We present Adaptive Multilinear Meshes (AMM), a new framework that
significantly reduces the memory footprint compared to existing data
structures. AMM uses a hierarchy of cuboidal cells to create continuous,
piecewise multilinear representation of uniformly sampled data. Furthermore,
AMM can selectively relax or enforce constraints on conformity, continuity, and
coverage, creating a highly adaptive and flexible representation to support a
wide range of use cases. AMM supports incremental updates in both spatial
resolution and numerical precision establishing the first practical data
structure that can seamlessly explore the tradeoff between resolution and
precision. We use tensor products of linear B-spline wavelets to create an
adaptive representation and illustrate the advantages of our framework. AMM
provides a simple interface for evaluating the function defined on the adaptive
mesh, efficiently traversing the mesh, and manipulating the mesh, including
incremental, partial updates. Our framework is easy to adopt for standard
visualization and analysis tasks. As an example, we provide a VTK interface,
through efficient on-demand conversion, which can be used directly by
corresponding tools, such as VisIt, disseminating the advantages of faster
processing and a smaller memory footprint to a wider audience. We demonstrate
the advantages of our approach for simplifying scalar-valued data for commonly
used visualization and analysis tasks using incremental construction, according
to mixed resolution and precision data streams