We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate B-spline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric analysis [Hughes T.J. 2005]. Input data consists of both a closed triangle mesh representing the exterior geometric shape of the object and interior triangle meshes that can represent material attributes or other interior features. The trivariate B-spline geometric and attribute representations are generated from the resulting parameterization, creating trivariate B-spline material property representations over the same parameterization in a way that is related to [Martin and Cohen 2001] but is suitable for application to a much larger family of shapes and attributes. The technique constructs a B-spline representation with guaranteed quality of approximation to the original data. Then we focus attention on a model of simulation interest, a femur, consisting of hard outer cortical bone and inner trabecular bone. The femur is a reasonably complex object to model with a single trivariate B-spline since the shape overhangs make it impossible to model by sweeping planar slices. The representation is used in an elastostatic isogeometric analysis, demonstrating its ability to suitably represent objects for isogeometric analysis.

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a) 6.1 FPS (b) 3.8 FPS (c) 3.8 FPS (d) 3.8 FPS Figure 1: The backpack data set with 512 × 512 × 373 voxels rendered a) with Phong shading only; and b) with depth of field with α = 30.9 • focused on the spray can in the foreground, c) on the wires behind it and d) on the boxes with the other spray can in the background. In each image 1469 slices were taken and gradients were estimated on the fly. AbstractIn this paper, a method for interactive direct volume rendering is proposed for computing depth of field effects, which previously were shown to aid observers in depth and size perception of synthetically generated images. The presented technique extends those benefits to volume rendering visualizations of 3D scalar fields from CT/MRI scanners or numerical simulations. It is based on incremental filtering and as such does not depend on any precomputation, thus allowing interactive explorations of volumetric data sets via on-the-fly editing of the shading model parameters or (multi-dimensional) transfer functions.

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