Asger Nyman Christiansen

Combined shape and topology optimization of 3D structures

We present a method for automatic generation of 3D models based on shape and topology optimization. The optimization procedure, or model generation process, is initialized by a set of boundary conditions, an objective function, constraints and an initial structure. Using this input, the method will automatically deform and change the topology of the initial structure such that the objective function is optimized subject to the specified constraints and boundary conditions. For example, this tool can be used to improve the stiffness of a structure before printing, reduce the amount of material needed to construct a bridge, or to design functional chairs, tables, etc. which at the same time are visually pleasing.The structure is represented explicitly by a simplicial complex and deformed by moving surface vertices and relabeling tetrahedra. To ensure a well-formed tetrahedral mesh during these deformations, the Deformable Simplicial Complex method is used. The deformations are based on optimizing the objective, which in this paper will be maximizing stiffness. Furthermore, the optimization procedure will be subject to constraints such as a limit on the amount of material and the difference from the original shape. Graphical abstractDisplay Omitted HighlightsAutomatic design of 3D structures given a set of requirements for that structure.Efficient shape and topology optimization utilizing an adaptive tetrahedral mesh.Explicit shape representation made possible by the Deformable Simplicial Complex method.

Generic graph grammar : a simple grammar for generic procedural modelling

Methods for procedural modelling tend to be designed either for organic objects, which are described well by skeletal structures, or for man-made objects, which are described well by surface primitives. Procedural methods, which allow for modelling of both kinds of objects, are few and usually of greater complexity. Consequently, there is a need for a simple, general method which is capable of generating both types of objects. Generic Graph Grammar has been developed to address this need. The production rules consist of a small set of basic productions which are applied directly onto primitives in a directed cyclic graph. Furthermore, the basic productions are chosen such that Generic Graph Grammar seamlessly combines the capabilities of L-systems to imitate biological growth (to model trees, animals, etc.) and those of split grammars to design structured objects (chairs, houses, etc.). This results in a highly expressive grammar capable of generating a wide range of types of models. Models which consist of skeletal structures or surfaces or any combination of these. Besides generic modelling capabilities, the focus has also been on usability, especially user-friendliness and efficiency. Therefore several steps have been taken to simplify the workflow as well as to make the modelling scheme interactive. As proof of concept, a generic procedural modelling tool based on Generic Graph Grammar has been developed.