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Picture 4: Verified straight lines of some front panels. 
All straight lines above a minimal length of 10 pixels 
have been verified successfully. Actually, the algorithm 
does not distinguish between edges with the same 
direction and different orientation. So the opposite 
boundaries of a very small hole are indistinguishable 
without further model information. This happens at the 
little screw wholes with an extension up to 6 pixel. The 
verification of larger primitives is invariant under 
rotation and translation. 
fJ 
Picture 5: Verified straight lines of a rotated object. 
7. VERIFICATION OF CIRCLES AND LINES 
Straight line verification is organized as contour 
following of pixels with constant direction. Circles and 
arcs have no such simple direction features. Their 
generation algorithms may be classified as raster 
oriented approaches for creating the "true" line and 
those interpolating the shape by polygons, Bezier- 
curves, B-Splines etc. Disadvantages of both approaches 
are well known in computer graphics. The raster 
oriented approach needs new primitives which usually 
demand different data structures and algorithms e.g. 
extended clipping, transformation and projection 
algorithms. These operations may map a primitive type 
to a new one and the circle and arc generation 
algorithms can not prevent the necessity for higher 
ordered curve interpolation. The interpolation approach 
just looks for a curve approximation. Obviously, this 
approach is more efficient than the raster-oriented on. It 
is a useful alternative if its precision is acceptable and is 
applied here. 
P1 P2 
Picture 6: Circle approximation by direction segments. 
The segments created in the direction image are already 
an approximation of the curve (picture 6). Although the 
curve is given by a set of discrete pixels located on the 
curve to be approximated the pixel values classify them 
as straight line points. In this way circle verification is 
reduced to the verification of a set containing straight 
lines. The verification is always done clockwise. When 
reaching a new line, the direction code is incremented. 
FUNCTION verify. circle (ModelCircle, PictureCircle) 
BEGIN 
initialize i 
calculate start point Pi 
increment i 
DO 
calculate the next point Pi 
verify line (line(Pi-1, Pi),PictureLine) 
increment i 
WHILE( < 360/MINANGLE) 
approximate PictureCircle 
compare ModelCircle with PictureCircle 
END 
Algorithm 3: Circle verification using an interpolation 
approach. 
Picture 7 states the results of processing circles of 
different size. All circles with a diameter larger than 20 
pixels can be verified successfully. Smaller ones fall 
short of the minimal region size for straight line 
approximation. 
  
  
  
  
Picture 7: Results of circle verification using an 
interpolation approach based on 8 straight lines. The 
circle diameters lie within 30 to 85 pixels. 
Arc verification follows a closely related way. Instead of 
a fixed start point the first and last point have to be 
calculated by the circle equation. Additionally all 
involved sectors are determined. 
Pn 
P2 
Pi 
Picture 8: Arc verification where M - (8,8), r = 5, alpha = 
202,5 and beta = 112,5 based on 8 interpolating straight 
lines.