Implicit surfaces


Implicit surfaces provide an interesting alternative to parametric patches. Many operations (e.g. inside-outside testing, Boolean operations, ray-tracing, connecting to regular implicit surfaces) are more convenient using them. In general topology surface modeling, providing an implicit equation may be much simpler than calculating a parametric representation.

However, implicit forms may easily produce unexpected shape artifacts, so properly controlling these surfaces is an important research goal.


The I-patch is a classical implicit construction, built from side interpolant components. (In this sense it is somewhat similar to transfinite parametric patches.)

Á. Sipos, T. Várady, P. Salvi, M. Vaitkus, Multi-sided implicit surfacing with I-patches. Computers & Graphics, Vol. 90, pp. 29-42, 2020. DOIBibTeX

  • The basic formulation of I-patches, revisited.
  • New interpretation, orienting ribbons, shape parameters, handling special cases.
  • Applications: setback vertex blending and patchworks defined by control polyhedra.
  • Benefits, limitations, and comparisons with other schemes discussed.

Á. Sipos, T. Várady, P. Salvi, Implicit representations for multi-sided surface patches. Proceedings of the Tenth Hungarian Conference on Computer Graphics and Geometry, pp. 1-8, 2022. Full paperBibTeX

  • Conference version

Á. Sipos, T. Várady, P. Salvi, Approximating triangular meshes by implicit, multi-sided surfaces. Computer-Aided Design and Applications, Vol. 19(5), pp. 1015-1028, 2022. DOIFull paperBibTeX

  • A method for fitting I-patches on mesh data.
  • An equation of I-patches with a better distance approximation
  • Approximation with I-patches
  • Refinement of patch structure

Á. Sipos, T. Várady, P. Salvi, Approximating triangular meshes by implicit, multi-sided surfaces. Proceedings of the CAD Conference, pp. 236-240, 2021. DOIFull paperBibTeX

  • Conference version of the above


Á. Sipos, Corner-based implicit surfaces. Proceedings of the 13th Conference of PhD Students in Computer Science, pp. 12-16, 2022. Full paperBibTeX

Implicit tessellation

Our method for creating smooth preview meshes from implicit surfaces is presented in the following paper.

Á. Sipos, P. Salvi, Creating good quality meshes from smooth implicit surfaces. Proceedings of the Workshop on the Advances of Information Technology, pp. 47-51, 2021. Full paperBibTeX

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