Making sky lanterns from polygonal meshes

https://doi.org/10.1016/j.compeleceng.2014.02.001Get rights and content

Abstract

Releasing sky lanterns is a popular way of celebrating festivals and ceremonies in the Asian countries. This paper presents a computer-aided approach to help novice users to design flyable sky lantern with desired shape. Given a closed up-right 3D model with a user-specified cutting on the bottom, our system optimizes the shape by regularizing the boundary, smoothing the geometry and improving the volume-to-area ratio to make it feasible for flying. The optimized shape is then approximated by a set of developable patches. Next, through a physical analysis step that tests the flying condition and determines the optimal size, the approximated shape is flattened into 2D patches, which can be printed out and glued together to form the airbag. Finally, the user can attach the airbag to a bamboo frame and assemble the fuel cell. We successfully apply our prototype system to design and construct real sky lanterns.

Introduction

It is a recent trend to apply computer graphics techniques in various recreational applications, so that nonprofessional users can greatly enjoy from their own creations. Earlier examples include the generation of paper craft models from triangular meshes [1], [2], [3]. Later on, systems that making stuffed toys [4], [5], [6] or knitted animals [7] have been developed. Recently, several new approaches have been proposed to construct more complicated 3D models for recreational graphics, such as bas-relief sculpture [8], shadow art [9] and various puzzles [10], [11]. Following this trend, this paper introduces a new and interesting recreational application that facilitates the users to design sky lanterns from 3D polygonal meshes.

Sky lantern is an airborne lantern consisting of an air bag that is made of flame resistent paper or tissue and attached to a bamboo frame, inside which a small candle or fuel cell is placed (Fig. 1(c)). When lit, the flame heats the air inside the lantern that makes it buoyant since the hot air inside has a lower density than the relatively cold air outside the lantern. Unlike gas balloons, the sky lantern does not have to be sealed at the bottom since the air near the bottom of the lantern is at the same pressure as the surrounding air. Sky lanterns were originally invented as a type of spy blimp in wars in ancient China. Later on, these lanterns were subsequently incorporated into festivals like Chinese New Year and Mid-Autumn Festival. Nowadays, sky lanterns are a great and simple way to entertain guests, celebrate festivals and social events in eastern Asian countries. Launching them in big groups create amazing visual effects, see Fig. 2.

Launching sky lanterns is easy and exciting that allows everyone to participate in an elaborate firework show with great effect. However, most of the sky lanterns available in the markets are made in very simple shape like box, ball or cylinder. It is technically difficult to design and make sky lanterns in more complicated and interesting shapes. The reasons are two folded: First, from the assembling point of view, it is tricky to design the parts which are made in planar materials, such as papers, or plastic, and bent and glued together to form the desired shape. Second, it is hard to test whether or not the designed lantern can fly. Thus, it always relies on the experience and knowledge of the designer. If failed, the designer has to take another round from designing the shape, assembling the parts, to test. Thus, the whole design process may be very tedious and time consuming.

While the first problem is relatively easy to solve since there have been a lot research efforts on pattern design for paper craft [1], [2], [3] and stuffed toys [4], etc. With slight modifications, these methods can be borrowed to the sky lantern design. However, to the best of our knowledge, there are no existing work to solve the second issue. A widely used rule suggests making the sky lantern big enough to increase the buoyancy. Such a strategy always leads to big waste of materials and it is not convenient to carry and launch such a bulky sky lantern. More importantly, even such a conservative strategy can not ensure a successful construction. A beginner may feel very frustrated after several times of trial and failure.

To solve the aforementioned difficulties, this paper presents a semi-automatic framework that helps user make sky lanterns in desired 3D shapes. Taking an upright 3D model as input, our system analyzes its geometry, then approximates the shape by a set of developable patches automatically, and finally tests the physical conditions to guarantee the designed sky lantern is able to fly. Fig. 1 demonstrates a real case to make a sky lantern with the aid of our system.

The specific contributions of this paper include:

  • A shape optimization algorithm that improves the geometry of the input mesh and makes it more suitable for flying.

  • A feature-aware algorithm to approximate the input shape with a set of developable patches.

  • A physical analysis method to test the flying condition of the designed sky lantern.

The remaining of the paper is organized as follows: Section 2 presents the overview of the proposed computer-aided geometric design framework. Sections 3 Shape optimization, 4 Feature-aware developable surface approximation, 5 Physical analysis detail our algorithms in shape optimization, approximation and physical analysis. Section 6 shows the experimental results and discusses the strengths and limitations of the proposed method. Finally, Section 7 concludes the paper with several future research directions.

Section snippets

Overview

As shown in Fig. 3(a), our system takes a 3D polygonal mesh as input(The models are assumed to be upright). Then, the user cuts the model open on the bottom, see Fig. 3(b). Although there are many easy-to-use mesh scissoring tools, e.g, [12], we simply use cutting plane in this step, mainly because a planar boundary is easy to be attached on the bamboo frame. Next, a shape optimization algorithm is applied to regularize the open boundary and smooth the geometry, see Fig. 3(c). After that, we

Shape optimization

This section presents an optimization algorithm to make the lantern appropriately shaped for flying. Observe that the real lanterns usually have the following features: (1) The opening on the bottom is very regular such that one can attach a bamboo or metal frame easily (Fig. 4(a)). (2) The shape does not contain too much high-frequency details that are hard to construct using materials like paper or plastic. Thus, the lantern is usually smooth and can be depicted by some feature lines (Fig. 4

Feature-aware developable surface approximation

Since the sky lantern is made of flame resistent paper or tissue, we need to approximate the optimized shape using developable patches that can be flattened to the 2D plane. There are lot of research efforts on shape approximation using developable surfaces, including both quasi-developable [4], [6] and exact developable approximation [1], [2], [3]. Our goal is to compute an exact developable approximation of the input shape.

