• Chebyshev nets
• computational geometry
• computer graphics
• digital fabrication
• position-based dynamics

The use of computational tools in the design of real-world entities has revolutionized the way in which these are conceived and manufactured. Within an interdisciplinary field that combines mechanics, geometry, and numerical optimization, these tools allow to flawlessly exploit the underlying physical and geometrical properties of materials and structures not only to streamline various phases of the production process, from manufacture to distribution and deployment, but also to enable the fabrication of objects with specific functionalities that couldn't have been built without such computational support. In an attempt to broaden the horizon of what can be built, this thesis questions the use of reticular structures adhering to the discrete Chebyshev net model to support the fabrication of entities, analyzing their capabilities and limitations from a purely theoretical perspective. To this end, a physical simulator based on the position-based dynamics framework is first proposed and implemented, allowing for a natural, real-time virtual experimentation of such structures. Then, a novel method for adhering these nets to arbitrary surfaces is devised, facilitating their design within a virtually assisted process that is reminiscent of physically wrapping a cloth around an object. Finally, the simulator is used to test whether different nets can be coupled together to obtain a structure that exhibits better resistance to deformation caused by external forces.