Barycentric related code

    public static float sign(Vector3 p1, Vector3 p2, Vector3 p3) {
        return (p1.x - p3.x) * (p2.y - p3.y) - (p2.x - p3.x) * (p1.y - p3.y);
    }

    public static boolean checkPointInTriangle(Vector3 pt, Vector3 v1, Vector3 v2, Vector3 v3) {
        boolean b1, b2, b3;

        b1 = sign(pt, v1, v2) < 0.0f;
        b2 = sign(pt, v2, v3) < 0.0f;
        b3 = sign(pt, v3, v1) < 0.0f;

        return ((b1 == b2) && (b2 == b3));
    }

    // OR

    public static Vector3 checkPointInTriangle(Vector3 point, Vector3 p1, Vector3 p2, Vector3 p3) {
        // Compute vectors
        Vector3 v0 = Vector3.sub(p3, p1);
        Vector3 v1 = Vector3.sub(p2, p1);
        Vector3 v2 = Vector3.sub(point, p1);

        // Compute dot products
        float dot00 = v0.dot(v0);
        float dot01 = v0.dot(v1);
        float dot02 = v0.dot(v2);
        float dot11 = v1.dot(v1);
        float dot12 = v1.dot(v2);

        // Compute barycentric coordinates
        float denom = dot00 * dot11 - dot01 * dot01;
        float u = (dot11 * dot02 - dot01 * dot12) / denom;
        float v = (dot00 * dot12 - dot01 * dot02) / denom;

        return new Vector3(u, v, 1 - u - v);
    }

    public static Vector3 calculateCartesianCoordinate(Vector3 barycentric, Vector3 p1, Vector3 p2, Vector3 p3) {
        Vector3 result = Vector3.add(Vector3.add(Vector3.mul(p1, barycentric.x), Vector3.mul(p2, barycentric.y)), Vector3.mul(p3, barycentric.z));

        float x = result.x;
        result.x = result.y;
        result.y = x;

        return result;
    }