High-quality rendering of quartic spline surfaces on the GPU

Gerd Reis, Frank Zeilfelder, Martin Hering-Bertram, Gerald Farin, Hans Hagen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We present a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-Bézier techniques) for Phong illumination on the GPU. Inaccurate shading and artifacts appearing for triangular tesselated surfaces are completely avoided. Level of detail is automatic since all computations are done on a per fragment basis. We compare three different (quasi-) interpolating schemes for uniformly sampled gridded data, which differ in the smoothness and the approximation properties of the splines. The results show that our hardware-based renderer leads to visualizations (including texturing, multiple light sources, environment mapping, and so forth) of highest quality.

Original languageEnglish (US)
Article number4509429
Pages (from-to)1126-1139
Number of pages14
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number5
StatePublished - Sep 2008


  • GPU-based rendering
  • Graph surfaces
  • Ray tracing
  • Spline approximation

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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