The floating column algorithm for shaded, parallel display of function surfaces without patches

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The floating column algorithm is a new method for the shaded rendering of function surfaces. Derived from the monochromatic floating horizon algorithm, it uses the partial derivatives of the function to compute surface normals, thus enabling intensity or normal-interpolation shading. Current rendering methods require tiling the surface with patches, so higher resolution patching is required for zoom-in views or interactive modification or time-varying surfaces. The new algorithm requires no patching and uses only constant space, so it can be implemented on graphics cards and hand-held devices. Each pixel-column is displayed independently of the others, and this "independent column mode" makes the algorithm inherently parallel in image-space, so it is suitable for multiprocessor workstations and clusters and it is scalable in the resolution size. Furthermore, the sampling frequency of the surface can be controlled locally, matching local surface features, distance, or artifact elimination requirements. Space-efficient supersampling for antialiasing is also possible. The new algorithm, which allows orthogonal and perspective projections, produces pixel-wide strips which can be displayed in software or hardware. Various extensions are described, including shadows and texture mapping. These properties, together with the algorithm's parallelism, make it potentially useful for the real-time display of functionally defined textured terrains and the animated display of time-varying surfaces.

Original languageEnglish
Pages (from-to)76-91
Number of pages16
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
StatePublished - Jan 2002

Bibliographical note

Funding Information:
The author is indebted to the anonymous reviewers whose detailed comments have led to an improved presentation of the paper. The runtime experiments were performed on equipment funded by grant no. 19050101311 of the Israel Ministry of Science.


  • Floating column
  • Floating horizon
  • Function display
  • Functionally defined terrains
  • Graphics hardware
  • Height-fields
  • Local supersampling
  • Mathematical software packages
  • Parallel rendering

ASJC Scopus subject areas

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


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