纬编针织物线圈的三维模拟及变形实现
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摘要
针织物的仿真技术已经得到了纺织领域的关注,对经、纬针织物的二维线圈及一些三维线圈的仿真已经有了一定的发展,但对三维线圈模型线圈与线圈之间的牵扯而产生力的表现形变的研究却很少。本文以Peirce经典纬编模型为基础,通过对纬编针织物的基本线圈单元(成圈、集圈、浮线、移圈)进行几何结构分析利用三角函数构建线圈曲线段的数学模型利用曲线段的组合来拟合线圈屈曲形态,以线圈模型为基础运用计算机图形学设计原理结合OpenGL(Open Graphics Library)图库利用二维网格模拟由线圈构成的部分织物并关将网格单元与线圈单元动态关联实现线圈受力变形模拟,通过用线圈结构图设计纬编织物实现了从数组到意匠图再到结构图的便捷而直接的仿真,使纬编织物的仿真更直观、快速、准确。
本文首先将一段完整的线圈模型切分成若干以控制点为端点的曲线,用三角函数方程来建立曲线的屈曲形态并利用控制点将曲线以拟合成线圈,运用这种方法来绘制各种能满足纬针织物的线圈模型。利用二维数组的方法,将各种状态的线圈存储在数组之中通过数组排列实现对织物结构的基本模拟,将线圈与二维网格单元动态关联,利用改变矩形单元不同端点区域的位移拉扯矩形单元周围的单元来实现织物上线圈的变形。最终是利用OpenGL的图形工具结合以上原理,完成纬针织物三维动态仿真。
本课题成功的表示了线圈形变的三维图形,使得通过改变线圈的屈曲角度、长度、尺寸以获得各种相互关联线圈互相拉扯而产生变形效果得以实现。当线圈发生形变,线圈周围将发生相应的形变,如果一个目标线圈被纵向拉伸那么纵向线圈将会相应的被拉伸,理论上目标线圈左右的线圈将会相应的变宽。这种对三维线圈模拟的改进理论使得下机织物线圈之间牵扯变形的效果得到提高,改善对针织物设计的可预见性,并且使得织物设计更加高效和准确,极大的缩短生产周期,节省生产成本。
Simulation technique of knitted fabric structure has received much attentions in the textile community. Research and development has concentrated on the simple two-dimensional (2D) loops and some of the three-dimensional (3D) loops in warp and weft knitting structure. This paper on the foundation of Pierce model,make a analysis on the basic model loops(knit loop,tuck loop,float loop, loop transfer) employs the combination of trigonometric functions and lines to stimulate the flexing state of yarns. Based on loop model by using computer graphics design principle combined with OpenGL library using 2D grid simulation constitutes a part of the fabric of loop and close will mesh coil unit with dynamic correlative realize loop stressed deformation simulation, through using loop structure design weft basketwork realizes from array of loop-formed figure to chart to the convenient and direct simulation, make the simulation more intuitive weft basketwork, rapid and accurate.
A unbroken loop has been divided into some curve,a 3D geometry of a series of weft knitted loops are specified which includes the required parameters of the number of loops, planar orientation angle of a loop at the point of connectivity to another loop and dimensions. All 3D geometrical transformations in this section use homogenou column-major 2×2 matrics for loop addtion, traslation, rotation and reflection. All geometrical transformation operators transform loop from model space to world space to position and orient a loop in relation to its parent loop. The weft knitted loop was trasformed from three dimensions to a flattened and segmentd 2D approximation with each loop assuming an trapezoid shape by four corner points and by modifying the four corner points to control the trasformation of this loop.
The project have expressed coil deformation 3D graphics successfully, which made by changing the length of the coil Angle, buckling size to obtain various, interconnected coil mutual drag so the deformation effect can be realized. When the loop deformed the round of the loop are going about the corresponding deformation, if a goal loop by longitudinal extension so longitudinal loop will corresponding stretch, theoretically goals around loop winding will corresponding grows wider. This kind of 3D theoretically simulated improvement means loop can clearly see the fabric stressed deformation effect and improves the predictability of knitted fabric design, and make the fabric design more efficient and accurate, greatly shorten the production cycle, save the cost of production.
