David Hoffman

Vergence-accommodation conflicts hinder visual performance and cause visual fatigue.

Three-dimensional (3D) displays have become important for many applications including vision research, operation of remote devices, medical imaging, surgical training, scientific visualization, virtual prototyping, and more. In many of these applications, it is important for the graphic image to create a faithful impression of the 3D structure of the portrayed object or scene. Unfortunately, 3D displays often yield distortions in perceived 3D structure compared with the percepts of the real scenes the displays depict. A likely cause of such distortions is the fact that computer displays present images on one surface. Thus, focus cues-accommodation and blur in the retinal image-specify the depth of the display rather than the depths in the depicted scene. Additionally, the uncoupling of vergence and accommodation required by 3D displays frequently reduces ones ability to fuse the binocular stimulus and causes discomfort and fatigue for the viewer. We have developed a novel 3D display that presents focus cues that are correct or nearly correct for the depicted scene. We used this display to evaluate the influence of focus cues on perceptual distortions, fusion failures, and fatigue. We show that when focus cues are correct or nearly correct, (1) the time required to identify a stereoscopic stimulus is reduced, (2) stereoacuity in a time-limited task is increased, (3) distortions in perceived depth are reduced, and (4) viewer fatigue and discomfort are reduced. We discuss the implications of this work for vision research and the design and use of displays.

The zone of comfort: Predicting visual discomfort with stereo displays

Recent increased usage of stereo displays has been accompanied by public concern about potential adverse effects associated with prolonged viewing of stereo imagery. There are numerous potential sources of adverse effects, but we focused on how vergence-accommodation conflicts in stereo displays affect visual discomfort and fatigue. In one experiment, we examined the effect of viewing distance on discomfort and fatigue. We found that conflicts of a given dioptric value were slightly less comfortable at far than at near distance. In a second experiment, we examined the effect of the sign of the vergence-accommodation conflict on discomfort and fatigue. We found that negative conflicts (stereo content behind the screen) are less comfortable at far distances and that positive conflicts (content in front of screen) are less comfortable at near distances. In a third experiment, we measured phoria and the zone of clear single binocular vision, which are clinical measurements commonly associated with correcting refractive error. Those measurements predicted susceptibility to discomfort in the first two experiments. We discuss the relevance of these findings for a wide variety of situations including the viewing of mobile devices, desktop displays, television, and cinema.

The strong halfspace theorem for minimal surfaces

D. Hoffman and W.H. Meeks, III Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA In [6] Jorge and Xavier constructed examples of complete nonplanar minimal surfaces contained between two parallel planes in •3. Recently Rosenberg and Toubiana have found complete minimally immersed annuli that are proper in an open slab 1-12]. On the basis of these and other results, the question has arisen as to whether or not there could exist a properly immersed minimal surface in ~3 that was contained between two parallel planes. The answer is negative, an immediate consequence of the following theorem.

High-speed switchable lens enables the development of a volumetric stereoscopic display

Stereoscopic displays present different images to the two eyes and thereby create a compelling three-dimensional (3D) sensation. They are being developed for numerous applications including cinema, television, virtual prototyping, and medical imaging. However, stereoscopic displays cause perceptual distortions, performance decrements, and visual fatigue. These problems occur because some of the presented depth cues (i.e., perspective and binocular disparity) specify the intended 3D scene while focus cues (blur and accommodation) specify the fixed distance of the display itself. We have developed a stereoscopic display that circumvents these problems. It consists of a fast switchable lens synchronized to the display such that focus cues are nearly correct. The system has great potential for both basic vision research and display applications.

Embedded minimal surfaces of finite topology

In this paper we prove that any complete, embedded minimal surface M in R 3 with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface M with boundary punctured in a finite number of interior points and that M can be represented in terms of meromorphic data on its conformal completion M . In particular, we demonstrate that M is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior ofM .

Constant mean curvature surfaces in

The subject of this paper is properly embedded H-surfaces in Riemannian three manifolds of the form M 2 x R, where M 2 is a complete Riemannian surface. When M 2 = R 2 , we are in the classical domain of H-surfaces in R 3 . In general, we will make some assumptions about M 2 in order to prove stronger results, or to show the effects of curvature bounds in M 2 on the behavior of H-surfaces in M 2 x R.

Temporal presentation protocols in stereoscopic displays: Flicker visibility, perceived motion, and perceived depth.

Most stereoscopic displays rely on field-sequential presentation to present different images to the left and right eyes. With sequential presentation, images are delivered to each eye in alternation with dark intervals, and each eye receives its images in counter phase with the other eye. This type of presentation can exacerbate image artifacts including flicker, and the appearance of unsmooth motion. To address the flicker problem, some methods repeat images multiple times before updating to new ones. This greatly reduces flicker visibility, but makes motion appear less smooth. This paper describes an investigation of how different presentation methods affect the visibility of flicker, motion artifacts, and distortions in perceived depth. It begins with an examination of these methods in the spatio-temporal frequency domain. From this examination, it describes a series of predictions for how presentation rate, object speed, simultaneity of image delivery to the two eyes, and other properties ought to affect flicker, motion artifacts, and depth distortions, and reports a series of experiments that tested these predictions. The results confirmed essentially all of the predictions. The paper concludes with a summary and series of recommendations for the best approach to minimize these undesirable effects.

EMBEDDED MINIMAL-SURFACES WITH AN INFINITE NUMBER OF ENDS

We prove the existence of an infinite family of periodic properly embedded minimal surfaces with an infinite number of annular ends. 25 refs., 29 figs.

The computer-aided discovery of new embedded minimal surfaces

In 1984, Bill Meeks and I established the existence of an infinite family of complete embedded minimal surfaces in R 3. For each k > 0, there exists an example which is homeomorphic to a surface of genus k from which three points have been removed. Figure 30-1 is a picture of the genus-one example. The equations for this remarkable surface were established by Celsoe Costa in his thesis, but they were so complex that the underlying geometry was obscured. We used the computer to numerically approximate the surface and then construct an image of it. This gave us the clues to its essential properties which we then established mathematically. The programming expertise of James T. Hoffman, who is mainly responsible for the quality of the illustrations here, was a central ingredient in our research use of computer graphics. Without the use of a new programming environment, of which he is the principal creator, we would not have made the discoveries I will attempt to describe.

Computer graphics tools for the study of minimal surfaces

Recent research indicates machine computation and mathematical theory have proceeded hand in hand and have proved to be of great benefit to one another.