ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
Figure 5:
face
Surface approximation with translational sur-
As an example, Fig. 5 shows the initial (top) and the fi-
nal position (bottom) of a translational B-spline surface
(dark surface) that approximates a given translational sur-
face (light surface). The control points are iteratively re-
computed as described above, such that the B-spline sur-
face ’flows’ towards the target shape. As a boundary con-
dition, only two diagonally opposite vertices of the moving
surface are kept fixed. Note that no information on the di-
rection and shape of the translated curves c(u) and d(v)
of the target surfaces have been used. These characteristic
curves have been 'detected' by our algorithm.
Future research on this topic will include the recogni-
tion of ruled surfaces and translational surfaces, applying
methods of both projective and affine differential geometry
(Blaschke, 1923, Bol, 1950).
ACKNOWLEDGEMENTS
This work has been carried out in part within the K plus
Competence Center Advanced Computer Vision and was
funded from the K plus program.
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