A Survey of Developable Surfaces: From Shape Modeling to Manufacturing

Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, and mechanical materials, as well as in the development of tangible interaction and deformable robots, with the characteristics of easy-to-product, low-cost, transport-friendly, and deformable. Transforming shapes into developable surfaces is a complex and comprehensive task, which forms a variety of methods of segmentation, unfolding, and manufacturing for shapes with different geometry and topology, resulting in the complexity of developable surfaces. In this paper, we reviewed relevant methods and techniques for the study of developable surfaces, characterize them with our proposed pipeline, and categorize them based on digital modeling, physical modeling, interaction, and application. Through the analysis to the relevant literature, we also discussed some of the research challenges and future research opportunities.Comment: 20 pages, 24 figures, Author submitted manuscrip

Discrete Differential Geometry of Thin Materials for Computational Mechanics

Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation

Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Automatic mesh generation

The objective of this thesis project is a study of Pre-Processors and development of an Automatic Mesh Generator for Finite Element Analysis. The Mesh Generator developed in this thesis project can create triangular finite elements from the geometric database of Macintosh Applications. The user is required to give the density parameter to the program for mesh generation. The research is limited to Mesh Generators of planar surfaces. Delauny Triangulation method maximizes the minimum angles of a triangle. Watson\u27s Delauny Triangulation method can mesh only the \u27convex hull\u27 of a set of nodes. This algorithm has been modified to create triangular elements in convex and non-convex surfaces. The surfaces can have holes also. A node generation algorithm to place nodes on and inside a geometry has been developed in this thesis project. The mesh generation is very efficient and flexible. Geometric modeling methods have been studied to understand and integrate the Geometric Modeler with the Finite Element Mesh Generator. Expert Systems can be integrated with Finite Element Analysis. This will make Finite Element Method fully automatic. In this thesis project, Expert Systems in Finite Element Analysis are reviewed. Proposals are made for future approach for the integration of the two fields

Discrete Differential Geometry

This is the collection of extended abstracts for the 26 lectures and the open problem session at the fourth Oberwolfach workshop on Discrete Differential Geometry

Modeling And Simulation Of a Continious Folding Process Of An Origami Pattern

The engineering applications of origami has gathered tremendous attention in recent years. Various aspects of origami have different characteristics based on its application. The shape changing aspect is used in areas where size is a constraint. The structural rigidity aspect is utilized where strength is needed with a minimal increase in weight. When polymer or metal sheets are processed to have origami creases, they exhibit an improvement in mechanical properties. The sheets which create a specific local texture by means of tessellated folds patterns are called folded textured sheets[1]. These sheets are utilized to create fold cores. These light-weight sandwiched structures are heavily used in the aerospace industry, due to its ability to prevent moisture accumulation on the aeronautical structures at higher altitudes. The objective of the current research is to explore a new method for the continuous production of these folded textured sheets. The method uses a laser etching setup to mark the sheet with the origami pattern. The pattern is then formed by dies and passes through a conveyor system which is specifically arranged like a funnel to complete the final stage of the forming process. A simulation approach is utilized to evaluate the method. Results show the feasibility of the process along with its limitations. The design is made to be feasible for scaling up for large scale manufactur

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry