Finding a boundary between valid and invalid regions of the input space

In the context of robustness testing, the boundary between the valid and invalid regions of the input space can be an interesting source of erroneous inputs. Knowing where a specific software under test (SUT) has a boundary is essential for validation in relation to requirements. However, finding where a SUT actually implements the boundary is a non-trivial problem that has not gotten much attention. This paper proposes a method of finding the boundary between the valid and invalid regions of the input space. The proposed method consists of two steps. First, test data generators, directed by a search algorithm to maximise distance to known, valid test cases, generate valid test cases that are closer to the boundary. Second, these valid test cases undergo mutations to try to push them over the boundary and into the invalid part of the input space. This results in a pair of test sets, one consisting of test cases on the valid side of the boundary and a matched set on the outer side, with only a small distance between the two sets. The method is evaluated on a number of examples from the standard library of a modern programming language. We propose a method of determining the boundary between valid and invalid regions of the input space and apply it on a SUT that has a non-contiguous valid region of the input space. From the small distance between the developed pairs of test sets, and the fact that one test set contains valid test cases and the other invalid test cases, we conclude that the pair of test sets described the boundary between the valid and invalid regions of that input space. Differences of behaviour can be observed between different distances and sets of mutation operators, but all show that the method is able to identify the boundary between the valid and invalid regions of the input space. This is an important step towards more automated robustness testing.Comment: 10 pages, conferenc

A "Piano Movers" Problem Reformulated

It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a "Piano Mover's Problem" which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form.Comment: 8 pages. Copyright IEEE 201

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine

Laser path planning is an important step in solid freeform fabrication processes such as Stereolithography (SLA). An important consideration in the laser path planning is to compensate the shape of laser beam. Currently the compensation is divided into two steps, Z-compensation and X-Y compensation, and the shape of laser beam is assumed to be uniform for the whole platform. In this research, we present a sampling based non-uniform offsetting method which accounts for the different shapes of laser beam at various locations. We discuss the related steps and algorithms. We demonstrate its effectiveness by using various test cases. Besides improving the accuracy of SLA machine, non-uniform offsetting can also be applied to address other accuracy issues caused by thermal and structural variationsMechanical Engineerin

Towards Automated Boundary Value Testing with Program Derivatives and Search

A natural and often used strategy when testing software is to use input values at boundaries, i.e. where behavior is expected to change the most, an approach often called boundary value testing or analysis (BVA). Even though this has been a key testing idea for long it has been hard to clearly define and formalize. Consequently, it has also been hard to automate. In this research note we propose one such formalization of BVA by, in a similar way as to how the derivative of a function is defined in mathematics, considering (software) program derivatives. Critical to our definition is the notion of distance between inputs and outputs which we can formalize and then quantify based on ideas from Information theory. However, for our (black-box) approach to be practical one must search for test inputs with specific properties. Coupling it with search-based software engineering is thus required and we discuss how program derivatives can be used as and within fitness functions. This brief note does not allow a deeper, empirical investigation but we use a simple illustrative example throughout to introduce the main ideas. By combining program derivatives with search, we thus propose a practical as well as theoretically interesting technique for automated boundary value (analysis and) testing

Influence of hand position on the near-effect in 3D attention

Voluntary reorienting of attention in real depth situations is characterized by an attentional bias to locations near the viewer once attention is deployed to a spatially cued object in depth. Previously this effect (initially referred to as the ‘near-effect’) was attributed to access of a 3D viewer-centred spatial representation for guiding attention in 3D space. The aim of this study was to investigate whether the near-bias could have been associated with the position of the response-hand, always near the viewer in previous studies investigating endogenous attentional shifts in real depth. In Experiment 1, the response-hand was placed at either the near or far target depth in a depth cueing task. Placing the response-hand at the far target depth abolished the near-effect, but failed to bias spatial attention to the far location. Experiment 2 showed that the response-hand effect was not modulated by the presence of an additional passive hand, whereas Experiment 3 confirmed that attentional prioritization of the passive hand was not masked by the influence of the responding hand on spatial attention in Experiment 2. The pattern of results is most consistent with the idea that response preparation can modulate spatial attention within a 3D viewer-centred spatial representation