The normal of a fractal surface

Wayne O. Cochran, Robert R. Lewis, John C. Hart

Research output: Contribution to journalArticle

Abstract

We have discovered a class of fractal functions that are differentiable. Fractal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fractal interpolation function remains a fractal interpolation function, and this new fractal interpolation function is differentiable. Tensor products of pairs of these fractal functions form fractal surfaces with a well-defined tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirror.

Original languageEnglish (US)
Pages (from-to)209-218
Number of pages10
JournalVisual Computer
Volume17
Issue number4
DOIs
StatePublished - Jun 2001

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Fractals
Interpolation
Tensors
Mirrors

Keywords

  • Fractal
  • Fractal function
  • Fractal terrain
  • Iterated function system
  • Recurrent modeling

ASJC Scopus subject areas

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

Cite this

The normal of a fractal surface. / Cochran, Wayne O.; Lewis, Robert R.; Hart, John C.

In: Visual Computer, Vol. 17, No. 4, 06.2001, p. 209-218.

Research output: Contribution to journalArticle

Cochran, WO, Lewis, RR & Hart, JC 2001, 'The normal of a fractal surface', Visual Computer, vol. 17, no. 4, pp. 209-218. https://doi.org/10.1007/PL00013408
Cochran, Wayne O. ; Lewis, Robert R. ; Hart, John C. / The normal of a fractal surface. In: Visual Computer. 2001 ; Vol. 17, No. 4. pp. 209-218.
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