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.