本文首先将一段完整的线圈模型切分成若干以控制点为端点的曲线,用三角函数方程来建立曲线的屈曲形态并利用控制点将曲线以拟合成线圈,运用这种方法来绘制各种能满足纬针织物的线圈模型。利用二维数组的方法,将各种状态的线圈存储在数组之中通过数组排列实现对织物结构的基本模拟,将线圈与二维网格单元动态关联,利用改变矩形单元不同端点区域的位移拉扯矩形单元周围的单元来实现织物上线圈的变形。最终是利用OpenGL的图形工具结合以上原理,完成纬针织物三维动态仿真。
本课题成功的表示了线圈形变的三维图形,使得通过改变线圈的屈曲角度、长度、尺寸以获得各种相互关联线圈互相拉扯而产生变形效果得以实现。当线圈发生形变,线圈周围将发生相应的形变,如果一个目标线圈被纵向拉伸那么纵向线圈将会相应的被拉伸,理论上目标线圈左右的线圈将会相应的变宽。这种对三维线圈模拟的改进理论使得下机织物线圈之间牵扯变形的效果得到提高,改善对针织物设计的可预见性,并且使得织物设计更加高效和准确,极大的缩短生产周期,节省生产成本。
Simulation technique of knitted fabric structure has received much attentions in the textile community. Research and development has concentrated on the simple two-dimensional (2D) loops and some of the three-dimensional (3D) loops in warp and weft knitting structure. This paper on the foundation of Pierce model,make a analysis on the basic model loops(knit loop,tuck loop,float loop, loop transfer) employs the combination of trigonometric functions and lines to stimulate the flexing state of yarns. Based on loop model by using computer graphics design principle combined with OpenGL library using 2D grid simulation constitutes a part of the fabric of loop and close will mesh coil unit with dynamic correlative realize loop stressed deformation simulation, through using loop structure design weft basketwork realizes from array of loop-formed figure to chart to the convenient and direct simulation, make the simulation more intuitive weft basketwork, rapid and accurate.
A unbroken loop has been divided into some curve,a 3D geometry of a series of weft knitted loops are specified which includes the required parameters of the number of loops, planar orientation angle of a loop at the point of connectivity to another loop and dimensions. All 3D geometrical transformations in this section use homogenou column-major 2×2 matrics for loop addtion, traslation, rotation and reflection. All geometrical transformation operators transform loop from model space to world space to position and orient a loop in relation to its parent loop. The weft knitted loop was trasformed from three dimensions to a flattened and segmentd 2D approximation with each loop assuming an trapezoid shape by four corner points and by modifying the four corner points to control the trasformation of this loop.
The project have expressed coil deformation 3D graphics successfully, which made by changing the length of the coil Angle, buckling size to obtain various, interconnected coil mutual drag so the deformation effect can be realized. When the loop deformed the round of the loop are going about the corresponding deformation, if a goal loop by longitudinal extension so longitudinal loop will corresponding stretch, theoretically goals around loop winding will corresponding grows wider. This kind of 3D theoretically simulated improvement means loop can clearly see the fabric stressed deformation effect and improves the predictability of knitted fabric design, and make the fabric design more efficient and accurate, greatly shorten the production cycle, save the cost of production.
