UvA GA Group Talks

On this page you find a list of talks in approximate chronological order (latest first).

Talk Titles:

Talk Details:

Exploring the conformal model of 3D Euclidean Geometry pdf

Leo Dorst.
ITM2003,
Kyoto
November 2003

Estimating Rigid Body Motions of Point Clouds pdf, ps.gz

Leo Dorst.
April 1, 2003
The well known Procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals. In this paper we perform a complete error analysis of this method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion. These results are much more specific than the error bounds which have been established in numerical analysis. We provide an intuitive understanding of the outcome to facilitate direct use in applications.

Geometric Algebra: the Framework for Geometric Computations. GAViewer, pdf

Daniel Fontijne, Leo Dorst.
Presented at Game Developers Conference, March 2003
This lecture was presented at Game Developers Conference 2003 and adapted for self study. It explains basic 3D GA, the homogeneous model in GA, Pluecker coordinates, and gives some details on implementation and performance of GA implementations.

An Algebraic Approach to Programming Geometry pdf, ps.gz

Leo Dorst.
February 2003
Philips Natlab, Eindhoven
ASCI course, Utrecht
CWI, Amsterdam

Geometric Algebra: the framework for geometric computations pdf, ps.gz

Leo Dorst.
GIVE, Utrecht, April 17, 2002

Processing Orientation Measurements pdf, ps.gz

Leo Dorst.
February 19, 2002
Orientation measurements estimate relative rotations of objects. Such estimates may need to be averaged according to their covariances, e.g. for a Kalman filter. The non-commutative algebra of rotations makes transference of techniques inspired by the usual vector-based approaches for translations non-trivial. This paper shows in tutorial fashion how the rotor representation of rotations (which is an embedded form of the quaternion representation) permits straightforward computations with rotation estimates, from averaging and interpolation to ltering. We characterise rotational noise and present a way to combine estimates of orientations which minimises error covariance.

The Inner Products of Geometric Algebra pdf, ps.gz

Leo Dorst.
Making derived products out of the geometric product requires care in consistency. We show how a split based on outer product and scalar product necessitates a slightly different inner product than usual. We demonstrate the use and geometric significance of this contraction, and show how it simplifies treatment of meet and join. We also derive the sufficient condition for covariance of expressions involving outer, inner and scalar products.

"Object Recognition" in Geometric Algebra pdf, ps.gz

T.A. Bouma.
December 11, 2001
In Geometric Algebra, the objects in the model (points, lines, circles, surfaces, etcetera) belong to the same Algebra as the operations (translations, reflections, rotations, etcetera). Therefore if you are given an element of the algebra expressed as coordinates on a basis, it might not be obvious what kind of element it is. This talk catalogues the main types of elements and shows how to identify which type a particular element is. Future work will allow this identification to be more active by allowing us to correct for accidental errors. Error correction can force an element back to the type it was originally supposed to be.

Collision avoidance, wave propagation and boundary representations pdf, ps.gz

Leo Dorst.
Invited plenary speaker at the 5th International Conference on Clifford Algebras and their Applications, Ixtapa, Mexico, June 27 - July 4, 1999.

We provide representations in geometric algebra for m­dimensional boundaries, to describe and analyze the geometry of wave propagation. This operation also is the essence of collision avoidance in robotics, object growing in graphics, and milling. The most promising result is to represent boundaries as versors in an (m + 1; 1)­dimensional Minkowski space; wave propagation then becomes a geometric product of versors.

Geometric (Clifford) algebra:
a practical tool for efficient geometrical representation pdf, ps.gz

Leo Dorst.
At Mathematics Dept., U. of Amsterdam, March 1998, at Physics Dept., TUDelft, August 1998; at FEL/TNO May 1999.