Variational Discrete Developable Surface Interpolation

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Wen-Yong Gong ◽  
Yong-Jin Liu ◽  
Kai Tang ◽  
Tie-Ru Wu
Keyword(s):  
Computer Aided Design ◽  
Dynamic Programming Method ◽  
Developable Surface ◽  
Optimization Scheme ◽  
Developable Surfaces ◽  
Surface Interpolation ◽  
Point Condition ◽  
Aided Design ◽  
Boundary Curves ◽  
Triangle Strip

Modeling using developable surfaces plays an important role in computer graphics and computer aided design. In this paper, we investigate a new problem called variational developable surface interpolation (VDSI). For a polyline boundary P, different from previous work on interpolation or approximation of discrete developable surfaces from P, the VDSI interpolates a subset of the vertices of P and approximates the rest. Exactly speaking, the VDSI allows to modify a subset of vertices within a prescribed bound such that a better discrete developable surface interpolates the modified polyline boundary. Therefore, VDSI could be viewed as a hybrid of interpolation and approximation. Generally, obtaining discrete developable surfaces for given polyline boundaries are always a time-consuming task. In this paper, we introduce a dynamic programming method to quickly construct a developable surface for any boundary curves. Based on the complexity of VDSI, we also propose an efficient optimization scheme to solve the variational problem inherent in VDSI. Finally, we present an adding point condition, and construct a G1 continuous quasi-Coons surface to approximate a quadrilateral strip which is converted from a triangle strip of maximum developability. Diverse examples given in this paper demonstrate the efficiency and practicability of the proposed methods.

Newer Theory and More Robust Algorithms for Computer-Aided Design of Developable Surfaces

2005 ◽  
Vol 42 (03) ◽  
pp. 71-79
Author(s):  
B. Konesky
Keyword(s):  
Computer Aided Design ◽  
Developable Surface ◽  
Robust Algorithms ◽  
Developable Surfaces ◽  
Space Curves ◽  
Surface Areas ◽  
C Programming ◽  
Computer Aided ◽  
Reliable Solution ◽  
Aided Design

The use of developable surfaces in design is of engineering importance because of the relative ease with which they can be manufactured. The problem of how to make surfaces developable is not new. The usual technique is by using two space curves, defining the edges of the surface. These are first created, and then a set of rulings are constructed between the space curves under the constraint of being developable. A problem with existing algorithms for designing developable surfaces is the tendency to include nondevelopable portions of the surface: areas of regression. A more reliable solution to the problem of creating a developable surface is presented. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the resulting developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. Intersecting adjacent developable surfaces and generating the flat plate layouts were also accomplished. This paper presents research and development that started around 1987. The algorithms were implemented using ANSI C++ programming language and commercial computer-aided design and manufacturing (CAD and CAM) software programs.

Computer-Aided Design of Developable Hull Surfaces

1971 ◽  
Vol 8 (02) ◽  
pp. 233-242
Author(s):  
T. J. Nolan
Keyword(s):  
Digital Computer ◽  
Computer Aided Design ◽  
Horizontal Plane ◽  
Design Procedure ◽  
Developable Surface ◽  
Surface Design ◽  
Computer Aided ◽  
Aided Design ◽  
Approximating Polynomials ◽  
Boundary Curves

An algorithm mathematizes a developable surface design procedure for the digital computer. Given points on a pair of boundary curves, the algorithm generates spline-approximating polynomials to represent the boundary curves and computes a set of closely spaced rulings which lie in the surface spanning the boundary curves. Offsets to the surface are then computed at any specified transverse, vertical, or horizontal plane cutting the surface. The procedure emphasizes freedom of shape but does not guarantee the existence of a developable surface. In this case, the results will be information describing the developability violation rather than offsets describing the surface. The outstanding advantages of a computer-aided approach to developable surface design are speed and precision.

An approach for designing a developable and minimal ruled surfaces using the curvature theory

2020 ◽  
Vol 18 (01) ◽  
pp. 2150015
Author(s):  
Fatma Güler
Keyword(s):  
Computer Graphics ◽  
Computer Aided Design ◽  
Research Topic ◽  
Ruled Surfaces ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Curvature Theory ◽  
Active Research ◽  
Aided Design

Developable surfaces are defined to be locally isometric to a plane. These surfaces can be formed by bending thin flat sheets of material, which makes them an active research topic in computer graphics, computer aided design, computational origami and manufacturing architecture. We obtain condition for developable and minimal ruled surfaces using rotation frame. Also, the validity of the theorems is illustrated with examples.

An Origami Crease Pattern Generating Methodology for “Origami 3D Printer”

2019 ◽  
Author(s):  
Yang Yang ◽  
Ichiro Hagiwara ◽  
Luis Diago ◽  
Junichi Shinoda
Keyword(s):  
Computer Aided Design ◽  
Normal Families ◽  
Engineering System ◽  
3D Printer ◽  
Layer By Layer ◽  
Developable Surface ◽  
3D Data ◽  
2D Pattern ◽  
System 2 ◽  
Aided Design

Abstract The additive 3D printer (hereafter called Add-3D) creates a 3D object with materials being added together layer by layer. Before printing an object, some professional processes are indispensable, such as creating the 3D printable models by computer-aided design (CAD), or 3D scanner, and STL data modification, which are difficult for normal families. As we know, primordially, origami is the ancient art of folding a flat-piece of paper into a 3D shape, that even can be played by kids. So we aim to develop an Origami 3D printer (hereafter called Ori-3D) that can be used by ordinary families with the features of effort and no size limit of model. In Ori-3D, the object is constructed by human hands or by an Origami robot using 2D patterns generated from 3D data (obtained from photos or CAD). Ori-3D includes the following steps: 1) the surface of an object is segmented to several developable surfaces as large as possible using segmentation technique which is used in reverse engineering system. 2) Each developable surface is developed to 2D pattern with mountain & valley lines and glue parts. 3) The 2D crease pattern is optimized by a tree structure method to be easily folded by an Origami Robot. 4) With Origami robot, the object is easily constructed from the improved 2D crease pattern. This paper focuses on discuss the steps 1∼ 3: generation of the 2D crease pattern.

Representation of Developable Surfaces and Achievement of the Algorithm

2006 ◽  
Vol 532-533 ◽  
pp. 813-816
Author(s):  
Min Zhou ◽  
Zheng Lin Ye ◽  
Guo Hua Peng ◽  
Yun Qing Yang ◽  
Hong Chan Zheng
Keyword(s):  
Efficient Method ◽  
Computer Aided Design ◽  
Control Parameter ◽  
Geometric Design ◽  
B Spline ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Aided Design ◽  
Traditional Approaches

In order to overcome the difficulties in representation of developable surfaces utilizing traditional approaches, and resolve the problems in adjusting and controlling the position and shape of developable surfaces that often faced in Engineering. In this paper, we propose a directly explicit and efficient method of computer-aided design for developable surfaces based on triangle-B spline. The shapes of developable surfaces can be adjusted using a control parameter. Meanwhile, we show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design. The algorithms are explained in detail, and demonstrated with the examples in the paper.

Sign in / Sign up

Export Citation Format

Share Document