Step 2: 3D Model of the Scenario (Including Coordinate System)

The 3D model of the scenario is computed automatically by MASC. Depending on the approximation of the circle by polygons, different objects are generated. If a polygon with six corners is used for the mast, the following 64 objects are generated to describe the scenario:

(All coordinates in meter. One line describes one object. Each object has four corners.

Syntax: Number Corner 1.x, Corner 1.y, Corner 1.z Corner 2.x, Corner 2.y, Corner 2.z,…)

Mast:
1 0.217, 0.125, 0.000 0.000, 0.250, 0.000 0.000, 0.250, 10.000 0.217, 0.125, 10.000
2 0.217, -0.125, 0.000 0.217, 0.125, 0.000 0.217, 0.125, 10.000 0.217, -0.125, 10.000
3 0.217, -0.125, 0.000 -0.000, -0.250, 0.000 -0.000, -0.250, 10.000 0.217, -0.125, 10.000
4 -0.000, -0.250, 0.000 -0.217, -0.125, 0.000 -0.217, -0.125, 10.000 -0.000, -0.250, 10.000
5 -0.217, -0.125, 0.000 -0.217, 0.125, 0.000 -0.217, 0.125, 10.000 -0.217, -0.125, 10.000
6 0.000, 0.250, 0.000 -0.217, 0.125, 0.000 -0.217, 0.125, 10.000 0.000, 0.250, 10.000

Arm 1, lower part:
7 0.025, -0.550, 8.700 0.025, -0.215, 8.700 -0.025, -0.215, 8.700 -0.025, -0.550, 8.700
8 0.025, -0.550, 8.750 0.025, -0.215, 8.750 -0.025, -0.215, 8.750 -0.025, -0.550, 8.750
9 -0.025, -0.550, 8.700 -0.025, -0.215, 8.700 -0.025, -0.215, 8.750 -0.025, -0.550, 8.750
10 0.025, -0.550, 8.700 0.025, -0.215, 8.700 0.025, -0.215, 8.750 0.025, -0.550, 8.750

Arm 1, upper part:
11 0.025, -0.550, 9.250 0.025, -0.215, 9.250 -0.025, -0.215, 9.250 -0.025, -0.550, 9.250
12 0.025, -0.550, 9.300 0.025, -0.215, 9.300 -0.025, -0.215, 9.300 -0.025, -0.550, 9.300
13 -0.025, -0.550, 9.250 -0.025, -0.215, 9.250 -0.025, -0.215, 9.300 -0.025, -0.550, 9.300
14 0.025, -0.550, 9.250 0.025, -0.215, 9.250 0.025, -0.215, 9.300 0.025, -0.550, 9.300

Arm 1, vertical tube:
15 0.025, -0.600, 8.500 -0.025, -0.600, 8.500 -0.025, -0.600, 9.500 0.025, -0.600, 9.500
16 0.025, -0.550, 8.500 -0.025, -0.550, 8.500 -0.025, -0.550, 9.500 0.025, -0.550, 9.500
17 -0.025, -0.600, 8.500 -0.025, -0.550, 8.500 -0.025, -0.550, 9.500 -0.025, -0.600, 9.500
18 0.025, -0.600, 8.500 0.025, -0.550, 8.500 0.025, -0.550, 9.500 0.025, -0.600, 9.500

Arm 1, Antenna 1-1, Radome :
19 -0.075, -0.600, 8.600 -0.075, -0.650, 8.600 0.075, -0.650, 8.600 0.075, -0.600, 8.600
20 -0.075, -0.600, 9.400 -0.075, -0.650, 9.400 0.075, -0.650, 9.400 0.075, -0.600, 9.400
21 0.075, -0.650, 8.600 0.075, -0.600, 8.600 0.075, -0.600, 9.400 0.075, -0.650, 9.400
22 -0.075, -0.650, 8.600 -0.075, -0.600, 8.600 -0.075, -0.600, 9.400 -0.075, -0.650, 9.400
23 0.075, -0.600, 8.600 -0.075, -0.600, 8.600 -0.075, -0.600, 9.400 0.075, -0.600, 9.400
24 0.075, -0.650, 8.600 -0.075, -0.650, 8.600 -0.075, -0.650, 9.400 0.075, -0.650, 9.400