引文
[1]张佩华,沈为.针织产品设计[M].北京:中国纺织出版社, 2008. 2-10
[2]陈国芬.针织产品与设计[M].上海:东华大学出版社, 2005, 06. 10-22
[3]陈辉,沈毅.关于织物仿真技术的综述[J].丝绸, 2005(08): 42-45
[4]刘哲.羊毛衫计算机辅助设计系统的开发[J].针织工业, 2001, 4: 41-43
[5]邓中明.肖军.小提花织物CAD系统的开发[J].棉纺织技术, 2000, (01): 38-40
[6]邓中民,陈明珍,吕红梅.贾卡提花织物的电脑辅助设计[J].纺织学报, 2000, 24(05): 70-73
[7]李华,王田田,邓中民.建立经编线圈的数学模型及仿真[J].纺织科技进展, 2009. 6
[8]王华,颜钢锋.一种新的小提花织物计算机模拟方法[J].江南大学学报, 2003, (03): 279-282
[9] Tang W.3D CAD visualization of weft knitted fabrics[J]. Textile Asia, 1998(07): 33-37
[10] I. S. Trai. AngelMaiet CAD Technology for Cutting and Design[J]. Knitting Technology, 1966, 18(01): 22-25
[11]刘瑞叶.任洪林,李志民.计算机仿真技术基础[M].电子工业出版社, 2004. 5-20
[12]王辉,方圆,潘优华.纬编针织物线圈模型的分析与研究[J].浙江理工大学学报, 2008, (05): 521-525
[13]吴奕立,颜钢锋.织物计算机模拟显示方法的探索[J].纺织学报. 1999,
[14]汪育桑,冯勋伟.基于几何模型的纬编提花织物结构计算机辅助设计[J].中国纺织大学学报, 2000(6): 66-70
[15]杜虎兵.针织物线圈单元模型分析与线圈长度求解[J].河南纺织高等专科学校, 2007, 3: 12-14
[16]张克和,方圆.针织物结构研究与计算机仿真[J].浙江理工大学报, 2006, (01): 8-12
[17]刘来福,数学模型与数学建模[M].北京:师范大学出版社, 1997. 9. 10-60
[18]许海燕,李炜,冯勋伟.针织基本组织动态模拟[J].东华大学学报, 2001, (04): 88-92
[19]汪秀琛.基于线圈模型的羊毛衫花型仿真模拟[J].毛纺科技, 2009, (12): 51-54
[20]龙海如.针织学[M].北京:中国纺织出版社, 2008, 06. 1-60
[21] Pattern recognition and stitch symbol generating system for knit designing[J]. Computers&Industrial Engineering. 1995, 29(4): 669-673
[22]和平鸽工作室OpenGL三维图形系统开发与实用技术[M].清华大学出版社, 2003, 8.
[23]和平鸽工作室OpenGL高级编程与可视化系统开发[M].中国水利水电出版社, 2003.
[24]范辉. Visual C++6.0程序设计简明设计[M].北京:电子工业出版社, 2001
[25]潘云鹤,董金祥,陈德人编著,计算机图形学原理方法及应用[M].北京:高等教育出版社, 2003, 12. 221-234
[26]张祖媛.贝塞尔曲线的几何构型[J].四川工业学院学报, 1998, (04): 32-35
[27]陈国华. C++ Bezier曲线类的构造[J].江西师范大学学报, 1997, (02): 127-132
[28]王渭彪.三次Bezier曲线反算的C语言实现[J].电脑知识与技术(学术交流), 2007, (11): 24-26
[29]织物结构的数学建模与虚拟成像技术[C].全国第15届计算机科学与技术应用学术会议论文集, 2003. 9: 1/2
[30]史晓丽,耿兆丰.针织三维效果仿真的研究及实现[J].东华大学学报自然科学版, 2003, (03): 47-50
[31] L.H.de Carvalho, J.M.P.Cavalcante, et al. Comparison of the Mechanical Behavior of Plain Weave and Plain Weft Knit Jute Fabric-Polyester-Reinforced Composites [J]. Polymer-Plastics Technology and Engineering. 2006, 45: 791–797
[32] Arif Kurbak, Tuba Aplyildiz. A geometrical model for the double lacoste knits [J]. Textile Research Journal. 2008, 78: 232-247
[33] Hu Jinlian. Theories of Woven Fabric Geometry[J]. Textile Aisa, 1995(1)
[34]柳世龙.线圈几何形态对纬编针织物性质影响的初探[J].上海纺织科技, 1995, (03): 47-48
[35] ZhangY, LiC.Y, XuJ.E.A Micro—mechanical model of knitted fabric in wale direction and the analysis of buckling under tension along wale direction[J]. PartI;Micro—mechanical Model. Acta Mechanica Sinica 20(6). 2004, 623-631
[36]赵龙,兰伟基于弹簧—质点模型的织物仿真算法及其性能分析[J].现代纺织技术, 2007, 3: 15-18
[37]樊劲,周济,王启付,袁铭辉.基于弹簧质点模型的二维/三维映射算法[J].软件学报, 1999, 2: 34-37
