Hyperbolic geometry is a useful visualization technique for displaying a large quantity of two dimensional data simultaneously. What distinguishes this technique is that one particular area can be displayed in full detail with all other areas displayed in lesser detail. In this way, the entire scene is still on the screen so that the entire set of relationships, as well as emergency indicators, can always be seen. But, because the hyperbolic transformation equation is non-linear, it cannot be placed in the standard graphics hardware 4x4 homogeneous matrix. Thus, using the hyperbolic transformation prevents full use of the graphics pipeline hardware, and drastically reduces interactive speed. This paper discusses a way to recoup this display performance by encoding the hyperbolic transform into an OpenGL vertex shader that resides on the graphics GPU hardware. In this way, the hyperbolic transform can still be used interactively, even for very complex 2D scenes.

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