The paper describes a camera control interface for the exploration of 3D virtual space implemented by using a 2D input device, a joystick. The interface uses a helicopter maneuver metaphor: the viewpoint of the virtual camera is controlled as if the user sits in a helicopter and controls its motion. To control the helicopter by a 2D input device, the 6D space of the helicopter motion is decomposed into six 2D subspaces. The 2D subspaces are visualized by means of the helicopter model and some auxiliary means, e.g. plane meshes and circles, to suggest the kind of motion allowed in each subspace. The visualized subspaces are used as camera control widgets controlled by the 2D input device. The six widgets are arranged so that the transition from one widget to another may be performed by one movement of the input device. This interface provides a simple and consistent kinesthetic correspondence between the movement of the joystick and the motion of the helicopter i.e. the virtual camera. We have conducted an evaluation of our camera control interface through a questionnaire study. Though it indicates that users of different levels find our interface easier to use compared to other interfaces, we need more rigorous evaluation studies to prove it. The main claim of the paper is that the proposed interface has a cleaner and more logical design obtained by strictly following a good design principle, i.e. systematic decomposition and intuitive visual clues.

When volume data is visualized by the ray casting method, the color value of each pixel in the image is obtained by composing the color contributions of the sample points that lie on the ray cast from the pixel point. In most ray tracing methods, including M. Levoy's (1988; 1990) classical method, the color composition is formulated as a summation of the color contributions of the discrete sample points. However the more precise color composition is formulated as differential equations over the color contributions of the continuous sample points. The discrete formulation is used, because analytical solutions to the continuous formulation are hard to find. However we have discovered a semi-analytical solution to the continuous formulation of a typical ray tracing of volume data. We have applied both Levoy's method and ours to the same set of data, and compared the visual quality of both results. The comparison shows that our method produces a more fine grained visualization of volume data.

Abstract Graphs with weights and delays associated with their edges and/or vertices are often used to model communication and signal flow networks. Network performance can be improved by upgrading the network vertices. Such an upgrade reduces the edge/vertex delays and comes at a cost. We study different formulations of this network performance improvement problem and show that these are NP‐hard. We then consider one of the formulations and develop polynomial time algorithms for some special cases and pseudopolynomial time algorithms for others.

Examines the vertex deletion problem for weighted directed acyclic graphs (WDAGs). The objective is to delete the fewest number of vertices so that the resulting WDAG has no path of length >/spl delta/. Several simplified versions of this problem are shown to be NP-hard. However, the problem is solved in linear time when the WDAG is a rooted tree, and in quadratic time when the WDAG is a series-parallel graph.>

We develop polynomial time algorithms to optimally fold stacked bit sliced architectures to minimize area subject to height or width constraints. These algorithms may also be applied to folding problems that arise in standard cell and sea-of-gates designs.>