Kees van Overveld

Is there an ethics of algorithms

We argue that some algorithms are value-laden, and that two or more persons who accept different value-judgments may have a rational reason to design such algorithms differently. We exemplify our claim by discussing a set of algorithms used in medical image analysis: In these algorithms it is often necessary to set certain thresholds for whether e.g. a cell should count as diseased or not, and the chosen threshold will partly depend on the software designer’s preference between avoiding false positives and false negatives. This preference ultimately depends on a number of value-judgments. In the last section of the paper we discuss some general principles for dealing with ethical issues in algorithm-design.

Rendering cracks in Batik

We present an algorithm for simulating the cracks found in Batik wax painting and dyeing technique used to make images on cloth. The algorithm produces cracks similar to those found in batik due to the wax cracking in the dyeing process. The method is unlike earlier simulation techniques used in computer graphics, in that it is based on the Distance Transform algorithm rather than on a physically based simulation such as using spring mass meshes or finite element methods. Such methods can be difficult to implement and computationally costly due to the large numbers of equations that need to be solved. In contrast, our method is simple to implement and takes only a few seconds to produce convincing patterns that capture many of the characteristics of the crack patterns found in real Batik cloth.

Shrinkwrap: An efficient adaptive algorithm for triangulating an iso-surface

An algorithm is presented which generates a triangular mesh to approximate an iso-surface. It starts with a triangulation of a sphere and next applies a series of deformations to this triangulation to transform it into the required surface. These deformations leave the topology invariant, so the final iso-surface should be homeomorphic with a sphere. The algorithm is adaptive in the sense that the lengths of the sides of the triangles in the mesh vary with the local curvature of the underlying surface. A quantitative analysis of the accuracy of the algorithm is given along with an empirical comparison with earlier algorithms.

POLYGONIZATION OF IMPLICIT SURFACES WITH CONSTRUCTIVE SOLID GEOMETRY

A polygonization algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference operators. The geometric primitives that form the operands are soft objects bounded by the iso-surfaces resulting from suitable potential fields. These potential fields are parameterized by configurations of so called skeletal elements. The resulting system, unlike most CSG systems, combines blended and unblended primitives. The polygonization algorithm produces a mesh of triangles to facilitate fast viewing and rendering.

Combining CSG modeling with soft blending using Lipschitz-based implicit surfaces

In this paper a general method is given for combining CSG modeling with soft blending using implicit surfaces. A class of various blending functions sharing some desirable properties like differentiability and intuitive blend control are given. The functions defining the CSG objects satisfy the Lipschitz condition that gives the possibility of fast root finding but can also prove useful in the field of collision detection and adaptive triangulation.

All You Need Is Force: a constraint-based approach for rigid body dynamics in computer animation

Over the last few years, simulating the motion of linked articulated rigid bodies based on classical rigid body dynamics has become a valuable paradigm for making realistic 3-D computer animations. Although several operational methods for dynamical simulation have been developed, in general these are both conceptually and computationally complex. To inspire further research in devising alternative and possibly simpler schemes for dealing with articulated rigid bodies, this paper discusses an alternative approach to rigid body dynamics which is based on (conceptually much simpler) point mechanics. Geometric constraints, e.g. the requirement that the distance between two points should be conserved, take the form of additional algebraic equations. We propose to solve these algebraic constraints in concert with the numerical integration. First, we give a general formulation of such a scheme. Next, we describe a preliminar implementation on the basis of a very naive numerical solver for ODE’s (ordinary differential equations).

Subdivision Surfaces for Fast Approximate Implicit Polygonization

We propose a fast method of generating an approximate polygonal mesh from an implicit surface. Current workstations are still not capable of producing polygon meshes fast enough for the interactive modelling of complex implicit models. We propose a hybrid method that combines current implicit polygonization techniques with the faster sub-division surface technique applied as a post-process to smooth the implicit mesh. In an interactive enviroment the smooth mesh points can be migrated to the implicit surface, in idle moments when the user is not interacting with the model. The technique can be further enhanced by providing tools for the user to indicate areas of interest that can be preferentially smoothed.

Chain codes and their application in curve design

A representation for discrete curves based on the notion of chain codes is defined; the parameterization of these curves is also part of the representation, which renders these curves well-suited, e.g., for specifying motion paths in computer animation. Algorithms are defined for both generation and manipulation of these curves.

Applications of the method of invariants in computer graphics

In order to evoke a discussion about possible future research themes for the Eindhoven Department of Mathematics and Computing Science, a small overview about the scientific background of the group is presented. We sketch the global framework of the method of invariants in deriving algorithms, and we apply this method to two well-known basic algorithms in computer graphics.

Quality Criteria for Mathematical Models in Relation to Models’ Purposes: Their Usefulness in Engineering Education

A taxonomy of eight quality criteria for mathematical models was developed for the common basic modelling course in the innovated BSc curriculum of Eindhoven University of Technology. First year engineering students of all disciplines reflected on their group modelling projects, indicating how their models could be improved, using the criteria. The students were also asked to indicate the purpose(s) of their models from a list of 16 purposes. This study explores the usefulness of the purposes and criteria, defined as relevance combined with understandability. Optimisation proved to be the most relevant purpose, followed by analysis, prediction (what), and verification.Specialisation, genericity, scalability, distinctiveness, and convincingness criteria proved useful; but audience, impact, and surprise did not.