Pattern flattening for orthotropic materials

In many applications it is necessary to define good-fitting 2D flattened patterns for user-defined regions of a larger 3D surface. This paper describes the major stages involved in pattern flattening and illustrates the process with examples. In generating 2D patterns, some distortion is inevitably involved if the target 3D surface is not developable. For situations where distortion is required, it can be quantified in terms of the energy that must be imparted to the 2D flattening in localised areas so that it takes-up the original 3D region of the surface. An orthotropic strain model is adopted to convert the strain values to energy values. Starting with a bi-parametric definition of a large 3D surface, an arbitrary defined region is specified by the user in terms of a contiguous series of cubic curves lying on the bi-parametric plane. To extract the 3D region, a polygon list is generated to represent the surface. The triangulation process is based on a 'marching front' algorithm. A process is described which then flattens this polygon list and performs an energy minimisation analysis every time the process attempts to flatten an over-constrained triangle. Further consideration is made of seam insertion in the 3D surface definition and of adaptively modifying the triangulation process so that more triangles are used in areas of high-energy concentration. Examples are also presented to illustrate the sensitivity of the strain profiles to the fabric grain direction when the pattern is applied to the 3D surface.