  3D volume rendering is widely used to reveal insightful intrinsic patterns of
volumetric datasets across many domains. However, the complex structures and
varying scales of volumetric data can make efficiently generating high-quality
volume rendering results a challenging task. Multivariate functional
approximation (MFA) is a new data model that addresses some of the critical
challenges: high-order evaluation of both value and derivative anywhere in the
spatial domain, compact representation for large-scale volumetric data, and
uniform representation of both structured and unstructured data. In this paper,
we present MFA-DVR, the first direct volume rendering pipeline utilizing the
MFA model, for both structured and unstructured volumetric datasets. We
demonstrate improved rendering quality using MFA-DVR on both synthetic and real
datasets through a comparative study. We show that MFA-DVR not only generates
more faithful volume rendering than using local filters but also performs
faster on high-order interpolations on structured and unstructured datasets.
MFA-DVR is implemented in the existing volume rendering pipeline of the
Visualization Toolkit (VTK) to be accessible by the scientific visualization
community.
