# Implicit surfaces

[edit]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.

## I-patch

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. DOI • BibTeX

*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 paper • BibTeX

*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.
DOI • Full paper • BibTeX

*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.
DOI • Full paper • BibTeX

*Conference version of the above*

## Corner-I-patch

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

## 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 paper • BibTeX