Higher-Order Spline Approximation for Isosurface Rendering

These are the first results from experimenting with higher-order spline approximation for isosurface rendering of trivariate functions sampled over rectilinear grids. The used methods treats the sampled values as control points of a trivariate uniform B-spline. Therefore, the method does not interpolate sample values, but creates Cⁿ approximations of the sampled function. The following images display several small test data sets, and results of ray tracing iso-surfaces of higher-order reconstructions of the sampled functions.

Box Data Set

This 8 x 8 x 8 data set represents a "wireframe cube." (Click on any of the images to see the original 800x600 rendering.)


Trilinear approximation	Triquadratic approximation	Tricubic approximation

Small Sphere Data Set

This 8 x 8 x 8 data set represents a sphere of radius 2. (Click on any of the images to see the original 800x600 rendering.)


Trilinear approximation	Triquadratic approximation	Tricubic approximation

Triquartic approximation

Large Sphere Data Set

This 32 x 32 x 32 data set represents a sphere of radius 12. (Click on any of the images to see the original 800x600 rendering.)


Trilinear approximation	Triquadratic approximation	Tricubic approximation

Triquartic approximation	Triquintic approximation	Trisexic - no, -septic, umm, -degree-six-approximation

Tri-degree-ten-approximation

Skull CT Data Set

This 68 x 256 x 256 data set is the ubiquitous skull CT. To emphasize the differences between different degrees of approximation, I used a reflective surface for the skull. (Click on any of the images to see the original 800x600 rendering.)


Trilinear approximation	Tricubic approximation	Tri-degree-six approximation

Tri-degree-ten approximation