We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multi-field, multifaceted, and multi-attribute) volume data. First, we perform local linear fitting in the spatial neighborhood of each volume sample using principal component analysis, accelerated by hierarchical spatial data structures. This local linear information is then visualized as continuous indexed points in parallel coordinates: a density representation of indexed points in a continuous domain. With our new method, multivariate volume data can be analyzed using eigenvector information from local spatial embeddings. We utilize both 1-flat and 2-flat indexed points, allowing us to identify correlations between two variables and even three variables, respectively. An interactive occlusion shading model facilitates good spatial perception of the volume rendering of volumetric correlation characteristics. Interactive exploration is supported by specifically designed multivariate transfer function widgets working in the image plane of parallel coordinates. We show that our generic technique works for multi-attribute datasets. The effectiveness and usefulness of our new method is demonstrated through a case study, an expert user study, and domain expert feedback.

We present angle-uniform parallel coordinates,a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallelcoordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structuresmay be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines becomesmooth curves and a symmetric representation of data correlations is achieved. We further propose a combinedsubsampling and density visualization approach to reduce visual clutter caused by overdrawing. Ourmethod enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.