Using geometric shape variations to create an inverse model for a sheet metal process

The output of the sheet metal forming process is subject to much variation. This paper develops a method to measure shape variation in channel forming and relate this back to the corresponding process parameter levels of the manufacturing set-up to create an inverse model. The shape variation in the channels is measured using a modified form of the point distribution model (also known as the active shape model). This means that channels can be represented by a weighting vector of minimal linear dimension that contains all the shape variation information from the average formed channel.

The inverse models were created using classifiers that related the weighting vectors to the process parameter levels for the blank holder force (BHF), die radii (DR) and tool gap (TG) of the parameters. Several classifiers were tested: linear, quadratic Gaussian and artificial neural networks. The quadratic Gaussian classifiers were the most accurate and the most consistent type of classifier over all the parameters.

Secondary students` perceptions of a constructivist-informed teaching and learning environment for geometric optics

This article describes an exploration of a class of secondary school students perceptions of a constructivist informed teaching and learning environment for geometric optics. The students perceived the environment as one where they could freely express their ideas and be involved in activities. What was also apparent in this exploration was the students' preference for a classroom that involved small group discussions to whole class discussions that reflected a need for time to think about issues. They also have a preference for relevant, practical work that tests their ideas and a preference to have fewer notes that they construct themselves rather than notes dictated by the teacher.

NT: Refereed article. Includes bibliographical references.

Geometric shape errors in forging: developing a metric and an inverse model

The complexity of the forging process ensures that there is inherent variability in the geometric shape of a forged part. While knowledge of shape error, comparing the desired versus the measured shape, is significant in measuring part quality the question of more interest is what can this error suggest about the forging process set-up? The first contribution of this paper is to develop a shape error metric which identifies geometric shape differences that occur from a desired forged part. This metric is based on the point distribution deformable model developed in pattern recognition research. The second contribution of this paper is to propose an inverse model that identifies changes in process set-up parameter values by analysing the proposed shape error metric. The metric and inverse models are developed using two sets of simulated hot-forged parts created using two different die pairs (simple and 'M'-shaped die pairs). A neural network is used to classify the shape data into three arbitrarily chosen levels for each parameter and it is accurate to at least 77 per cent in the worst case for the simple die pair data and has an average accuracy of approximately 80 per cent when classifying the more complex 'M'-shaped die pair data.

Passive angle measurement based localization consistency via geometric constraints

In this paper, we examine the geometric relations between various measured parameters and their corresponding errors in angle-measurement based emitter localization scenarios. We derive a geometric constraint formulating the relationship among the measurement errors in such a scenario. Using this constraint, we formulate the localization task as a constrained optimization problem that can be performed on the measurements in order to provide the optimal values such that the solution is consistent with the underlying geometry.

Geometric formations in swarm aggregation: an artificial formation force based approach

Cooperative control of multiple mobile robots is an attractive and challenging problem which has drawn considerable attention in the recent past. This paper introduces a scalable decentralized control algorithm to navigate a group of mobile robots (swarm) into a predefined shape in 2D space. The proposed architecture uses artificial forces to control mobile agents into the shape and spread them inside the shape while avoiding inter-member collisions. The theoretical analysis of the swarm behavior describes the motion of the complete swarm and individual members in relevant situations. We use computer simulated case studies to verify the theoretical assertions and to demonstrate the robustness of the swarm under external disturbances such as death of agents, change of shape etc.

Geometric and material constraints in parametric modelling : the design to fabrication process

Parametric modelling, commonly used in the automotive and aerospace industries, has recently been adopted in the architecture and construction fields. The ability to design small repeatable components and apply them to a larger governing surface geometry is one area of parametric modelling that has great design potential. This two level modelling control, of component and overall surface, can allow designers to explore new types of form generation subject to parametric constraints. This paper reports on the design to fabrication process using repeatable components over a governing or carrier surface. The paper reports on our study of the requirements and possible solutions for successfully controlling a repeatable element, known as a Representative Volumetric Element (RVE), using geometric parameters of a larger governing surface geometry and material properties. This modelling process, coupled with Rapid
Manufacturing (RM) and Computer Numerically Controlled (CNC) machines has the potential to significantly reduce the interface between design and fabrication.

Geometric approximations towards free specular comic shading

We extend the standard solution to comic rendering with a comic-style specular component. To minimise the computational overhead associated with this extension, we introduce two optimising approximations; the perspective correction angle and the vertex face-orientation measure. Both of these optimisations are generally applicable, but they are especially well suited for applications where a physically correct lighting simulation is not required. Using our optimisations we achieve performances comparable to the standard solution. As our approximations favour large models, we even outperform the standard approach for models consisting of 10,000 triangles or more, which we can render exceeding 40 frames per second, including the specular component.

Emerging hypothesis verification using function-based geometric models and active vision strategies

This paper describes an investigation into the use of parametric 2D models describing the movement of edges for the determination of possible 3D shape and hence function of an object. An assumption of this research is that the camera can foveate and track particular features. It is argued that simple 2D analytic descriptions of the movement of edges can infer 3D shape while the camera is moved. This uses an advantage of foveation i.e. the problem becomes object centred. The problem of correspondence for numerous edge points is overcome by the use of a tree based representation for the competing hypotheses. Numerous hypothesis are maintained simultaneously and it does not rely on a single kinematic model which assumes constant velocity or acceleration. The numerous advantages of this strategy are described.