Draping 2D patterns onto 3D surfaces using geodesic curves

This research studies the issues related to the draping algorithm using Geodesic Curves. The main work here is the development of a simple new CAD operator that allows draping of given 2D patterns onto a 3D mold. The 2D pattern is any closed, connected polygon or a polygonal approximation of a shape bounded by curves. The mold can be any well behaved composite surface made up of twice differentiable patches; here it will be assumed to be a NURBS or B-Splines surface. The basic idea of draping is to map skeletal lines on the 2D pattern onto corresponding geodesic curves on the 3D surface. A major difference between the proposed method with the past works is that we are doing the inverse mapping of surface development, which flattening a sheet covering the 3D surface into an equivalent 2D pattern. We also explore how to minimize the distortion caused by the draping function due to the non-developable surface, by developing the algorithm that using the properties of geodesic curves. The draping function is implemented within commercial CAD system, and examples are provided to demonstrate its performance. The motivation of this research is consistent with our major application area, which is footwear design. A direct application in this industry, which is an important sector in Hong Kong manufacturing, can be obtained