kai hormann mail

via giuseppe buffi 13
6904 lugano
yes, that's me
phone +41.58.666.4327
fax +41.58.666.4536
e-mail [email protected]

publications publication 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 coordinates 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.
parameterization 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 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.
reconstruction 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.
remeshing 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.
volume 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.
polygon a little off my main research track, i got interested in computational geometry and discovered an efficient algorithm for clipping polygons, which was later extended to also handle degenerate intersections correctly. moreover, we analyzed various algorithms for deciding whether a point is in the interior of a polygon or exterior to it and developed a very efficient inside test that is apparently being used in matlab and R.

phd students phd qingjun chang · generalized barycentric coordinates · since 2021
andriamahenina ramanantoanina · barycentric rational curves and surfaces · since 2020
chiara fuda · numerical stability of barycentric rational interpolation · since 2020
emiliano cirillo · advances in barycentric rational interpolation of a function and its derivatives · 2019
elena volontè · subdivision schemes for curve design and image analysis · 2018
teseo schneider · theory and applications of bijective barycentric mappings · 2017
dmitry anisimov · analysis and new constructions of generalized barycentric coordinates in 2d · 2017
randolf schärfig · efficient multi-bounce lightmap creation using gpu forward mapping · 2016
tim winkler · processing mesh animations (from static to dynamic geometry and back) · 2011
federico ponchio · multiresolution structures for interactive visualization of very large 3d datasets · 2008

conferences, workshops, etc. conferences, etc. june 2022 · csf workshop on generalized barycentric coordinates in computer graphics and computational mechanics · co-organizer · ascona switzerland
june 2019 · siam conference on computational geometric design (gd19) · co-chair · vancouver canada
may 2019 · conference eurographics 2019 · doctoral consortium co-chair · genova italy
july 2017 · mini-symposium new trends in generalized barycentric coordinates · organizer · siam gd · pittsburgh usa
june 2015 · conference geometric modeling and processing (gmp 2015) · co-chair · lugano switzerland
may 2015 · conference eurographics 2015 · state of the art reports co-chair · zürich switzerland
october 2014 · symposium on solid and physical modeling (spm 2014) · programme co-chair · hong kong
june 2014 · conference geometric modeling and processing (gmp 2014) · co-chair · singapore
november 2013 · siam conference on geometric & physical modeling (gd/spm13) · programme co-chair · denver usa
september 2013 · 18th international workshop on vision, modeling and visualization (vmv 2013) · co-chair · lugano switzerland
september 2012 · international workshop new trends in subdivision and related applications · co-organizer · milano italy
july 2012 · nsf workshop on barycentric coordinates and finite/boundary element methods · co-organizer · new york usa
june 2012 · conference geometric modeling and processing (gmp 2012) · programme co-chair · huangshan china
february 2012 · international workshop new trends in applied geometry · co-organizer · villa cagnola italy
october 2011 · mini-symposium theory and applications of barycentric coordinates · organizer · siam gd/spm · orlando usa
june 2010 · mini-symposium non-linear subdivision schemes · organizer · curves & surfaces · avignon france
december 2008 · course mesh parameterization · co-organizer · siggraph asia · singapore
june/july 2008 · mathfilm festival · co-organizer · clausthal university of technology · clausthal germany
november 2007 · mini-symposium barycentric coordinates and transfinite interpolation · co-organizer · siam gd · san antonio usa
august 2007 · course mesh parameterization · co-organizer · siggraph · san diego usa
may 2005 · summer school subdivision schemes in geometric modelling · co-organizer · pontignano italy

journals journals computer aided geometric design · associate editor · since 2009
dolomites research notes on approximation · associate editor · since 2012
punjab university journal of mathematics · associate editor · since 2022
ieee transactions on visualization and computer graphics · associate editor · 2019—2023
computers & graphics · associate editor · 2015—2023
computer graphics forum · associate editor · 2010—2013

biography information january 2018—august 2018 · visiting professor · nanyang technological university singapore
september 2015—august 2017 · dean · università della svizzera italiana switzerland
august 2015 · marie born · richterswil switzerland
since september 2014 · full professor · università della svizzera italiana switzerland
may 2013 · peter born · lugano switzerland
september 2009—august 2014 · associate professor · università della svizzera italiana 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 to margherita · 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