Arm 2, lower part:
25 -0.025, 0.700, 8.700 -0.025, 0.215, 8.700 0.025, 0.215, 8.700 0.025, 0.700, 8.700
26 -0.025, 0.700, 8.750 -0.025, 0.215, 8.750 0.025, 0.215, 8.750 0.025, 0.700, 8.750
27 0.025, 0.215, 8.700 0.025, 0.700, 8.700 0.025, 0.700, 8.750 0.025, 0.215, 8.750
28 -0.025, 0.215, 8.700 -0.025, 0.700, 8.700 -0.025, 0.700, 8.750 -0.025, 0.215, 8.750

Arm 2, upper part:
29 -0.025, 0.700, 9.250 -0.025, 0.215, 9.250 0.025, 0.215, 9.250 0.025, 0.700, 9.250
30 -0.025, 0.700, 9.300 -0.025, 0.215, 9.300 0.025, 0.215, 9.300 0.025, 0.700, 9.300
31 0.025, 0.215, 9.250 0.025, 0.700, 9.250 0.025, 0.700, 9.300 0.025, 0.215, 9.300
32 -0.025, 0.215, 9.250 -0.025, 0.700, 9.250 -0.025, 0.700, 9.300 -0.025, 0.215, 9.300

Arm 2, vertical tube:
33 0.025, 0.750, 8.500 -0.025, 0.750, 8.500 -0.025, 0.750, 9.500 0.025, 0.750, 9.500
34 0.025, 0.700, 8.500 -0.025, 0.700, 8.500 -0.025, 0.700, 9.500 0.025, 0.700, 9.500
35 0.025, 0.700, 8.500 0.025, 0.750, 8.500 0.025, 0.750, 9.500 0.025, 0.700, 9.500
36 -0.025, 0.700, 8.500 -0.025, 0.750, 8.500 -0.025, 0.750, 9.500 -0.025, 0.700, 9.500

Arm 2, Antenna 2-1, Sub-arm (lower part):
37 -0.032, 0.729, 8.910 -0.004, 0.757, 8.910 -0.039, 0.792, 8.910 -0.067, 0.764, 8.910
38 -0.032, 0.729, 8.950 -0.004, 0.757, 8.950 -0.039, 0.792, 8.950 -0.067, 0.764, 8.950
39 -0.004, 0.757, 8.910 -0.039, 0.792, 8.910 -0.039, 0.792, 8.950 -0.004, 0.757, 8.950
40 -0.032, 0.729, 8.910 -0.067, 0.764, 8.910 -0.067, 0.764, 8.950 -0.032, 0.729, 8.950

Arm 2, Antenna 2-1, Sub-arm (upper part):
41 -0.032, 0.729, 9.050 -0.004, 0.757, 9.050 -0.039, 0.792, 9.050 -0.067, 0.764, 9.050
42 -0.032, 0.729, 9.090 -0.004, 0.757, 9.090 -0.039, 0.792, 9.090 -0.067, 0.764, 9.090
43 -0.004, 0.757, 9.050 -0.039, 0.792, 9.050 -0.039, 0.792, 9.090 -0.004, 0.757, 9.090
44 -0.032, 0.729, 9.050 -0.067, 0.764, 9.050 -0.067, 0.764, 9.090 -0.032, 0.729, 9.090

