Search results for "Parallelogram"
showing 3 items of 3 documents
Textile and tile pattern design automatic cataloguing using detection of the plane symmetry group
2004
We present an integrated management system of pattern design for the textile and tile industries providing automatic cataloguing capabilities based on the application of the scientific theory of symmetry groups. To do this, a process of analysis is performed which starts from an initial image of the decorative element, which in turn is subjected to a number of segmentation and labelling operators that allow to detect the objects present in the image. These objects are vectorized, compared, and their isometries obtained; subsequently they are grouped and the isometries of the groups of objects detected. Finally, a composition analysis is carried out that, on the basis of the repetitions and …
On stability of linear dynamic systems with hysteresis feedback
2020
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the appli…
On Fine and Wilf's theorem for bidimensional words
2003
AbstractGeneralizations of Fine and Wilf's Periodicity Theorem are obtained for the case of bidimensional words using geometric arguments. The domains considered constitute a large class of convex subsets of R2 which include most parallelograms. A complete discussion is provided for the parallelogram case.