kai hormann		faculty of informatics university of lugano via giuseppe buffi 13 6904 lugano switzerland
		+41.58.666.4327
		+41.58.666.4536
		kai.hormann@usi.ch
publications		abstracts, bibtex entries, and pdf files of my publications can be found in chronological order as well as sorted by topic or by type of publication. to help referencing my publications, a complete list of bibtex entries is available.
research interests		barycentric coordinates are a common tool in graphics and other fields to express a point inside a triangle as a convex combination of the triangle corners. this concept can be extended in various ways to general convex polygons. one such extension are floater's mean value coordinates that even work for arbitrary polygons. this makes them an ideal tool for interpolation and particular applications in graphics are image warping and rendering of quadrilateral primitives. adapting the ideas to the univariate setting further leads to interesting rational interpolation schemes. for more details, visit the webpage of our minisymposium at the 10th siam conference on geometric design & computing.
		one of my main interests over the last few years has been in parameterization of triangle meshes and a good summary can be found in our survey. parameterization methods for triangle meshes with a simple, disc-like topology can be devided in two groups. linear methods are well understood and very fast but it is still unclear how the boundary should be treated. non-linear methods are able to solve this problem but remain a slow alternative even if hierarchical solvers are used. triangle meshes with arbitrary topology can be parameterized by segmenting them into disc-like patches, or by using a polycube as parameter domain. the latter option yields an ideal tool for texture mapping. for more details, visit the webpage of our courses at siggraph asia 2008 and siggraph 2007.
		subdivision is a great tool in graphics to get smooth curves and surfaces out of initial control polygons and control meshes. one of the most famous schemes for curves is the interpolating 4-point scheme that is based on local cubic interpolants. the idea of local cubic sampling can also be used to create a dual 4-point scheme, which is only approximating but has higher smoothness. remarkably, both schemes turn out to be the first two members of a whole family of schemes, all with cubic precision. i have also studied the structure of regular triangle meshes and developed a neat algorithm for detecting this regularity in a given mesh.
		an important application of parameterizations is found in reverse engineering, where they are an essential ingredient for fitting free form surfaces to 3d data points. a common pre-processing step is to first triangulate the input points and then approximate the triangulation. tensor product b-splines are still the most common free form surfaces in cad-based industrial design and the use of hierarchical surfaces improves performance considerably. it is even possible to reconstruct objects with arbitrary topology with b-spline patches. i have also studied other kinds of surface reconstruction, for example reconstructing terrain from contour lines and energy landscapes for shape-memory alloys.
		another application of parameterizations is remeshing. given a triangle mesh with arbitrary connectivity the task is to approximate it with a regular mesh. the most important regular meshes are triangle meshes with subdivision connectivity, but regular quadrilateral meshes are also of interest. last but not least i worked on the problem of optimizing triangle meshes using discrete curvature analysis.
		i have also worked with volumetric data and the extraction of iso-surfaces from ct-scans. in a cooperation with the archaeological institute, we were able to reconstruct the surfaces of historical artefacts with the aim of exhibiting them in a virtual museum one day.
		a little off my main research track, i got interested in computational geometry. i discovered an efficient algorithm for clipping polygons and analyzed various inside tests which decide whether a point is in the interior or the exterior of a polygon.
phd students		federico ponchio · multiresolution structures for interactive visualization of very large 3d datasets
		tim winkler · interactive 3d reconstruction from depth cameras
		markus melato · surface reconstruction using neural networks
		randolf schärfig · gpu algorithms for interactive global illumination
teaching		fall 2009 · calculus · university of lugano germany summer 2009 · geometric modelling · clausthal university of technology germany winter 2008 · course on mesh parameterization · siggraph asia 2008 singapore winter 2008 · computer graphics · clausthal university of technology germany winter 2008 · 3d game programming · clausthal university of technology germany summer 2008 · geometric modelling · clausthal university of technology germany winter 2007 · scientific visualization · freie universität berlin germany summer 2007 · course on mesh parameterization · siggraph 2007 san diego usa summer 2007 · geometry processing · clausthal university of technology germany winter 2006 · geometric modelling · clausthal university of technology germany summer 2006 · computer graphics 2 · clausthal university of technology germany winter 2005 · computer graphics 1 · clausthal university of technology germany summer 2005 · summer school on subdivision schemes in geometric modelling · pontignano italy summer 2005 · applied computer science 2 · clausthal university of technology germany winter 2004 · applied computer science 1 · clausthal university of technology germany spring 2003 · topics in geometric modelling · caltech usa winter 2001 · geometric modelling · university of erlangen germany
biography		since september 2009 · associate professor · university of lugano switzerland november 2007—march 2008 · visiting bms professor · freie universität berlin germany september 2004—august 2009 · assistant professor · clausthal university of technology germany september 2004 · married · castello di rossena italy june 2003—august 2004 · postdoctoral dfg research fellow · cnr italy june 2002—may 2003 · postdoctoral dfg research fellow · caltech usa february 2002 · phd in computer science · university of erlangen germany september 2000—february 2001 · mingle research fellow · sintef norway august 2000 · research visitor · tel aviv university israel july 1998—may 2002 · phd student · university of erlangen germany july 1997 · diploma in mathematics · university of erlangen germany november 1992—july 1997 · student · university of erlangen germany may 1992 · abitur · leibniz-gymnasium bad schwartau germany september 1974 · born · lübeck germany