Test Scenario

The windowing functions described theoretically in the previous section were tested in practice with two different data sets which were reconstructed with always the same reconstruction scheme so that the only difference between the pictures is the windowing function used for gradient reconstruction.

The first data set was simply a distance function (i.e., its iso-surfaces are spheres), sampled on a 64 by 64 by 64 grid. It is depicted with analytically calculated gradients in Fig. 3 on the top left.

The second data set was a, by now quite standard, test signal proposed by Marschner and Lobb [9], it is depicted with analytically calculated gradients in Fig. 4 on the top left. This signal was sampled on a 40 by 40 by 40 grid in the range -1 < x,y,z < 1 (however, the actual part depicted is zoomed in to the middle portion), it is a little bit more complex than a sphere and should therefore provide more clues of the differences between and the applicability of the various windowed cosc functions.

Figure 4: Marschner Lobb function with analytically calculated gradients on the left, central differences used for gradient reconstruction in the middle and Catmull-Rom derivative on the right.

Additionally to the windowed cosc functions, the central differences operator and the derivative of a piece-wise cubic spline, known as Catmull-Rom spline [1], were used for comparison purposes.