When Can You Fold a Map?

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by +-180 degrees. We first consider the analogous questions in one dimension lower -- bending a segment into a flat object -- which lead to interesting problems on strings. We develop efficient algorithms for the recognition of simply foldable 1D crease patterns, and reconstruction of a sequence of simple folds. Indeed, we prove that a 1D crease pattern is flat-foldable by any means precisely if it is by a sequence of one-layer simple folds. Next we explore simple foldability in two dimensions, and find a surprising contrast: ``map'' folding and variants are polynomial, but slight generalizations are NP-complete. Specifically, we develop a linear-time algorithm for deciding foldability of an orthogonal crease pattern on a rectangular piece of paper, and prove that it is (weakly) NP-complete to decide foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper, (2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a square piece of paper, and (3) crease patterns without a mountain/valley assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks to referees, including formal definitions of simple folds, more figures, table summarizing results, new open problems, and additional reference

Manufacturability analysis for non-feature-based objects

This dissertation presents a general methodology for evaluating key manufacturability indicators using an approach that does not require feature recognition, or feature-based design input. The contributions involve methods for computing three manufacturability indicators that can be applied in a hierarchical manner. The analysis begins with the computation of visibility, which determines the potential manufacturability of a part using material removal processes such as CNC machining. This manufacturability indicator is purely based on accessibility, without considering the actual machine setup and tooling. Then, the analysis becomes more specific by analyzing the complexity in setup planning for the part; i.e. how the part geometry can be oriented to a cutting tool in an accessible manner. This indicator establishes if the part geometry is accessible about an axis of rotation, namely, whether it can be manufactured on a 4th-axis indexed machining system. The third indicator is geometric machinability, which is computed for each machining operation to indicate the actual manufacturability when employing a cutting tool with specific shape and size. The three manufacturability indicators presented in this dissertation are usable as steps in a process; however they can be executed alone or hierarchically in order to render manufacturability information. At the end of this dissertation, a Multi-Layered Visibility Map is proposed, which would serve as a re-design mechanism that can guide a part design toward increased manufacturability

COMPUTATIONAL TOOLS FOR IMPROVING ROUTE PLANNING IN AGRICULTURAL FIELD OPERATIONS

In farming operation, machinery represents a major cost; therefore, good fleet management can have a great impact on the producer’s profit, especially considering the increasing costs of fuel and production inputs in recent years. One of the tasks to be accomplished in order to improve fleet management is planning the path that the machine should take to cover the field while working. Information such as distance traveled, time and fuel consumption as well as agricultural inputs wasted due to off-target-application areas are crucial in the path planning process. Parameters such as field boundary size and geometry, machine total width as well as control width resolution present a great impact on the information necessary for path planning. Researchers around the world have proposed methods that approach specific aspects related to path planning, the majority addressing machine field efficiency per-se, which a function of total time spent in the field as well as effective working time. However, wasted inputs due to off-target-application areas in the maneuvering regions, especially in oddly shaped agricultural fields might be as important as field efficiency when it comes down to the total operation cost. Thus, the main purpose of this research was to develop a path planning method that accounts for not only machinery field efficiency, but also the supply inputs. This research was accomplished in a threefold approach where in the first step an algorithm for computing off-target application area was developed, implemented and validated resulting in a computational tool that can be used to evaluate potential savings when using automatic section control on agricultural fields of complex field boundary. This tool allowed accomplishment of the second step, which was an investigation and better understanding of field size and shape as well as machine width of the effects on off-target application areas resulting in an empirical method for such estimations based on object shape descriptors. Finally, a path planning algorithm was developed and evaluated taking into consideration the aspects of machine field efficiency as well as off-target application areas

Implementing Rapid Prototyping Using CNC Machining (CNC-RP) Through a CAD/CAM Interface

This paper presents the methodology and implementation of a rapid machining system using a CAD/CAM interface. Rapid Prototyping using CNC Machining (CNC-RP) is a method that has been developed which enables automatic generation of process plans for a machined component. The challenge with CNC-RP is not the technical problems of material removal, but with all of the required setup, fixture and toolpath planning, which has previously required a skilled machinist. Through the use of advanced geometric algorithms, we have implemented an interface with a CAD/CAM system that allows true automatic NC code generation directly from a CAD model with no human interaction; a capability necessary for a practical rapid prototyping system.Mechanical Engineerin

Monitoring of Plant Species and Communities on Coastal Cliffs: Is the Use of Unmanned Aerial Vehicles Suitable?

Cliffs are reservoirs of biodiversity; therefore, many plant species and communities of inland and coastal cliffs are protected by Council Directive 92/43/EEC (European Economic Community), and their monitoring is mandatory in European Union countries. Surveying plants on coastal cliff by traditional methods is challenging and alternatives are needed. We tested the use of a small Unmanned Aerial Vehicle (UAV) as an alternative survey tool, gathering aerial images of cliffs at Palinuro Cape (Southern Italy). Four photo-interpreters analysed independently the derived orthomosaic and plotted data needed for the monitoring activity. Data showed to be not affected by photo-interpreters and reliable for the prescribed monitoring in the European Union (EU). Using the GIS analysis tools, we were able to: (a) recognise and map the plant species, (b) derive and measure the area of distribution on the cliff of habitat and species, and (c) count Eokochia saxicola individuals and gather quantitative data on their projected area. Quality of the images represented the main constraint, but incoming technological improvements of sensors and UAVs may overcome this problem. Overall results support the use of UAVs as an affordable and fast survey technique that can rapidly increase the number of studies on cliff habitats and improve ecological knowledge on their plant species and communitie