Fitting Woven Fabric to Surfaces in Three Dimensions

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Abstract
A computational method is presented for fitting woven fabric to nonalgebraic surfaces by using numerical-analysis techniques. The method is based upon modelling the process of smoothing fabric over a surface. Fabric co–ordinates are mapped onto the surface to be fitted. No assumptions are made about the surface to be fitted other than that it is continuously differentiable. Important assumptions made about the fabric are that warp/weft intersections act as pivot points and that the distance between adjacent warp and weft intersections is small enough for the curvature of the surface to be nearly constant between intersections. The method presented produces results that agree well with empirical data and with values calculated by using Hack and Taylor's fitting equations for surfaces of rotation. The method presented, however, can be used for any surface, whether or not an analytical equation is available.

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