09111 Abstracts Collection -- Computational Geometry

From March 8 to March 13, 2009, the Dagstuhl Seminar 09111 ``Computational Geometry \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Learned navigation in unknown terrains: A retraction method

The problem of learned navigation of a circular robot R, of radius delta (is greater than or equal to 0), through a terrain whose model is not a-priori known is considered. Two-dimensional finite-sized terrains populated by an unknown (but, finite) number of simple polygonal obstacles are also considered. The number and locations of the vertices of each obstacle are unknown to R. R is equipped with a sensor system that detects all vertices and edges that are visible from its present location. In this context two problems are covered. In the visit problem, the robot is required to visit a sequence of destination points, and in the terrain model acquisition problem, the robot is required to acquire the complete model of the terrain. An algorithmic framework is presented for solving these two problems using a retraction of the freespace onto the Voronoi diagram of the terrain. Algorithms are then presented to solve the visit problem and the terrain model acquisition problem

Terrain prickliness: theoretical grounds for high complexity viewsheds

An important task when working with terrain models is computing viewsheds: the parts of the terrain visible from a given viewpoint. When the terrain is modeled as a polyhedral terrain, the viewshed is composed of the union of all the triangle parts that are visible from the viewpoint. The complexity of a viewshed can vary significantly, from constant to quadratic in the number of terrain vertices, depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible perspectives. We show that the prickliness effectively captures the potential of 2.5D terrains to have high complexity viewsheds, and we present near-optimal algorithms to compute the prickliness of 1.5D and 2.5D terrains. We also report on some experiments relating the prickliness of real word 2.5D terrains to the size of the terrains and to their viewshed complexity.Peer ReviewedPostprint (author's final draft

Query-by-Pointing: Algorithms and Pointing Error Compensation

People typically communicate by pointing, talking, sketching, writing, and typing. Pointing can be used to visualize or exchange information about an object when there is no other mutually understood way of communication. Despite its proven expressiveness, however, it has not yet become a frequently used modality to interact with computer systems. With the rapid move towards the adoption of mobile technologies, geographic information systems (GISs) have a particular need for advanced forms of interaction that enable users to query the geographic world directly. To enable pointing-based query system on a handheld device, a number of fundamental technical challenges have to be overcome. For such a system to materialize we need models stored in the device\u27s knowledge base that can be used as surrogate of real world objects. These computations, however, assume that (1) the pointing direction matches with the line-of-sight and (2) the observations about location and direction are precise enough so that a computational model will determine the same object as what the user points at. Both assumptions are not true. This thesis, therefore, develops an efficient error compensation model to reduce the discrepancy between the line-of-sight of the eye and the pointer direction. The model is based on a coordinate system centered at the neck and distances measured from neck to eye, neck to shoulder, shoulder to handheld pointer, and the pointing direction. An experiment was conducted using a gyro-enhanced sensor and three subjects who pointed at marked targets in a given room. It showed that the error compensation algorithm significantly reduces errors in pointing with arms outstretched