Data Display

The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the polynomial basis. The framework has been designed using the adaptor design pattern, meaning that the visualization system need not reimplement basis functions, rather it communicates with the simulation package via simple programmatic queries. We demonstrate our method on several examples, and have implemented the framework in the open-source visualization system VTK.

Determine the effects of display viewing distance on both the visual and musculoskeletal systems while the text height is held constant across viewing distances. The distance from the eyes to a computer display may affect visual and neck comfort. If the angular size of the characters remains the same, it is recommended that the display be placed at a farther viewing distance (e.g., 70-100 cm). However, in common usage, the character sizes are not adjusted based on viewing distance. Participants under the age of 35 years (N = 24) performed visually demanding tasks using a computer display for 2 hr each at three viewing distances (mean: 52.4, 73.0, and 85.3 cm) while torso and head posture were tracked. At the end of each task, eye accommodation was measured and symptoms were recorded. The near distance was associated with significantly less blurred vision, less dry or irritated eyes, less headache, and improved convergence recovery when compared with the middle and far distances. Participants moved their torsos and heads closer to the monitor at the far distance. If the computer screen character sizes are close to the limits of visual acuity, it is recommended that the computer monitor be positioned between the near (52 cm) and middle (73 cm) distance from the eyes. The location of a computer display should take into account the size of the characters on the screen and the visual acuity of the user.