Ioannis Fudos

Geometric constraint solver

Abstract The paper reports on the development of a 2D geometric constraint solver. The solver is a major component of a new generation of cad systems based on a high-level geometry representation. The solver uses a graph-reduction directed algebraic approach, and achieves interactive speed. The paper describes the architecture of the solver and its basic capabilities. Then, it discusses in detail how to extend the scope of the solver, with particular emphasis on the theoretical and human factors involved in finding a solution, in an exponentially large search space, so that the solution is appropriate to the application, and so that the way of finding it is intuitive for an untrained user.

A graph-constructive approach to solving systems of geometric constraints

A graph-constructive approach to solving systems of geometric constraints capable of effeciently handling well-constrained, overconstrained, and underconstrained configurations is presented. The geometric constraint solver works in two phases: in the analysis phase the constraint graph is analyzed and a sequence of elementary construction steps is derived, and then in the construction phase the sequence of construction steps in actually carried out. The analysis phase of the algorithm is described in detail, its correctness is proved, and an efficient algorith to realized it is presented. The scope of the graph analysis is then extended by utilizing semantic information in the form of anlge derivations, and by extending the repertoire of the construction steps. Finally, the construction phase is briefly discussed.

Correctness Proof of a Geometric Constraint Solver

We present a correctness proof of a graph-directed variational geometric constraint solver. First, we prove that the graph reduction that establishes the sequence in which to apply the construction steps defines a terminating confluent reduction system, in the case of well-constrained graphs. For overconstrained problems there may not be a unique normal form. Underconstrained problems, on the other hand, do have a unique normal form. Second, we prove that all geometric solutions found using simple root-selection rules must place certain triples of elements in the same topological order, no matter which graph reduction sequence they are based on. Moreover, we prove that this implies that the geometric solutions derived by different reduction sequences must be congruent. Again, this result does not apply to overconstrained problems.

Constraint-Based Parametric Conics for CAD

We describe how to construct conic blending arcs from constraints, using a unified rational parametric representation that combines the separate cases of blending parallel and non-parallel edges. The possible constraints are that the arc must have a given distance from a line, a point, or a circle, or else intersect a circle or a line at a prescribed angle. Our representation is easily converted into a rational B-spline with positive weights, and is therefore compatible with internal representations used by most solid modeling systems. Finally, we discuss how we integrated this work with an algebraic constraint solver.

A parametric feature-based CAD system for reproducing traditional pierced jewellery *

Abstract In this paper, we introduce ByzantineCAD, a parametric CAD system for the design of pierced medieval jewellery, which is jewellery created by piercing, a traditional Byzantine technique. ByzantineCAD is an automated parametric system where the design of a piece of jewellery is expressed by a collection of parameters and constraints and the users participation in the design process is through the definition of the parameter values. We present an approach to designing traditional pierced jewellery using a voxel-oriented feature-based Computer Aided Design paradigm: a large complex pierced design is created by appropriately placing elementary structural elements. We also present a scaling algorithm for enlarging pierced designs without altering the size of the elementary structural elements used to construct them.

An efficient hierarchical scheme for locating highly mobile users

To accommodate the increase in user population in future personal communication systems, hierarchical architectures of location databases have been proposed. In this paper, a scheme based on forwarding pointers is presented, that reduces the cost of the overall network and database traac generated by frequent location updates in such hierarchical architectures. To reduce the number of forwarding pointers that need to be traversed to locate a user, auxiliary caching techniques are presented. Various conditions for purging the chain of forwarding pointers and updating the database are also introduced. Special care is given so that the scheme correctly supports the concurrent execution of updates and lookups. The applicability of the scheme and the performance of the caching techniques are demonstrated through a number of experiments for a range of call to mobility ratios and for a variety of moving and calling behaviors. 1 Introduction Advances in wireless telecommunications and in the development of portable computers have provided for the emergence of mobile computing. In mobile computing, users are not attached to a xed geographical location, instead their point of attachment to the network changes as they relocate from one support environment to another. Besides mobility in wireless networks, other forms of moving objects are also emerging. Software mobile agents, that roam the Internet searching for information, provide a popular such example. Since delivering any message to mobile objects requires locating them rst, deriving eecient strategies for tracking moving users is central to mobile computing. In particular, for future Personal Communication Service (PCS) systems, with high user populations and numerous customer services, such signaling and database traac for locating users is expected to increase dramatically 15]. To locate users, distributed location databases are deployed that maintain the current location of mobile users. To accommodate the increased traac associated with locating moving users, hierarchical distributed database architectures are built 15, 1,

Distributed Location Databases for Tracking Highly Mobile Objects

In current distributed systems, the notion of mobility is emerging in many forms and applications. Increasingly many users are not tied to a fixed access point but instead use wireless communications or dial-up services to access data independent of their physical location. Furthermore, mobile software, a popular example being mobile agents, is frequently used as a new form of building distributed network-centric applications. Tracking mobile objects, i.e. identifying their current location, is central to such settings. In this paper, we exploit the use of hierarchical distributed location databases, where each database site covers a specific geographical region and contains location information about all objects residing in it. For highly mobile objects, a scheme based on forwarding pointers enhanced with auxiliary caching techniques is presented, to reduce the cost of the overall network and database traffic generated by frequent location updates. The scheme is extended to support concurrency and failure recovery. Performance is demonstrated through a number of simulation experiments for a range of call to mobility ratios and for a variety of moving and calling behaviors.

S-buffer: Sparsity-aware Multi-fragment Rendering

This work introduces S-buffer, an efficient and memory-friendly gpu-accelerated A-buffer architecture for multifragment rendering. Memory is organized into variable contiguous regions for each pixel, thus avoiding limitations set in linked-lists and fixed-array techniques. S-buffer exploits fragment distribution for precise allocation of the needed storage and pixel sparsity (empty pixel ratio) for computing the memory offsets for each pixel in a parallel fashion. An experimental comparative evaluation of our technique over previous multi-fragment rendering approaches in terms of memory and performance is provided.

On pattern occurrences in a random text

Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have different probabilities of occurrence (i.e., the so-called asymmetric Bernoulli model). We are concerned with the probability of exactly r occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it behaves as αnrϱHn − r − 1, where α is an explicitly computed constant, and ϱH < 1 is the root of an equation depending on the structure of the pattern. We then extend these findings to random patterns.

A feature based approach to re-engineering objects of freeform design by exploiting point cloud morphology

Reverse engineering, the process of obtaining a geometric CAD model from measurements obtained by scanning an existing physical model, is widely used in numerous applications, such as manufacturing, industrial design and jewellery design. In this work we propose a framework for reverse engineering objects of freeform design to obtain a fully editable feature-based CAD model that can be reproduced or modified before production. We focus on the process of detecting features on a cloud point and we present a fast method for analyzing the morphology of the surface defined by the point cloud. We compute a point wise characteristic called point concavity intensity and we use this quantity to detect regions that are then refined to object features. The proposed algorithm takes overall O(nlogn) time, where n is the cardinality of the point cloud.