We have been working intensively on issues related to geometric modeling. Our main interest is in forms of representation that can represent volumetric objects and graded properties alike, and are suitable for modeling, simulation and 3D printing--without trading off mathematical precision and continuity.
For this purpose, we are developing subdivision methods and researching intuitive metaphors to interactively generate and modify real volumetric objects. These objects include those with locally varying properties as well as models--similar to CAE--that define the volume within an object and make it possible to model locally variable attributes, e.g., material densities. This distinguishes real volumetric models from traditional models in CAD, which define the surface (the edge) of an object but not the varying, graded properties within.
Combined with subdivision methods, we are researching parametric and procedural modeling techniques to automatically generate variants and quickly evaluate them in simulation (see also interactive simulation). This accelerates the discovery of good solutions in the design space. For the realm of 3D printing, we are focusing on modeling internal structures in order to use rapid FEM simulations to automatically optimize internal structures in terms of orientation, thickness and material properties.
Subdivision methods are particularly suited for organic forms, such as those arising from topology optimization and ideally generated via 3D printing. As an intuitive modeling form for creating subdivision models, we are combining sketch-based input methods with parametric modeling methods. Our solution combines the advantages of both methods: natural access for the user through sketch-based input and using parameters to manipulate the form of the model. To ultimately realize the subdivision models using 3D printing, we are developing efficient processes for slicing subdivision models with selectable resolution. This allows us to achieve a seamless transition to the 3D printing processes without approximation losses.
The depth of our representation of real volumetric objects makes superfluous the error-prone transitioning from a continuous CAD model to a discrete model for simulation/3D printing--a time-consuming process necessary in today’s industrial practice and one that is often repeated to address optimization issues (isogeometric analysis and additive manufacturing).