Geoscience Reference
InDepth Information
Fig. 11
Indoor building surveying by Trimble LaserAce 1000
To improve shape accuracy, researchers decided to measure three points on a
surface and calculate its infinite plane instead of just corners of a room. For a sim
ple room, six infinite planes need to be calculated. Three infinite planes intersect
each other in one point. Intersected point can be calculated by Eqs.
1

5
:
Plane 1
:
A1x
+
B1y
+
C1z
+
D1
=
0
(1)
Plane 2
:
A2x
+
B2y
+
C2z
+
D2
=
0
(2)
Plane 3
:
A3x
+
B3y
+
C3z
+
D3
=
0
(3)
Intersected point by three infinite planes can by calculated by determinant of three
plane's coefficients (See Eqs.
4
,
5
).
A
1
B
1
C
1
A
2
B
2
C
2
A
3
B
3
C
3
Det
=
=
0
(4)
D
1
B
1
C
1
D
2
B
2
C
2
D
3
B
3
C
3
A
1
D
1
C
1
A
2
D
2
C
2
A
3
D
3
C
3
A
1
B
1
D
1
A
2
B
2
D
2
A
3
B
3
D
3
(5)
x
=
y
=
z
=
Det
Det
Det
Results from intersection of three infinite planes in one point showed good accu
racy for distance bigger than 5 m with angles near 90°. Distance of less than 5 m
with wide and narrow angles showed distorted shapes (See Fig.
12
).