Computing surface area and volume of parachutes from 3D scans

Purpose – To explore three‐dimensional scanning technology in capturing the shape of inflated parachutes for accurate estimation of surface area and volume.Design/methodology/approach – The volume and surface area of an inflated round parachute are important parameters for the design and analysis of its performance. However, it is difficult to acquire the three‐dimensional (3D) surface shape of a parachute due to its flexible fabric and dynamic movement. This paper presents how we collect 3D data with a laser scanner and calculate volume and surface area of parachutes from their scans. The necessary data clean and approximation steps with non‐uniform B‐spline function are introduced and implemented. Numerical integration methods are employed to estimate surface area and volume. The approximation of the parachute based on an ellipsoid is compared with the numerical integration approach in their volumes and surface areas.Findings – It is found that 3D scanning technology, with help of mathematic program dev...

[1]  E. T. Y. Lee,et al.  Choosing nodes in parametric curve interpolation , 1989 .

[2]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[3]  Philip C. Treleaven,et al.  Building symbolic information for 3D human body modeling from range data , 1999, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062).

[4]  Aly A. Farag,et al.  Slicing, fitting, and linking (SFL): a modular triangulation approach , 1999, Electronic Imaging.

[5]  H. G. Heinrich,et al.  Analysis of parachute opening dynamics with supporting wind-tunnel experiments , 1968 .

[6]  Josef Hoschek,et al.  Intrinsic parametrization for approximation , 1988, Comput. Aided Geom. Des..

[7]  Robert Sedgewick,et al.  Algorithms in C , 1990 .

[8]  Jiann-Liang Chen,et al.  Data point selection for piecewise linear curve approximation , 1994, Comput. Aided Geom. Des..

[9]  Andrew W. Fitzgibbon,et al.  Direct Least Square Fitting of Ellipses , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  P. J. Hartley,et al.  Parametrization of Bézier-type B-spline curves and surfaces , 1978 .

[11]  In-Kwon Lee,et al.  Curve reconstruction from unorganized points , 2000, Comput. Aided Geom. Des..

[12]  Jindong Chen,et al.  Automatic Reconstruction of 3D CAD Models from Digital Scans , 1999, Int. J. Comput. Geom. Appl..

[13]  G. Stewart.  Introduction to matrix computations , 1973 .

[14]  Ioannis Stamos,et al.  3D modeling of historic sites using range and image data , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[15]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[16]  Les A. Piegl,et al.  On NURBS: A Survey , 2004 .

[17]  Andrew W. Fitzgibbon,et al.  Simultaneous registration of multiple range views for use in reverse engineering , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[18]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[19]  Chia-Hsiang Menq,et al.  Parameter optimization in approximating curves and surfaces to measurement data , 1991, Comput. Aided Geom. Des..