# Designing quad-dominant meshes with planar faces

Among the basic problems in freeform architecture which pertain to geometry processing is the decomposition of a freeform shape into a quad-dominant mesh whose faces are planar (or as planar as required by the intended manner of realizing that quad mesh in building construction). Such meshes are called PQ meshes. In this paper we take up the design of PQ meshes via conjugate curve networks and treat the following topics:

- The conjugacy relation between surface tangents, which is defined by the curvatures of the surface;
- an interpretation of the conjugacy relation in projective geometry terms which later allows us to encode a pair of conjugate directions by means of a single vector;
- fields of conjugate directions, and theoretical results on the elimination of singularities of such fields;
- a method based on level sets which converts direction fields into curve networks and subsequently into quad meshes or quad-dominant meshes.
- optimizing meshes generated in this way towards the PQ property.

BibTeX Entry:

@article{zadravec-2010-vf, title = "Designing Quad-dominant Meshes with Planar Faces", author = "Mirko Zadravec and Alexander Schiftner and Johannes Wallner", journal = "Computer Graphics Forum", volume = 29, number = 5, year = 2010, pages = "1671-1679", note = "{P}roc. Symp.\ Geometry Processing", url = "http://www.geometrie.tugraz.at/wallner/vfdesign.pdf" }

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