This paper is the result of a close collaboration of mechanical engineers and visualization researchers. It showcases how interdisciplinary work can lead to new insight and progress in both fields. Our case is concerned with one step in the product development process. Its goal is the design of mechanical parts that are functional, meet required quality measures and can be manufactured with standard production methods. The collaboration started with unspecific goals and first experiments with the available data and visualization methods. During the course of the collaboration many concrete questions arose and in the end a hypothesis was developed which will be discussed and evaluated in this paper. We facilitate a case study to validate our hypothesis. For the case study we consider the design of a reinforcement structure of a brake lever, a plastic ribbing. Three new lever geometries are developed on basis of our hypothesis and are compared against each other and against a reference model. The validation comprises standard numerical and experimental tests. In our case, all new structures outperform the reference geometry. The results are very promising and suggest potential to impact the product development process also for more complex scenarios.

This paper proposes a vector field visualization, which mimics a sketch-like representation. The visualization combines two major perspectives: Large scale trends based on a strongly simplified field as background visualization and a local visualization highlighting strongly expressed features at their exact position. Each component considers the vector field itself and its spatial derivatives. The derivate is an asymmetric tensor field, which allows the deduction of scalar quantities reflecting distinctive field properties like strength of rotation or shear. The basis of the background visualization is a vector and scalar clustering approach. The local features are defined as the extrema of the respective scalar fields. Applying scalar field topology provides a profound mathematical basis for the feature extraction. All design decisions are guided by the goal of generating a simple to read visualization. To demonstrate the effectiveness of our approach, we show results for three different data sets with different complexity and characteristics.

Abstract Tensors provide a powerful language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as the final result of simulations or as intermediate product. Due to their complexity, tensors are hard to interpret. This motivates the development of well‐conceived visualization methods. As a sub‐branch of scientific visualization, tensor field visualization has been especially pushed forward by diffusion tensor imaging. In this review, we focus on second‐order tensors that are not diffusion tensors. Until now, these tensors, which might be neither positive‐definite nor symmetric, are under‐represented in visualization and existing visualization tools are often not appropriate for these tensors. Hence, we discuss the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them. The goal of this paper is to reveal the importance of the field and to encourage the development of new visualization methods for tensors from various application fields.

We present a new method for the generation of anisotropic sample distributions on planar and two-manifold domains. Most previous work that is concerned with aperiodic point distributions is designed for isotropically shaped samples. Methods focusing on anisotropic sample distributions are rare, and either they are restricted to planar domains, are highly sensitive to the choice of parameters, or they are computationally expensive. In this paper, we present a time-efficient approach for the generation of anisotropic sample distributions that only depends on intuitive design parameters for planar and two-manifold domains. We employ an anisotropic triangulation that serves as basis for the creation of an initial sample distribution as well as for a gravitational-centered relaxation. Furthermore, we present an approach for interactive rendering of anisotropic Voronoi cells as base element for texture generation. It represents a novel and flexible visualization approach to depict metric tensor fields that can be derived from general tensor fields as well as scalar or vector fields.