Images for: Representation and Extraction of Volumetric Attributes Using Trivariate Splines: A Mathematical Framework.

William Martin and Elaine Cohen

The boundary of trivariate NURBS volume is shown in red. A scalar field has been specified over the volume, and two isosurfaces for a particular isovalue are visualized by showing spheres which bound the surfaces to a tolerance.

The same trivariate volume as above has been sliced with a plane. Spheres which bound the plane to a particular tolerance are visualized, each sphere colored according to the average isovalue it contains.

A disk with radially varying attribute data has been visualized using direct volume rendering. Two isosurfaces have been picked out approximately by specifying transfer functions which peak at those isovalues. From left to right, the red transfer function has been made to approach zero more quickly, thereby picking out the associated isosurface more exactly.

Using the same geometry and attribute data as the images above, the picture on the right has been rendered by tracing the path light would take if the attribute data specified an index of refraction. The image on the left is traced using a constant index of refraction. Both images have the same physical geometry with a flat top face. However, the curved path which light takes in the right image gives the impression that the top face is curved.