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The shape optimization design of developable surface is a critical and intractable technique in CAD/CAM and used in many manufacturing planning operations. In this paper, we study shape optimization by using a new cuckoo search (CS) algorithm to promote the development of generalized developable H-Bezier surfaces (or GDHBS, for short). According to the duality between points and planes in 3D projective space, the GDHBS shape optimization problem is formulated as an arc length, energy and curvature variation minimization problem of dual curve, respectively. Then, an adaptive CS optimization algorithm is applied to the solutions of those GDHBS shape optimization models. Finally, we illustrate the effectiveness and performance of the proposed methods by some representative and convictive examples.

In this work we study the evolution of one particular segment of the Southern Central Andes, the northern sector of the Malargue Fold and Thrust Belt (34 degrees-35 degrees LS), where limited access to the western section has delayed its exploration for years. Analyses of the structure, stratigraphy and sedimentology of different sections along the fold and thrust belt added to the recognition and analysis of growth strata geometries within the foreland basin allowed us to perform an evolutionary model. Our results suggest that during the Lower Jurassic a rift-related depocenter, the Alto Atuel depocenter, developed next to the international border between Argentina and Chile, which was characterized by an important volcanic contribution from the magmatic arc. During the Late Jurassic, a new extensional episode took place at these latitudes, where synextensional deposits were found in the Alto Atuel depocenter, suggesting that this region has suffered multiple extensional processes during the Jurassic. Growth strata within the Late Cretaceous Diamante Formation suggest that the orogenic front reached an eastern location at this time. Sedimentary and petrographic analyses support the hypothesis that the Diamante Formation represents a synorogenic unit. Furthermore, petrographic and provenance analyses developed in the Late Cretaceous to Miocene deposits suggest that during the Paleogene the main source areas were the magmatic arc and the Mesozoic deposits exhumed by the Andean orogen, in accordance with detrital zircon ages published by other authors. The final development of the fold and thrust belt during Neogene time generated growth strata within the wedge top section of the foreland basin. The detection of these geometries within the Agua de la Piedra Formation suggests that the last Neogene compressional phase started between 20 and 15 Ma.