machine model with exact real arithmetic. Substituting floating point

arithmetic for the assumed real arithmetic may cause implementations to

fail. Although this is well known, there is no comprehensive documentation of

what can go wrong and why.

In this extended abstract, we study a simple

incremental algorithm for planar convex hulls and give examples which make

the algorithm fail in all possible ways.

We also show how to construct failure-examples

semi-systematically and discuss the geometry of the floating point

implementation of the orientation predicate. We hope that our work will be

useful for teaching computational geometry. The full

paper is available

at~\\url{www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExamples.ps}. It contains

further examples, more theory, and color pictures. We strongly recommend to read

the

full paper instead of this extended abstract.},\nBOOKTITLE = {Algorithms -- ESA 2004},\nDEBUG = {editor: Albers, Susanne; editor: Radzik, Thomasz},\nPAGES = {702--713},\nSERIES = {Lecture Notes in Computer Science},\nVOLUME = {3221},\nADDRESS = {Bergen, Norway},\n}\n'