Each voxel is specified by a set of graphics primitives that we call display scalars, e.g., a pixel's location and size in a volume, its color, and its place in an animation sequence. Of course, designers of scientific displays already assume that primitive variables are mapped to graphics primitives. The remarkable thing is that we do not have to take this way of designing displays as an assumption, but that it is a consequence of the more fundamental expressiveness conditions. We are developing and implementing a system called VIS-AD that allows scientists to experiment with algorithms, steer their computations, and visualize the data objects they create in their programs. Just as data flow systems define a user interface for controlling data display based on abstraction of the rendering pipeline, the VIS-AD system defines a user interface for controlling data display based on the abstraction of mappings from scalars to display scalars.
Lattices provide a rigorous foundation for visualization.