Visualization of Volume Data with Quadratic Super Splines

  • Authors:

  • Christian Rossl;Frank Zeilfelder;Gunther Nurnberger;Hans-Peter Seidel

  • Affiliations:

  • Max-Planck-Institut für Informatik, Saarbrücken, Germany;Universität Mannheim, Institut für Mathematik, Mannheim, Germany;Universität Mannheim, Institut für Mathematik, Mannheim, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
  • Year:
  • 2003

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Abstract

We develop a new approach to reconstruct non-discrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition 驴. The approximating splines are determined in a natural and completely symmetric way by averaging local data samples, such that appropriate smoothness conditions are automatically satisfied. On each tetra-hedron of 驴, the quasi-interpolating spline is a polynomial of total degree two which provides several advantages including efficient computation, evaluation and visualization of the model. We apply Bernstein-Bézier techniques well-known in CAGD to compute and evaluate the trivariate spline and its gradient. With this approach the volume data can be visualized efficiently e.g. with isosurface ray-casting. Along an arbitrary ray the splines are univariate, piecewise quadratics and thus the exact intersection for a prescribed isovalue can be easily determined in an analytic and exact way. Our results confirm the efficiency of the quasi-interpolating method and demonstrate high visual quality for rendered isosurfaces.