[38]惠卫华,关正西.基于质点-弹簧模型的布料仿真研究[J].计算机工程与设计, 2007, (03): 21-24
[39]余昌盛,许力.基于弹簧质点模型的织物变形仿真技术[J].江南大学学报(自然科学版), 2005, 3: 33-36
[40] J.B.Hamilton General system of woven—fabric geometry[J]. J.Text.Inst. T66, 1964
[41] Olofsson,B.A,General Model of a Fabric as a Geometric Mechanical Structure, J. Text.Inst, 1964. 55: 55-89
[42] YitongZhang CuiyuLi JiafuXu. A micro-mechanical model of knitted fabric and its application to the analysis of buckling under tension in wale direction:buckling analysis[J]. Acta Mechanica Sinica, 2005, 21(2): 176-180
[43]龙海如.针织学[M].北京:中国纺织出版社, 2008, 06. 1-60
[44] Munden,D.L. The Geometry of a Knitted Fabric in its Relaxed Condition Hosiery Times, 1961
[45] Arif Kurbak, Ozgur Ekmen. Basic studies for mdeling complex weft knitted fabric structures part: A geometrical model for widthwise curlings of plain knitted fabrics [J]. Textile Research Journal, 2008, 78: 198-208
[46]费奇,孙德宝,王红卫.建模与仿真[M].北京:北京科学出版社, 2002. 1-20
[47] M.M.Toney. Computer Modelling of Fibrous Structures[J]. J.Text.Inst. 2000, Part3: 133-139
[48]官伟波.纬编提花组织的计算机识别[J].针织工业, 2005, (11): 14-16
[49] M.de Araajo,R.Fangueiro and H.Hon91. Modelling simulation of the mechanical behaviour of weft-Knitting fabrics for technical appl ications[J]. AUTEX Research Journal, 2003, 3(4): 169-171
[50] Peirce F.T..Geometrical Principles Applicable to The Design of Functional Fabrics[J]. J.Text.Inst.Transaction, 17, 1947:123
[2]陈国芬.针织产品与设计[M].上海:东华大学出版社, 2005, 06. 10-22
[3]陈辉,沈毅.关于织物仿真技术的综述[J].丝绸, 2005(08): 42-45
[4]刘哲.羊毛衫计算机辅助设计系统的开发[J].针织工业, 2001, 4: 41-43
[5]邓中明.肖军.小提花织物CAD系统的开发[J].棉纺织技术, 2000, (01): 38-40
[6]邓中民,陈明珍,吕红梅.贾卡提花织物的电脑辅助设计[J].纺织学报, 2000, 24(05): 70-73
[7]李华,王田田,邓中民.建立经编线圈的数学模型及仿真[J].纺织科技进展, 2009. 6
[8]王华,颜钢锋.一种新的小提花织物计算机模拟方法[J].江南大学学报, 2003, (03): 279-282
[9] Tang W.3D CAD visualization of weft knitted fabrics[J]. Textile Asia, 1998(07): 33-37
[10] I. S. Trai. AngelMaiet CAD Technology for Cutting and Design[J]. Knitting Technology, 1966, 18(01): 22-25
[11]刘瑞叶.任洪林,李志民.计算机仿真技术基础[M].电子工业出版社, 2004. 5-20
[12]王辉,方圆,潘优华.纬编针织物线圈模型的分析与研究[J].浙江理工大学学报, 2008, (05): 521-525
[13]吴奕立,颜钢锋.织物计算机模拟显示方法的探索[J].纺织学报. 1999,
[14]汪育桑,冯勋伟.基于几何模型的纬编提花织物结构计算机辅助设计[J].中国纺织大学学报, 2000(6): 66-70
[15]杜虎兵.针织物线圈单元模型分析与线圈长度求解[J].河南纺织高等专科学校, 2007, 3: 12-14
[16]张克和,方圆.针织物结构研究与计算机仿真[J].浙江理工大学报, 2006, (01): 8-12
[17]刘来福,数学模型与数学建模[M].北京:师范大学出版社, 1997. 9. 10-60
[18]许海燕,李炜,冯勋伟.针织基本组织动态模拟[J].东华大学学报, 2001, (04): 88-92
[19]汪秀琛.基于线圈模型的羊毛衫花型仿真模拟[J].毛纺科技, 2009, (12): 51-54
[20]龙海如.针织学[M].北京:中国纺织出版社, 2008, 06. 1-60
[21] Pattern recognition and stitch symbol generating system for knit designing[J]. Computers&Industrial Engineering. 1995, 29(4): 669-673
[22]和平鸽工作室OpenGL三维图形系统开发与实用技术[M].清华大学出版社, 2003, 8.
