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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 ). Search WWH ::

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