Christian Steinmetz

A hybrid approach for computing products of high-dimensional geometric algebras

Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics solutions. For example, the Conformal Geometric Algebra includes circles, spheres, planes and lines as algebraic objects, and intersections between these objects are also algebraic objects. More complex objects such as conics, quadric surfaces can also be expressed and be manipulated using an extension of the conformal Geometric Algebra. However due to high dimension of their representations in Geometric Algebra, implementations of Geometric Algebra that are currently available do not allow efficient realizations of these objects. This paper presents a Geometric Algebra implementation dedicated for both low and high dimensions. The proposed method is a hybrid solution for precomputed code with fast execution and runtime computations with low memory requirement. More specifically, the proposed method combines a precomputed table approach with a recursive method using binary trees. Some rules are defined to select the most appropriate choice, according to the dimension of the algebra and the type of multivectors involved in the product. The resulting implementation is well suited for high dimensional spaces (e.g. algebra of dimension 15) as well as for lower dimensional space. This paper details the integration of this hybrid method as a plug-in into Gaalop, which is a very advanced optimizing code generator. This paper also presents some benchmarks to show the performances of our method, especially in high dimensional spaces.

Potential and Influence of Industrie 4.0 in Oral Implantology Products and Their Production for Patient, Dentist and Dental Laboratory

The purpose of this paper is to identify on the one hand the influence of Industrie 4.0 to the horizontal value creation in the process chain patient-dentist and the process chain dentist-dental laboratory. On the other hand, the effect of Industrie 4.0 to the vertical value creation in the manufacturing process chain of implants, abutments and crowns in a dental laboratory are explained. In addition, the potential of the Industrie 4.0 in CAx-pre-processing and post-processing of each process chain is presented. Furthermore, the Human-Machine-Interaction in the modeling of oral implantology products and their individual medical service functional upgrade to a Smart Health Product is discussed [1]. Based on these results, new business models between the correlation patient, dentist and dental laboratory are generated.

Web-Based Application for Algorithm Based Product Development Process of Integral Bifurcated Sheet Metal Parts

Within the Collaborative Research Center 666 the algorithm based product development process has been established. It is based on state of the art product development methodologies and enhanced in order to optimize the product development process of integral bifurcated sheet metal parts. Algorithms based on mathematical optimization approaches as well as the initial product requirements and constraints information are applied to obtain an optimized design as CAD-Model. Regarding this methodology there are still some challenges to be solved, such as reduction of iterations steps to elaborate final product design as CAD-model, use of heterogeneous data as well as software and enhancement of information exchange. Therefore, this paper introduces a concept for a web-based application to support the algorithmic product development methodology and CAD modeling in CRC 666. It enables the development and adaptation of integral bifurcated parts based on the initial optimization data provided by XML-files. Besides the description of use cases and use scenarios, the concept is implemented as a web-based application for validation purposes. Based on the validation, advantages and limitations of the presented approach are discussed.