Hanspeter Bieri

Fully Dynamic Constrained Delaunay Triangulations

We present algorithms for the efficient insertion and removal of constraints in Delaunay Triangulations. Constraints are considered to be points or any kind of polygonal lines. Degenerations such as edge overlapping, self-intersections or duplicated points are allowed and are automatically detected and fixed on line. As a result, a fully Dynamic Constrained Delaunay Triangulation is achieved, able to efficiently maintain a consistent triangulated representation of dynamic polygonal domains. Several applications in the fields of data visualization, reconstruction, geographic information systems and collision-free path planning are discussed.

Elementary set operations with d-dimensional polyhedra

When approx ima te l y 15 years ago we became i n t e r e s t e d in the computat i o n a l geometry o f po lyhedra , we soon r e a l i z e d tha t c e r t a i n bas ic not i o n s (e .g . face o f a po lyhedron) were not p r o p e r l y de f ined , and tha t no a p p r o p r i a t e theory was a v a i l a b l e . Most th ings t h e r e f o r e had to be done on a p u r e l y i n t u i t i v e bas i s , lead ing i n to d i f f i c u l t i e s e s p e c i a l l y in c e r t a i n s i n g u l a r cases ( c f . [ 0 9 ] ) . Never the less a la rge number o f p u b l i c a t i o n s in the f i e l d have s ince appeared, e .g . [ 08 ] , [ 10 ] , [13] to [18] and [21] to mention on l y some of the most s i g n i f i c a n t .

Algorithms for the euler characteristic and related additive functionals of digital objects

The Euler characteristic, the volume, the surface, and the mean width belong to the more important geometric properties of the polytopes in R d . They may be considered as values of certain additive functionals belonging to the family of the so-called quermassintegrals which are more generally defined for all bounded polyhedra in R d . A first recursive algorithm is presented to compute all quermassintegrals of digital objects in R d and a second one just for the Euler characteristic. The digital objects are assumed to be represented as binary arrays. The complexity of both algorithms is shown to be of the order of the number of elements of the respective binary arrays.

Computing the euler characteristic and related additive functionals of digital objects from their bintree representation

Abstract A recursive algorithm for the computation of the Euler characteristic X , the volume V, the surface S, the mean width M, and other properties (i.e., quermassintegrals) of digital pictures is presented. Full generality with respect to dimension is achieved by understanding digital pictures as (nondegenerate) polyhedra ⊆ Rd—that is why we call them “digital objects”—and the respective properties as additive functionals on sets of digital objects. In preparation, we discuss the bintree representation of digital objects which our algorithm will presuppose as the underlying data structure.

A recursive sweep-plane algorithm, determining all cells of a finite division of R d .

Abstract“Sweep-plane” algorithms seem to become more and more important for the solution of certain geometrical problems. We present an algorithm of this kind that enumerates the cells of all dimensions into whichRd is partitioned by a finite set of hyperplanesFi0. A plane sweeping through space (remaining parallel to itself) finds new cells each time it includes an intersection of someFi0 (normally a point). An analysis of the intersection-properties allows the construction of an algorithm recursive with respect to the dimension of space. Full generality has been one of our main objectives.ZusammenfassungDen Gleitebenen-(„sweep-plane”)-Verfahren kommt für die Lösung gewisser geometrischer Probleme wachsende Bedeutung zu. Wir präsentieren einen Algorithmus dieser Art für die Aufzählung der Zellen aller Dimensionen, in dieRd durch endlich viele HyperebenenFi0zerlegt wird. Eine parallel zu sich selber durch den Raum gleitende Ebene trifft immer dann neue Zellen, wenn sie einen Durchschnitt gewisserFi0(im allgemeinen einen Schnittpunkt) enthält. Aus der Betrachtung der Schnitteigenschaften läßt sich ein bezüglich der Raumdimension rekursiver Algorithmus ableiten. Besonderer Wert wird auf volle Allgemeinheit gelegt.

