We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of userspecified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

Over the past few years, better knowledge of aerodynamics and structures and the permanent need to improve the performance and efficiency of aircraft have led to the generalized adoption of wingtip devices. The requirements faced by wingtip devices throughout the various flight conditions are, however, different. A static wingtip device (as is the case with existing designs) must be a compromise of these various conflicting requirements, resulting in less than optimal effectiveness in each flight condition. A morphing device, on the other hand, can adapt to the optimum configuration for each flight condition, leading to improved effectiveness. This article presents a morphing wingtip mechanism based on a servo-actuated articulated winglet, able to rotate about two different axes: vertical axis (toe angle) and aircraft’s longitudinal axis (cant angle). These can be controlled independently by servo-actuators. The wingtip behavior is a function of aerodynamic and structural loads which, in turn, are interdependent, requiring a multidisciplinary design optimization procedure in order to determine the ideal wingtip configuration for each case. The proposed concept is applied to a multi-mission unmanned aerial vehicle and the results show that a morphing wingtip can outperform an optimum fixed design. The optimum geometries for the different flight missions are presented and the feasibility of such a morphing wingtip is confirmed by a prototype. The performance metrics of the morphing wingtip are compared to those of a fixed wingtip to quantify the gain associated with the use of the morphing concept and it is seen that the improvement can reach 25%.

We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of userspecified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

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