Arm 2, Antenna 2-1, Radome:
45 0.000, 0.831, 8.600 -0.035, 0.866, 8.600 -0.141, 0.760, 8.600 -0.106, 0.725, 8.600
46 0.000, 0.831, 9.400 -0.035, 0.866, 9.400 -0.141, 0.760, 9.400 -0.106, 0.725, 9.400
47 -0.106, 0.725, 8.600 -0.141, 0.760, 8.600 -0.141, 0.760, 9.400 -0.106, 0.725, 9.400
48 0.000, 0.831, 8.600 -0.035, 0.866, 8.600 -0.035, 0.866, 9.400 0.000, 0.831, 9.400
49 0.000, 0.831, 8.600 -0.106, 0.725, 8.600 -0.106, 0.725, 9.400 0.000, 0.831, 9.400
50 -0.035, 0.866, 9.400 -0.141, 0.760, 9.400 -0.141, 0.760, 8.600 -0.035, 0.866, 8.600

Arm 2, Antenna 2-2, Sub-arm (lower part):
51 0.004, 0.757, 8.910 0.032, 0.729, 8.910 0.067, 0.764, 8.910 0.039, 0.792, 8.910
52 0.004, 0.757, 8.950 0.032, 0.729, 8.950 0.067, 0.764, 8.950 0.039, 0.792, 8.950
53 0.032, 0.729, 8.950 0.067, 0.764, 8.950 0.067, 0.764, 8.910 0.032, 0.729, 8.910
54 0.004, 0.757, 8.910 0.039, 0.792, 8.910 0.039, 0.792, 8.950 0.004, 0.757, 8.950

Arm 2, Antenna 2-2, Sub-arm (upper part):
55 0.004, 0.757, 9.050 0.032, 0.729, 9.050 0.067, 0.764, 9.050 0.039, 0.792, 9.050
56 0.004, 0.757, 9.090 0.032, 0.729, 9.090 0.067, 0.764, 9.090 0.039, 0.792, 9.090
57 0.032, 0.729, 9.090 0.067, 0.764, 9.090 0.067, 0.764, 9.050 0.032, 0.729, 9.050
58 0.004, 0.757, 9.050 0.039, 0.792, 9.050 0.039, 0.792, 9.090 0.004, 0.757, 9.090

Arm 2, Antenna 2-2, Radome:
59 0.106, 0.725, 8.600 0.141, 0.760, 8.600 0.035, 0.866, 8.600 0.000, 0.831, 8.600
60 0.106, 0.725, 9.400 0.141, 0.760, 9.400 0.035, 0.866, 9.400 0.000, 0.831, 9.400
61 0.000, 0.831, 9.400 0.035, 0.866, 9.400 0.035, 0.866, 8.600 0.000, 0.831, 8.600
62 0.106, 0.725, 9.400 0.141, 0.760, 9.400 0.141, 0.760, 8.600 0.106, 0.725, 8.600
63 0.106, 0.725, 8.600 0.000, 0.831, 8.600 0.000, 0.831, 9.400 0.106, 0.725, 9.400
64 0.141, 0.760, 8.600 0.035, 0.866, 8.600 0.035, 0.866, 9.400 0.141, 0.760, 9.400

(The origin of the coordinate system is the center of the mast ground plane. The center can be defined arbitrarily – important is only the relative location of the elements to one another).

The coordinates of all three antennas (each concentrated in a single point) in the above-mentioned coordinate system:


Antenna 1-1: x = 0.0 mm      y = -725.0 mm  z = 9000.0 mm
Antenna 2-1: x = -141.42 mm  y = 866.42 mm  z = 9000.0 mm
Antenna 2-2: x = 141.42 mm   y = 866.42 mm  z = 9000.0 mm

The coordinates of the (geometrical) point of radiation M_geo in the above-mentioned coordinate system is:

x_geo = (2 × 0.0 + 1× (-141.42) + 1 × 141.42) / 4 = 0.00 mm

y_geo = (2 × (-725.0)+ 1× 866.42 + 1 × 866.42) / 4 = 70.71 mm

z_geo = (2 × 9000.0 + 1× 9000.0 + 1 × 9000.0) / 4 = 9000.00 mm

Figure 1. 3D view of the 64 objects describing the scenario listed before.