How to draw walls in ThreeJS from path or 2d array

I need to draw a 3d house model (walls only) from a 2d path or array (explained later) I receive from FabricJS editor I've built. The type of data sent from 2d to 3d views doesn't matter.

My first (and only quite close to what I want to get) attempt was to create the array of 1s and zeros based on the room I want to draw, and then render it in ThreeJS as one cuboid per 'grid'. I based this approach on this ThreeJS game demo. So if the array look like this:

var map = [ //1  2  3  4  5  6  7  8
          [1, 1, 1, 1, 1, 1, 1, 1, 1, 1,],
          [1, 1, 0, 0, 0, 0, 0, 1, 1, 1,], // 1
          [1, 1, 0, 0, 1, 0, 0, 0, 0, 1,], // 2
          [1, 0, 0, 0, 1, 1, 0, 0, 0, 1,], // 3
          [1, 0, 0, 1, 1, 1, 1, 0, 0, 1,], // 4
          [1, 0, 0, 0, 1, 1, 0, 0, 1, 1,], // 5
          [1, 1, 1, 0, 0, 0, 0, 1, 1, 1,], // 6
          [1, 1, 1, 0, 0, 1, 0, 0, 1, 1,], // 7
          [1, 1, 1, 1, 1, 1, 0, 0, 1, 1,], // 8
          [1, 1, 1, 1, 1, 1, 1, 1, 1, 1,],
       ];

I iterate through the array and render one block for every 1, and calculate it's position from indexes from the 2d 'map' (my array).

var UNITSIZE = 250, units = mapW;
for (var i = 0; i < mapW; i++) {
    for (var j = 0, m = map[i].length; j < m; j++) {
        if (map[i][j]) {
            var wall = new t.Mesh(cube, material);
            wall.position.x = (i - units/2) * UNITSIZE;
            wall.position.y = WALLHEIGHT/2;
            wall.position.z = (j - units/2) * UNITSIZE;
            scene.add(wall);
        }
    }
}

It worked great till I wanted to place other models (.obj, but it doesn't matter. Let's call them furniture) near the walls. Each piece of furniture has it's (x=0, y=0, z=0) point in the center of the model, and since walls are cubes (with the same coord system, with 0 point in the center), furniture are rendered in the center of the wall (when we place it in the corner, only 1/4 of the model is visible). This is more/less how it looks like:

(black - how the walls should look like, blue - each cuboid of the wall, red - piece of furniture)

Thats why I would like to render walls as planes, probably from a 2d closed patch (I can export it from Fabric without a problem). I don't need walls to be thick nor to be visible "from behind", when camera moves through the wall. Any clues on how to achieve something like this?

"Help me StackOverflow, your my only hope."

You can manually populate the vertex and face arrays of a THREE.js mesh, so if you can export the closed path you need for example as an array of coordinates, you can iterate over it, and push needed information to your wall object.

Something like this

var coordArray = [...]; //Array of corner points of a closed shape from your source. Here assumed to be THREE.Vector2() for simplicity.

var walls = new THREE.Geometry();

for(var i = 0; i < coordArray.length(); i++){ //iterate over the coordinate array, pushing vertices to the geometry
  var coordinates = coordArray[i];
  walls.vertices.push(new THREE.Vector3(coordinates.x, coordinates.y, 0)); //vertex at floor level
  walls.vertices.push(new THREE.Vector3(coordinates.x, coordinates.y, 10)); //vertex at the top part of the wall, directly above the last
}
var previousVertexIndex = walls.vertices.length - 2; // index of the vertex at the bottom of the wall, in the segment we are creating faces for
for(var i = 0; i < walls.vertices.length; i += 2){
  walls.faces.push(new THREE.Face3(i, i + 1, previousVertexIndex));
  walls.faces.push(new THREE.Face3(i + 1, previousVertexIndex + 1, previousVertexIndex));
  previousVertexIndex = i;
}
walls.computeVertexNormals();
walls.computeFaceNormals();

scene.add(new THREE.Mesh(walls, new THREE.MeshLambertMaterial());