Development of Uniform Grain Mapping for Freeform Surface

A grain texture is frequently etched onto a die for plastic forming. Because depth control is difficult and very high skill is required for etching, machining has recently received attention as an alternative method. However, the amount of data for a grain texture for freeform surfaces designed in 3D-CAD is very large. This paper proposes a method for mapping a grain texture onto a freeform surface without distortion that does not utilize 3D-CAD. In the proposed method, the grain texture, in the form of an image, is mapped onto a target surface that is represented by parametric equations. Undistorted grain mapping to a non-developable applicable surface is essential. Equations that represent the isometric projection between the two-dimensional image and the parametric surface are derived. A case study is presented and the effectiveness of the proposed method is evaluated.