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Modeling the 3D geometric configuration of yarn is the base of building the 3D fabric structure. The surfaces of the yarns are modeled by many facets. To improve the efficiency of modeling, 3D yarn is usually designed by Bezier curve, spline curve or B-spline curve on the principle of Computer Graphics. The paper reviews different 3D modeling methods for single yarn from the view of cross-section and central line. Some improvements for a better visual effect such as inserting twist and hairiness are illustrated as well. Based on the single yarn, the folded yarn and some fancy yarns can also be modeled in 3D space as long as the cross-sections of the control sections of the component single yarn are determined. Applications of the various 3D yarns are demonstrated. The advantages and the drawbacks of various methods are explained and compared as well. Comparatively speaking, modeling technology based on spline curve is more convenient and flexible, perhaps it is the most popular tool since it is capable of designing different kinds of yarns mentioned above and gets the maximum support from the different developing platforms such as OpenGL, 3DS-MAX, Solid Works CAD, etc.

The geometrical structures of the woven fabrics, knitted fabrics or braided fabrics affect the physical properties of the fabric to a great extent. These fabrics are composed of yarns, therefore, the 3D geometrical configuration of the yarn has to be modeled before the 3D geometrical structures of the fabrics are to be modeled. Various methods were proposed in modeling the 3D yarns and the paper aims to give a complete illustration of how to model a 3D yarn.

The configuration of 3D yarn is modeled according to Computer Graphics. Generally speaking, the surface of the 3D yarn can be regarded as composed of many tiny facets. As soon as all the facets of the yarn surface are determined, the normal of the each facet is determined accordingly, then the shading effect of the yarn will be calculated according to Phong or Goround [

Obviously, it is a tedious work to construct an object by determining so many facets one by one. An efficient method must be found. Many surface modeling technologies were applied widely, such as Bezier surface, B- spline surface [

To a 3D yarn model, the surface of the yarn can be regarded as a closed surface. Therefore, to construct a 3D model for yarn configuration, there are two issues that have to be considered: 1) representation of the central line; 2) description of the cross-section. Peirce [

Based on these hypotheses, many 3D geometrical models of the yarn were setup. And these models will be introduced according to the method to control the shape of the central line or the cross-section. As for whether the cross-section is one of the shape stated above or how to calculate the true path of the central line by the fabric construction, which are beyond the research of the paper. What concerned in the paper are how to describe the shape of the central line of the yarn if some key points (or interpolated points) on the central line are determined and how to describe the special shape of the cross-section if the cross-section is given. Keep in mind that a good 3D model should not only be able to suit all those hypotheses available at present, but also to the ones may be proposed in future.

Liao and Adanur [

points. A unique plane through any point on the center line and perpendicular to it can be defined. By sweeping the base cross-section curve along the points on the center line, all the points that determine the quadrilateral facets are automatically generated by coordinate transformation. The principle is well explained in

Lomov [

In order to reflect the effects of the uneven yarn, Li [

Much work has been done to represent the different shapes of the yarn for the changing of shapes varies due to the flattening and strain. Gong and Ozgen [

Similar to Liao’s method, Zhang [

Jiang and Chen [

Nowadays, using B-spline surface is the most popular method to model the configuration of 3D yarn. B-spline curve technology gives the designer more convenience to model the shape of the yarn accurately. Lin and Newton [

curve, the control points have to be calculated reversely by interpolating points. Unlike Bezier curve, the control points are dependent on the initial conditions, which also causes no uniqueness in control the shape of the yarn. If there is a tiny difference in initial conditions, for example, the positions of the end points change, there may be a big difference in the shape of the curve generated.

