Drawing filled polygon with libGDX

You can use the ShapeRenderer API to draw simple, solid-color shapes with Libgdx.

The code you've given is a reasonable way to draw solid color polygons too. Its much more flexible than ShapeRenderer, but is a good bit more complicated. You'll need to use glColor4f to set the color, or add a Usage.Color attribute to each vertex. See the SubMeshColorTest example for more details on the first approach and the MeshColorTexture example for details on the second approach.

Another option to think about is using sprite textures. If you're only interested in simple solid colors objects, you can use very simple 1x1 textures of a single color and let the system stretch that across the sprite. Much of Libgdx and the underlying hardware are really optimized for rendering textures, so you may find it easier to use even if you're not really taking advantage of the texture contents. (You can even use a 1x1 white texture, and then use a SpriteBatch with setColor and draw() to draw different color rectangles easily.)

You can also mix and match the various approaches, too.

I believe the ShapeRenderer class now has a polygon method for vertex defined polygons:

ShapeRenderer.polygon()

Here is a libGDX example which draws a 2D concave polygon.

Define class members for PolygonSprite PolygonSpriteBatch

PolygonSprite poly;
PolygonSpriteBatch polyBatch;
Texture textureSolid;

Create instances, 1x1 size texture used with red pixel as workaround. An array of coordinates (x, y) is used for initialization of the polygon.

ctor() {
    textureSolid = makeTextureBox(1, 0xFFFF0000, 0, 0); 
    float a = 100;
    float b = 100;
    PolygonRegion polyReg = new PolygonRegion(new TextureRegion(textureSolid),
      new float[] {
        a*0, b*0,
        a*0, b*2,
        a*3, b*2,
        a*3, b*0,
        a*2, b*0,
        a*2, b*1,
        a*1, b*1,
        a*1, b*0,
    });
    poly = new PolygonSprite(polyReg);
    poly.setOrigin(a, b);
    polyBatch = new PolygonSpriteBatch();
}

Draw and rotate polygon

void draw() {
    super.draw();
    polyBatch.begin();
    poly.draw(polyBatch);
    polyBatch.end();
    poly.rotate(1.1f);
}

Since recent updates of LibGDX, @Rus answer is using deprecated functions. However, I give him/her credits for the new updated version below:

PolygonSprite poly;
PolygonSpriteBatch polyBatch = new PolygonSpriteBatch(); // To assign at the beginning
Texture textureSolid;

// Creating the color filling (but textures would work the same way)
Pixmap pix = new Pixmap(1, 1, Pixmap.Format.RGBA8888);
pix.setColor(0xDEADBEFF); // DE is red, AD is green and BE is blue.
pix.fill();
textureSolid = new Texture(pix);
PolygonRegion polyReg = new PolygonRegion(new TextureRegion(textureSolid),
  new float[] {      // Four vertices
    0, 0,            // Vertex 0         3--2
    100, 0,          // Vertex 1         | /|
    100, 100,        // Vertex 2         |/ |
    0, 100           // Vertex 3         0--1
}, new short[] {
    0, 1, 2,         // Two triangles using vertex indices.
    0, 2, 3          // Take care of the counter-clockwise direction. 
});
poly = new PolygonSprite(polyReg);
poly.setOrigin(a, b);
polyBatch = new PolygonSpriteBatch();

For good triangulating algorithms if your polygon is not convex, see the almost-linear earclipping algorithm from Toussaint (1991)

Efficient triangulation of simple polygons, Godfried Toussaint, 1991