圆环面上纤维轨迹的计算机辅助设计

曲面上的曲线造型是计算机图形领域的一个新的研究热点，而且它们在纤维织物编织，三维服装裁剪以及复合材料的纤维缠绕轨迹设计等领域有十分广泛的应用，为了解决圆环面上纤维轨迹的计算机辅助设计问题，研究了圆环面上测地线的解析解以及拟测地线数值求解的具体算法并给出了其表达式，测地线是曲面上两点之间最短距离的曲线段，在一般曲面上没有解析解，但是在圆环面上却可求出其精确的解析解，但在曲面的边沿部分，测地线因不能实现自然的折返过渡，于是拟测地线就被引进到曲面上的曲线造型设计之中，在拟测地线分析研究基础上，给出了圆环面上拟测地线的方程及数值解法，通过其在一个实例中的应用结果证明，该方法可获得织物的纺织条纹以及缠绕物体的纤维轨迹。

Computer Aided Fiber Path Design to Torus in Filament Winding

Curve modeling on curved surface is paid much more attention recently because of its wide application in industry, which include fiber weaving, 3D garment clipping design and composite material product design. Computer aided design for filament winding is a basic technique in the area of production of composite materials. Torus is a typical product made of composite material; they are used as tube joints widely in chemistry and oil industry. The manufacture of torus is usually by means of filament winding. The main step for filament winding is fiber path design. The design of fiber path on torus is main topic of this paper. In the first part of the paper, the fiber path is designed as geodesics, the solution to the geodesics on a torus is discussed; in the second part of the paper, a formula for computing the semi geodesics on a torus is derived, a numerical calculation for semi geodesics from the formula is analyzed in detail. Lastly, the method is applied in a practical example.