[23]和平鸽工作室OpenGL高级编程与可视化系统开发[M].中国水利水电出版社, 2003.
[24]范辉. Visual C++6.0程序设计简明设计[M].北京:电子工业出版社, 2001
[25]潘云鹤,董金祥,陈德人编著,计算机图形学原理方法及应用[M].北京:高等教育出版社, 2003, 12. 221-234
[26]张祖媛.贝塞尔曲线的几何构型[J].四川工业学院学报, 1998, (04): 32-35
[27]陈国华. C++ Bezier曲线类的构造[J].江西师范大学学报, 1997, (02): 127-132
[28]王渭彪.三次Bezier曲线反算的C语言实现[J].电脑知识与技术(学术交流), 2007, (11): 24-26
[29]织物结构的数学建模与虚拟成像技术[C].全国第15届计算机科学与技术应用学术会议论文集, 2003. 9: 1/2
[30]史晓丽,耿兆丰.针织三维效果仿真的研究及实现[J].东华大学学报自然科学版, 2003, (03): 47-50
[31] L.H.de Carvalho, J.M.P.Cavalcante, et al. Comparison of the Mechanical Behavior of Plain Weave and Plain Weft Knit Jute Fabric-Polyester-Reinforced Composites [J]. Polymer-Plastics Technology and Engineering. 2006, 45: 791–797
[32] Arif Kurbak, Tuba Aplyildiz. A geometrical model for the double lacoste knits [J]. Textile Research Journal. 2008, 78: 232-247
[33] Hu Jinlian. Theories of Woven Fabric Geometry[J]. Textile Aisa, 1995(1)
[34]柳世龙.线圈几何形态对纬编针织物性质影响的初探[J].上海纺织科技, 1995, (03): 47-48
[35] ZhangY, LiC.Y, XuJ.E.A Micro—mechanical model of knitted fabric in wale direction and the analysis of buckling under tension along wale direction[J]. PartI;Micro—mechanical Model. Acta Mechanica Sinica 20(6). 2004, 623-631
[36]赵龙,兰伟基于弹簧—质点模型的织物仿真算法及其性能分析[J].现代纺织技术, 2007, 3: 15-18
[37]樊劲,周济,王启付,袁铭辉.基于弹簧质点模型的二维/三维映射算法[J].软件学报, 1999, 2: 34-37
[38]惠卫华,关正西.基于质点-弹簧模型的布料仿真研究[J].计算机工程与设计, 2007, (03): 21-24
[39]余昌盛,许力.基于弹簧质点模型的织物变形仿真技术[J].江南大学学报(自然科学版), 2005, 3: 33-36
[40] J.B.Hamilton General system of woven—fabric geometry[J]. J.Text.Inst. T66, 1964
[41] Olofsson,B.A,General Model of a Fabric as a Geometric Mechanical Structure, J. Text.Inst, 1964. 55: 55-89
[42] YitongZhang CuiyuLi JiafuXu. A micro-mechanical model of knitted fabric and its application to the analysis of buckling under tension in wale direction:buckling analysis[J]. Acta Mechanica Sinica, 2005, 21(2): 176-180
[43]龙海如.针织学[M].北京:中国纺织出版社, 2008, 06. 1-60
[44] Munden,D.L. The Geometry of a Knitted Fabric in its Relaxed Condition Hosiery Times, 1961
[45] Arif Kurbak, Ozgur Ekmen. Basic studies for mdeling complex weft knitted fabric structures part: A geometrical model for widthwise curlings of plain knitted fabrics [J]. Textile Research Journal, 2008, 78: 198-208
[46]费奇,孙德宝,王红卫.建模与仿真[M].北京:北京科学出版社, 2002. 1-20
[47] M.M.Toney. Computer Modelling of Fibrous Structures[J]. J.Text.Inst. 2000, Part3: 133-139
[48]官伟波.纬编提花组织的计算机识别[J].针织工业, 2005, (11): 14-16
[49] M.de Araajo,R.Fangueiro and H.Hon91. Modelling simulation of the mechanical behaviour of weft-Knitting fabrics for technical appl ications[J]. AUTEX Research Journal, 2003, 3(4): 169-171
[50] Peirce F.T..Geometrical Principles Applicable to The Design of Functional Fabrics[J]. J.Text.Inst.Transaction, 17, 1947:123