Distortional Properties of the Bijective Pattern Map (Part II: Change of Reference)

This is the part n of the study of distortion property of the Bijective Pattern Map maps. In part I, the generic distortion was presented. In this article, the distortion using different set of reference points and pre - image is compared with the result in part I. Moreover, the distortion induced by a change of reference is illustrated with examples. The formulation of the relationship between the distortion and the Gaussian curvature will be followed.     

Detection of Design Fault in Dart Placement - intersecting Dart

It is easy to apply lines in design drawings to create different styles, however, there is no guarantee that all the style lines drawn are able to be manufactured. In this paper, we focus on one undeliverable style to enhance our understanding of the relationship between the design sketch and the pattern design process. In order to evidence that such style is unworkable, a systematic display of pattern development, and to be reinforced by mathematical evaluation, will be introduced and addressed. When one can easily detect design fault, waste of product development time can be minimized.     

DISTORTIONAL PROPERTIES OF THE BIJECTIVE PATTERN MAP (PART I: DISTORTION IN LENGTH)

The Bijective Pattern Map maps the 3D surface patch to the 2D flat pattern. The bijection property has been proved. However, since the 3D Algebraic Mannequin is not developeable, meaning that it is not isometric to the 2D plane, the intrinsic geometry of the 3D surface patches is different from their images on the 2D plane. Consequently, distortion exists. The distortional property of the Bijective Pattern Map is discussed in this article.