A sweep-plane algorithm for computing the Euler-characteristic of polyhedra represented in Boolean form

We present an algorithm EULER for the computation of the Euler-characteristic χ(P) of bounded polyhedraP⊂ℝd. It is first shown that χ(P) is uniquely determined by the local properties ofP at its vertices. It is therefore possible to compute χ(P) using a plane sweeping through ℝd, collecting the local information available at every vertex. There is a close relationship with an algorithm for the computation of the volumeV (P) published earlier (cf. [4]). The reason is that both ofV and χ are additive functionals.ZusammenfassungWir präsentieren einen Algorithmus EULER für die Berechnung der Eulerschen Charakteristik χ(P) beschränkter PolyederP⊂ℝd. Es wird gezeigt, daß χ(P) durch die lokalen Eigenschaften vonP in seinen Ecken eindeuting bestimmt ist. Deshalb ist es möglich, χ(P) mit Hilfe einer Ebene zu berechnen, die durch den Raum gleitet („sweep-plane”) und die in den Ecken verfügbare Information „sammelt”. Es besteht eine enge Beziehung zu einem früher publizierten Algorithmus für die Berechnung des VolumensV (P) (vgl. [4]). Der Grund liegt darin, daßV und χ beide additive Funktionale sind.

Wissensverarbeitung und Expertensysteme

Unter Expertensystemen versteht man Programmsysteme, mit denen versucht wird, das Sachwissen von qualifizierten Fachleuten (menschlichen Experten) und ihre Fahigkeit, Schlussfolgerungen zu ziehen, nachzubilden. Dies mit dem Ziel, fur Probleme eines bestimmten Fachgebiets Losungen zu finden. Expertensysteme sind in der Lage, explizit formuliertes Wissen (z.B. in Form von Fakten und Regeln) uber ein (moglichst gut abgrenzbares) Fachgebiet zu bearbeiten und aufgrund von Zusammenhangen daraus Schlusse zu ziehen. Im Rahmen des Losungsfindungsprozesses, der soweit wie moglich automatisiert wird, fuhren Expertensysteme mit dem Benutzer einen Dialog. In diesem Dialog erklart der Benutzer dem Expertensystem sein Problem, z.B. durch die Beantwortung von Fragen, die das System stellt. So verschafft sich das Expertensystem die fur die Losung benotigten Angaben. Ferner gibt das Expertensystem dem Benutzer auf Wunsch nahere Auskunft daruber, warum eine bestimmte Frage gestellt wurde, was die Frage bedeutet, welche Antworten moglich sind bzw. wie und warum das System gewisse Schlussfolgerungen gezogen hat. Eine wichtige Eigenschaft von Expertensystemen besteht darin, dass sie nicht bloss mit absolut sicherem Wissen arbeiten konnen. Sie besitzen i.a. die Fahigkeit, auch aus unsicherem Wissen gewisse Schlusse zu ziehen.

A Web3D toolbox for creating H-Anim compatible actors

The H-ANIM TOOLBOX is a Java applet containing a collection of easy-to-use tools to create 3D actors for Web applications. The generated actors have a scenegraph-based VRML/X3D structure with a skeleton-like joint-segment hierarchy complying with the H-Anim standard. A variety of actors is supported: from simple segmented models with predefined animations via organic bodies with seamless deformations up to personalized avatars with specific head geometry and face texture.

Collaboration on Scene Graph Based 3D Data

Professional 3D digital content creation tools, like Alias Maya or discreet 3ds max, offer only limited support for a team of artists to work on a 3D model collaboratively. We present a scene graph repository system that enables fine-grained collaboration on scenes built using standard 3D DCC tools by applying the concept of collaborative versions to a general attributed scene graph. Artists can work on the same scene in parallel without locking out each other. The artists’ changes to a scene are regularly merged to ensure that all artists can see each others progress and collaborate on current data. We introduce the concept of indirect changes and indirect conflicts to systematically inspect the effects that collaborative changes have on a scene. Inspecting indirect conflicts helps maintaining scene consistency by systematically looking for inconsistencies at the right places.

Digital restoration of medieval tapestries

Medieval Burgundian tapestries belong to the most valuable treasures of historical museums, in particular of the Bern Historical Museum. Many of them are well preserved, but much of their color is highly faded. Thus their todays appearance is very different from the original one. This paper deals with the digital restoration of the appearance of such tapestries. Two methods are developed and examined, one using the back side of the tapestry, the other one using color clustering. Our main criteria are a convincing approximation of the expected appearance and - due to the large size of many of the tapestries - a high degree of automation.