Prediction of approximate values now can go vertically 
from one level to a neighbouring level, either up or down or 
horizontally within one level. This may go along with the 
actual measuring process. The vertical prediction  corres- 
ponds to a hierarchical, the horizontal to a sequential mea- 
suring process. It is of course not necessary to store the 
measuring tree but only those nodes in the tree which are 
needed for the prediction of points to be measured in fu- 
ture. If the prediction is only based on the previous node, 
i. e. image patch in the same level, and the parent node. i. 
e. the image patch of the next higher level, then the infor- 
mation of only one node in each level has to be kept. 
3. Automatic Measurement Procedure 
  
The data structure consists of two graphs, the wire model 
and the measuring tree. The wire model is built up arc by 
arc, the latent measuring tree controls the sequence of the 
matching steps within the individual arc measurements. The 
strategies to build up the two graphs can be chosen in va- 
rious ways without needing to adapt the data structure. Spe- 
cifically a chosen strategy can be replaced by a new one if 
the matching algorithms provide better information about the 
surface (e. g. if they automatically detect break lines) or 
if one uses a more refined mathematical model for describing 
the surface, which may allow a different way of predicting 
approximate values. The following strategy is powerful 
enough for the determination of all intersections of a set 
of given planes with the objects surface. 
3.1 Automatic Procedure for Arc Measurement 
The measured arc consists of a sequence of points derived 
from LSM, FBM or manual measurements. The point density 
along the arc decreases with distance from the starting node 
and increases with the roughness of the surface. 
The measurement within one level of the measurement tree 
is performed in three steps: 
1.) Prediction: The actual point is predicted using the 
information of the two previously measured points in 
the same level and the point in the higher level, if 
available. The position and the slope of the surface 
point are predicted. The prediction within the measu- 
ring plane uses a first, second or third order poly- 
nomial, the degree depending on the available number 
of points. Prediction of the slope across the measu- 
ring plane is a linear extrapolation. The slopes of 
the points are included in the prediction as a good 
prediction can be used to decrease the point density 
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