This tutorial focuses on describing the implementation and use of reflections in the geometric algebras of three-dimensional (3D) Euclidean space and in the five-dimensional (5D) conformal model of Euclidean space. In the latter reflections at parallel planes serve to implement translations as well. Combinations of reflections allow to implement all isometric transformations. As a concrete exam...

This thesis investigates a new representation scheme for geometric modeling, based on an algebraic model for shapes and formalized using a boundary representation. The algebraic model is mathematically uniform for shapes of all kinds and provides a natural and intuitive framework for mixed-dimensional shapes. The corresponding maximal element representation is essential to the concept of shape ...

4 Summary A three dimensional (3D) geometric model including femur, tibia, patella, anterior and posterior cruci-ate ligaments and menisci is computed from 13 magnetic resonance (MR) acquisitions of a knee joint at varying degrees of exion. For this purpose, we use a method known as Delaunay Reconstruction to obtain a precise three-dimensional model of each part of the knee joint during motion....

Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA has been proposed first by Puntonet and Prieto [6] in order to separate linear mixtures. One major drawback of geometric algorithms is, however, an exponentially rising number of sam...

Computer simulation of the biomechanical and biological heat transfer in ophthalmology greatly relies on having a reliable computer model of the human eye. This paper proposes a novel method on the construction of a geometric model of the human eye based on tissue slice images. Slice images were obtained from an in vitro Chinese human eye through an embryo specimen processing methods. A level s...

Developing the ability to recognize a landmark from a visual image of a robot's current location is a fundamental problem in robotics. We describe a way in which the landmark matching problem can be mapped to that of learning a one-dimensional geometric pattern. We present an eecient noise-tolerant algorithm (designed using the statistical query model) to PAC-learn the class of one-dimensional ...

this paper addresses a multi-criteria decision based methodology to develop a road network cost function for route finding analysis in a geographic information system (gis). over the years, several studies relating to route planning process in gis and intelligent transportation systems (its) have been conducted, most of which rely on the use of one-dimensional variables like distance or time as...