Zheng [

Arif Kurbak [

To sum up,

Although realistic rendering technology provided by OpenGL can draw a yarn with shade effect as shown in

Here are some woven models from famous fabric CAD company such as Scot Weave [

Zheng [

Proposer | Method | Cross-section | Central line | Characteristics | Implementing platform |
---|---|---|---|---|---|

Liao, Adanur | Sweeping the cross-section along the yarn path | Uniform ellipse, circle or race-track | Line segment and arc | Auto-generated 3D yarn, flexible | Unknown |

Li | Assembling of circles | Circles of different diameters | Straight line | Straight yarn | MSVB |

Lomov | Assembling of solid | circle | Calculated by WisTex | Uniform cylinder, flexible | MSVC |

Lin, Long | Assembling of a serials of individual sections | Various cross-sections of quadratic B-spline curve, auto-generated by parameters | Bezier curve, calculate by TexGen | Shape and size of the cross-sections can be changed locally in fabric structure to avoid yarn penetrating | Python |

Gong, Azgen | 3D scanning of yarn by ESRF | Polynomial curve | Line segment and arc | The cross-sections are separated | MSVC |

Zhang | Beizer suface | Beizer curve | Cubic Beizer curve | Uniform cylinder | MSVB, |

Jiang, Chen | Spline curve and super ellipse | Uniform Super ellipse | Cubic spline curve, calculate by TexEng | The cross-section of the yarn can be edited, | Borland C, |

Lin, Sherburn | B-spline surface | Various cross-sections | Cubic B-Spline curve | Auto-generated 3D yarn including fancy yarn | MSVC |

Zheng | B-spline surface or NURBS | Various cross-sections of quadratic B-spline curve, auto-generated by parameters | Cubic shape-preserving B-spline curve | Auto-generated 3D yarn including fancy yarn | MSVC, OpenGL |

Zheng, Zhao | Assembling of a serials of individual sections | C-cardinal spline curve, arbitrary shape, | C-cardinal spline curve | Cross-section of the yarn including fancy yarn can be edited manually | MSVC, OpenGL |

Arif Kurbak | Circle and parabolic helix | Circle | Ellipse or parabolic helix in 2 dimensions | Circular cylinder | 3DS-MAX |

In order to improve the twist effects, Zheng [

Zhao [

Sriprateep [

constructed by NURBS. The migration parameters include twisting tension, migration period and amplitude, initial phase and frequency of migration pattern. The geometry of yarn structures is eventually modeled by using the Solid Works CAD software package and the model is validated by imitating the process of spinning rayon yarn (see

A realistic model for 3D yarn should reflect the hairiness effect. Zhong [

Folded yarn comprises of two or more single yarn, so it can be designed if the central paths of all the component yarns are determined. In Zheng [

It is certain that the fancy yarn can be modeled by 3D technology although it is rare. For fancy yarn, there are varied sections along the yarn path. It can be folded yarn whose components are of various color, thickness or configuration in space. Based on Zheng’s [

modeled on the principle. In fact, loop yarn, knop yarn, slub yarn, snarly yarn can also be designed when the frequency/size of the effect spot, path/color of the component single yarn are designed. Based on C-Cardinal spline curve, Zhao [

Zhuge [

If the geometric structure in a woven, knitted or braid fabric is calculated, or in other words, the shape and the path of the each yarn in fabric is determined, the 3D geometric structure of the fabric can be imitated.

Multiple approaches have been reviewed for modeling 3D yarn geometric configuration. The yarns are shaped on the theory of Peirce while the 3D constructing technology is based on Computer Graphics. And all the methods are related with designing the cross-sections along the yarn path. Comparatively speaking, the method based on spline curve is the most popular one since it gives the most flexibility in designing not only non-uniform single yarn with different cross-sections and twist effect, but also folded yarn, fancy yarn including slub yarn, knep yarn. The yarn can bent or deform in 3D space freely so it can be used in woven fabric’s structure conveniently. The model can also be applied to the structure of the knitted fabric, braided fabric so long as the central line of the yarn is given.

Authors would like to thank Henan Provincial Collaborative Innovation Center for Textiles and Appeals, Zheng- zhou Municipal Bureau of Science and Technology for supporting the research.