Detection and reconstruction of freeform sweeps

• Published in: Computer graphics forum 2014-05, Vol.33 (2), p.23-32
• Main Authors: Bartoň, M., Pottmann, H., Wallner, J.
• Format: Article
• Language: English
• Subjects: Analysis; Approximation; Categories and Subject Descriptors (according to ACM CCS); Computer aided design; Computer graphics; Computer Graphics [I.3.5] Computational Geometry and Object Modeling; Mathematical analysis; Optimization; Reconstruction; Rejection; Searching; Studies; Tasks
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12287

We study the difficult problem of deciding if parts of a freeform surface can be generated, or approximately generated, by the motion of a planar profile through space. While this task is basic for understanding the geometry of shapes as well as highly relevant for manufacturing and building construction, previous approaches were confined to special cases like kinematic surfaces or “moulding” surfaces. The general case remained unsolved so far. We approach this problem by a combination of local and global methods: curve analysis with regard to “movability”, curve comparison by common substring search in curvature plots, an exhaustive search through all planar cuts enhanced by quick rejection procedures, the ordering of candidate profiles and finally, global optimization. The main applications of our method are digital reconstruction of CAD models exhibiting sweep patches, and aiding in manufacturing freeform surfaces by pointing out those parts which can be approximated by sweeps.