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Visualization of volume data with quadratic super splines

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45303

Rössl,  Christian
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45792

Zeilfelder,  Frank
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Volltexte (frei zugänglich)

MPI-I-2004-4-006.pdf
(beliebiger Volltext), 2MB

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Zitation

Rössl, C., Zeilfelder, F., Nürnberger, G., & Seidel, H.-P.(2003). Visualization of volume data with quadratic super splines (MPI-I-2004-4-006). Saarbrücken: Max-Planck-Institut für Informatik. Retrieved from http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2004-4-006.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0014-6AE8-D
Zusammenfassung
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 $\Delta$. 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 tetrahedron of $\Delta$ , the spline is a polynomial of total degree two which provides several advantages including the e cient computation, evaluation and visualization of the model. We apply Bernstein-B{\´e}zier techniques wellknown in Computer Aided Geometric Design to compute and evaluate the trivariate spline and its gradient. With this approach the volume data can be visualized e ciently 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 e ciency of the method and demonstrate a high visual quality for rendered isosurfaces.