of the garage. The bay's mullions and the garage's intersecting triangular roof plus its porthole window made a geometrically upsetting view to diners.

The previous remodeling had resulted in a tacked-on living room with a second bay, and, to the Coxes, a second problem. The bay in the living room had no windows, just a hole in the wall for an air conditioner over a built-in banquette. It was, to say the least, peculiar. To the left was a window neither small nor large. Across the room was a door, which seemed rather left over when the Coxes opened up one side of the room with an 8-foot-high set of sliding glass doors.

Today, after hard work on everybody's part, including contractor Eric Guille, and a fair amount of money, everyone agrees that the problems have been solved. The solutions are not only adequate but dramatic. When Szoradi's architectural changes were complete, the Coxes took over to make the decorating as dramatic as the architecture. The last piece, the splendid Jack Lenor Larsen rug with the custom border, arrived the other day.

The biggest part of the job was the dining room. Szoradi's answer to the problem was to extend the dining room by 14 by 17 feet to make an informal greenhouse/eating area. The roof is a dramatic steep sweep of bronze-tinted glass which starts above the second-floor master bedroom windows and extends down to the far wall.

In the daytime, the heavy muntins and mullions (the wood divisions between glass) make all sorts of patterns on the floor and walls, including one very intersting zebra stripe. "At night, the ceiling becomes a great mirror, reflecting the candlelight and flowers, and making other reflections in the glass top," Alan Cox said the other day, showing visitors through the house with Szoradi.

Half the far wall is solid, to block out the garage as totally as though it had been torn down. It also serves to hold the Coxes' Eskimo prints. The other section has an unusual triangular bay which cantilevers out to steal a view of a decorative magnolia tree (thankfully spared from last winter's magnum magnolia kill). Another wall has a tall and skinny window and an outside glass door with a pleasant garden glimpse. The third wall has buffet with built-in lighting for both daily and party service.

The table is a Knoll design by Warren Platner, with a glass top substituted by Cox. It is 45 inches around, a figure arrived at by Cox as ideal for the five members of the family. For that reason there are five, not six Harvey Probber chairs around the table.

The floor is a practical ceramic tile, impervious to spills from the plants or the table.

The original glass ceiling was a medium tint of bronze. "I never can convince my clients to order the darkest tint. They always think it will be too dark," said Szoradi. But after living with the brilliant east sun for a while, the Coxes added a thin solar mylar covering which still is completely transparent, but cuts down on the solat radiation, and increases the nighttime reflectivity.

The Coxes then went on to redecorate the dining room to reflect the extension. They bought a handsome Pace table with a top and Y-shaped base both made of solar bronze glass with bronze mountings. On the table is a plastic base for a copper-ore rock, an arresting natural sculpture.

The addition would cost about $15,000 to do now, Cox figures.

In the living room, the answer was to subtract rather than add. Szoradi straightened out the far wall, eliminating the bay and installing two tall, skinny fixed-glass windows for light. In between is a magnificent Louise Nevelson Print, a very limited edition indeed, one of 20.

On another wall is a fine Japanese screen which fits as though the wall were made for it. The leftover French door on a far wall was closed and walled over.

Two Mies van der Rohe/Lilly Reich Barcelona chairs sit across the matching X-based glass table and two wicker chairs. The wickers were originally bought because they looked indestructible enough for the children's TV room, but everyone thought they would add a nice warmth to the classic modern living room, which they do. The rug is almost a tapestry, with a great nubby weave, worked in Switzerland.

Outside, the walls of the new addition are stuccoed, grooved vertically every so often to keep it from cracking.

In the garden, the Coxes also had help from landscape gardener Eric Paepcke. Szoradi noted right away that the old hedge in the garden completely obscured the view of the oval swimming pool from the living room. The narrow existing walk was left over from the original screen porch, which vanished several owners and several remodelings ago.

The hedge was removed, and the whole patio taken up and relaid to link the pool with the house. The Coxes haven't yet decided what to do with the old wading pool, another leftover from one of the house's previous lives. The small octagonal pool has a stopper in it. When you pull it out, water fills up from the big one.

The vast expanse of flagstone is relieved by pot of flowers, changed by Mrs. Cox to exploit whatever's blooming.

And then, for the future, there's the cabana, designed by Szoradi in a triangular shape with a great fan-shaped glass marquise, designed to fit in an outside corner. But that's another day.