Curvature-Based Transfer Functions
for Direct Volume Rendering

The green area in vicinity of the origin corresponds to planar points. The blue-yellow transition area specifies the curvature change inside parabolic structures and is intended to reflect the diameter change within solid cylinders presented in data sets. The red area corresponds to elliptic points.

Demonstration of the curvature change inside solid cylinders of a 38 x 38 x 38 cube. Note, that the diameter of cylinders in the data set is less then six voxels. In order to attract the user's attention, the high values of first principal curvature (i.e. small diameters) has been mapped to bright yellow. The smooth transition to blue towards lower values of first principal curvature corresponds to diameter increase. As the cylinder axes do not define a surface, they have been excluded from curvature computation and therefore do not affect the final image. The red parts correspond to elliptic points.

The transfer function has been specified in the same way as for prevoiuss figure, with more emphasis on smaller cylinders (depicted in yellow). A staircase effect in diagonal directions can be noticed. The resolution of the data set is 59 x 59 x 59 voxels.

A 38 x 38 x 38 data set as that of previous figure with attached faces. The transfer function maps the corresponding (i.e. zero) curvatures to transparent green. The joint of faces with cylinders was not smooth and exhibits therefore high curvature depicted in yellow. Similarly as before, the red areas correspond to elliptical points.

The transfer function has been set to distinguish among elliptic (red), parabolic (green) and hyperbolic (blue) points of a 59 x 59 x 20 torus. The green points on the outer side are identified as planar due to a volume crop.

Visualization of low (green) and high curvature (red) points of a 50 x 52 x 16 thickened Möbius strip.