Predicting Geometric Errors and Failures in Additive Manufacturing

Additive manufacturing is a process that has facilitated the cost effective production of complicated designs. Objects fabricated via additive manufacturing technologies often suffer from dimensional accuracy issues and other part specific problems such as thin part robustness, overhang geometries that may collapse, support structures that cannot be removed, engraved and embossed details that are indistinguishable. In this work we present an approach to predict the dimensional accuracy per vertex and per part. Furthermore, we provide a framework for estimating the probability that a model is fabricated correctly via an additive manufacturing technology for a specific application. This framework can be applied to several 3D printing technologies and applications. In the context of this paper, a thorough experimental evaluation is presented for binder jetting technology and applications.Comment: This version has been published in the Rapid Prototyping Journal (2023

Tree-decomposable and underconstrained geometric constraint problems

Preprin

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. Keywords: geometric constraint solving, computer aided design 1. Introduction Geometric constraint solving has broad applications in a wide range of subje..

Constraint solving for computer-aided design

An approach to solving systems of geometric constraints appropriate for computer aided design is described, its scope is characterized and its correctness is proved. Various ways to extend the scope of the method are investigated and efficient algorithms are presented. Special consideration is given to the problem of navigating the geometric constraint solver to a real solution that is appropriate to the application and is intuitive to the user

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 ffn r ae n\Gammar\Gamma1 H , where ff is an explicitly computed constant, and ae H ! 1 is the root of an equation depending on the structure of the pattern. We then extend these findings to random patterns. Key Words: Pattern occurrence, Bernoulli model, autocorrelation polynomial, generating functions, asymptotic analysis. Research of this author was supported by NSF Grants CCR-9201078 and NCR-9206315, and NATO Collaborative Grant CGR.950060. 1. INTRODUCTION Repeated patterns and related phenomena in words (sequences, strings) are known to play a central role in many facets..