Piecewise Linear Approximation of Isovalued Surfaces

  • Cornelia Zahlten
Part of the Focus on Computer Graphics book series (FOCUS COMPUTER)


Continuation methods provide a frame for the efficient approximation of isovalued surfaces in 3D space. We discuss two related algorithms in this field. The first one is based on subdividing space into cubes, while the second one uses a triangulation approach. For the latter, an efficient implementation is presented. The algorithms determine all cubes (or simplices) intersecting the surface and then generate an oriented polygonal approximation. Comparison shows that the cube approach takes less time and memory. The resulting surfaces have different properties concerning symmetry and connectedness. For demonstration and comparison we use several fractal and smooth surfaces. These surfaces are implicitly defined by a function, however it is also possible to apply both methods to 3D volume data.


Continuation Method Piecewise Linear Approximation Transverse Face Common Face Polygonal Approximation 
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© EUROGRAPHICS The European Association for Computer Graphics 1992

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  • Cornelia Zahlten

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