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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
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0 Crossing | Angle 
  
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Differential calculus value 
(b) Angle Calculated for Some Side 
Fig.12 The Calculated Result of The Angle at The 
Circumference 
" 
" Curved. point of the, circumference " is extracted 
using the principle of the inner product used in a 
vector. Figure 11 and the equation 2 present the 
inner product. 
First, the angle between: the vectors in 3D space, 
which is used in the inner product, is calculated 
using the 3D data of the interest point and the two 
reference points. Distance of the interest point and 
the reference point is set with 15¢m, and this 
distance 1s classified on the basis of the mask size. 
The differential calculus value is calculated just 
before the angle value. 
Figure 12 presents the results of the calculation of 
the angle at the circumference. When the crossing of 
the difference share value becomes 0, the curved 
points can be found at the 0 crossing point. 
Therefore, in this process, the curved point of the 
circumference is automatically extracted. 
Figure 13 shows the result when the method was 
applied by real data. 
  
OCurved Point 
(b) Classified Result as Flat Part 
  
  
          
  
  
  
  
  
  
  
  
  
  
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(c) Calculated Result about Angle in Flat Part 
Fig.13 Calculation Result of The Angle in Real Data 
From this figure, frequent angle change by error of 
measurement results is confirmed, and a lot of 
points are extracted by 0 crossing. 
Thus the mean of angle data with attention point and 
point of surroundings (each two points of front and 
back) was calculated, and differential value was 
demanded. Figure 14 present calculation result of 
the angle using the result of calculated mean, and 0 
crossings at curve point are confirmed. Unnecessary 
points to make 3D model are reduced by this work. 
  
  
  
  
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Fig.14 Calculation Result of The Angle in 
consideration of the mean 
3.6 The Modeling Method 
The curved points and the circumference points are 
at the circumference of the flat area, however, they 
may not be at the edge of the object being measured. 
Thus, the points on the circumference are confirmed 
by the existence. of. ihe break -lind at the 
circumference. Further, when there is a break -line, 
the point is moved on the break-line. Figure 15 
present the movement of the circumstance points.