The surface is first segmented into regions. Each region Ri is

Physical analysis

After the shape optimization and approximation, the physical analysis step is conducted to test the flying condition of the designed lantern.

Before introducing our approach, we first take a look at how sky lanterns fly. The sky lantern consists of an airbag attached to a bamboo frame and a fuel (e.g., candle) placed in the center of the frame. When lit, the flame heats the air inside the airbag. As a result, the hot air inside has a lower density than the relatively cold air outside the

Results and discussion

We have implemented a prototype system in C++. TAUCS [19] is used in the surface optimization step to solve the sparse linear system. GSL [20] is used for Levenberg–Marquardt method and linear regression. We made a real sky lantern using our system as shown in Fig. 1(c). The area density of the flame resistent paper is 60g/m2. The length density of the bamboo frame is 18g/m. We set the temperature Th=333K and Ta=300K (depending on the test environment). We use a candle (50g) as the fuel cell.

Conclusion

This paper presents a computer aided geometric design approach that facilitates the users to design sky lanterns from polygonal meshes. Taking an up-right 3D model as input, our system optimizes the shape to better fit the flying requirements by regularizing the boundary, smoothing the geometry and improving the volume-to-area ratio. Then the optimized shape is approximated by a set of developable patches. Next, a physical analysis is conducted to test its flying condition and then determine

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61202142, 61100032), Joint Funds of the Ministry of Education of China and China Mobile (No. MCM20122081), the National Key Technology R&D Program Foundation of China (No. 2013BAH44F00) and the Fundamental Research Funds for the Central Universities (Nos. 2010121070, 2010121072, 2013121030). AcRF 69/07, Singapore NRF Interactive Digital Media R&D Program under research grant NRF2008IDM-IDM004-006. Jiazhi Xia is

Juncong Lin is now an associate professor at Xiamen University. He received the Ph.D. degree in Computer Science from Zhejiang University. His research interests include geometry processing and sketch based modeling.

References (20)

  • J. Mitani et al.

    Making papercraft toys from meshes using strip-based approximate unfolding

    ACM Trans Graph

    (2004)
  • I. Shatz et al.

    Paper craft models from meshes

    Visual Comput

    (2006)
  • Massarwi F, Gotsman C, Elber G. Papercraft models using generalized cylinders. In: Proceedings of the 15th Pacific...
  • D. Julius et al.

    D-charts: quasi-developable mesh segmentation

    Comput Graphics Forum

    (2005)
  • Y. Mori et al.

    Plushie: an interactive design system for plush toys

    ACM Trans Graphics

    (2007)
  • C.C. Wang

    Computing length-preserved free boundary for quasi-developable mesh segmentation

    IEEE Trans Visualization Comput Graphics

    (2008)
  • Y. Igarashi et al.

    Knitting a 3d model

    Comput Graphics Forum

    (2009)
  • T. Weyrich et al.

    Digital bas-relief from 3d scenes

    ACM Trans Graphics

    (2007)
  • N.J. Mitra et al.

    Shadow art

    ACM Trans Graphics

    (2009)
  • Lo K-Y, Fu C-W, Li H. 3d polyomino puzzle. ACM Trans Graphics...
There are more references available in the full text version of this article.

Juncong Lin is now an associate professor at Xiamen University. He received the Ph.D. degree in Computer Science from Zhejiang University. His research interests include geometry processing and sketch based modeling.

Xing Gao is now an assistant professor at Xiamen University, P.R.China. He received the Ph.D. degree in Computer Science from Harbin Institute of Technology. His research interests include sketch based modeling.

Minghong Liao is a professor of Software School of Xiamen University. He received his Ph.D. degree in Computer Science in 1993 from Harbin Institute of Technology of China. His research interests include Intelligent Network, Pervasive Computing and Computer Graphics.

Jiazhi Xia received the BS and MS degrees in Computer Science from Zhejiang University, China, and the PhD degree in Computer Science from Nanyang Technological University. He is currently a lecturer at the School of Information Science and Engineering, Central South University, China. His research interests include computer graphics, multimedia, and human-computer interaction.

Guilin Li is now a lecturer at Xiamen University, P.R.China. He received the Ph.D. degree in Computer Science from Harbin Institute of Technology. His research interests includes CPS, distributed computing.

Ying He received the BS and MS degrees in Electrical Engineering from Tsinghua University, China, and the PhD degree in Computer Science from the State University of New York (SUNY), Stony Brook. He is an associate professor at NTU, Singapore. His research interests fall in the broad area of visual computing.

Reviews processed and recommended for publication to Editor-in-Chief by Associate Editor Dr. Jian Li.

View full text