Abstract-This paper introduces a novel technique for smooth and efficient zooming and panning based on dynamical systems in hyperbolic space. Unlike the technique of van Wijk and Nuij, the animations produced by our technique are smooth at the endpoints and when interrupted by a change of target. To analyze the results of our technique, we introduce world/screen diagrams, a novel technique for visualizing zooming and panning animations.
IZooming and panning is an interaction technique that solves the problem of fitting too-much data on a too-small screen. Zooming refers to the manipulation of scale-zooming in shows less in more detail, and zooming out shows more in less detail. Panning refers to the manipulation of the viewing window-panning left or right slides more information into view from one side of the screen, while information on the other side slides out of view.In many user interfaces, the user zooms and pans manually by pinching a touch screen, rolling a scroll wheel, or by dragging the mouse. This paper does not focus on these problems-instead, this paper introduces techniques for automatically zooming and panning in response to user interactions.For example, consider a home search application that shows homes matching the user's query in two ways: in a list and on a map. A user who hovers the mouse over a home in the list will likely want to also see the home's location on the map, and if this home is currently off-screen, this will require zooming and panning. If the user interface performs this navigation abruptly, jumping instantaneously from the old view to the new view, then the user loses all context about the spatial relationship between the current house and the previous house. By smoothly zooming and panning from one view to the next, the user gains a clearer understanding of the locations of the houses.It can also be useful to combine manual zooming and automatic zooming. For example, imagine a stock price time series visualization in which the user manually zooms and pans on the time axis. As the user adjusts the time axis view, previously off-screen data will become visible, and some of this data may be outside the current range of the price axis. To prevent the user from having to manually readjust the price axis after zooming and panning on the time axis, it would be helpful for the interface to automatically zoom and pan on the price axis in order to continually accommodate the current range of prices.The current state-of-the art technique for automatic zooming and panning is the smooth and efficient technique introduced by van Wijk and Nuij [18], which seeks to find a navigation animation that satisfies two properties:1. The animation is smooth in the second order, i.e. both position and velocity are continuous.2. The animation is efficient, i.e. it minimizes perceptual cost. For example, panning directly from a zoomed-in view of Seattle to a zoomed-in view of London is perceptually costly because the animation will require a long duration in order to avoid excessive motion blurring....