This paper presents a novel method for mapping a texture for machining onto a freeform surface. When a grain texture designed on a 2D plane is projected onto a freeform surface simply, the texture is distorted along the curvature of the surface in the projection direction. Therefore, a method is required to suppress this distortion. The algorithm proposed in this paper rapidly generates a point cloud that represents a texture with less distortion on a simply connected parametric surface. Specifically, four equations that express local geometry constraints instead of conventional parameterization methods are presented to reduce the distortion between adjacent points on the point cloud. Solving these equations can generate grain textures on freeform surfaces. This paper examines two grain images mapped to two freeform surfaces that were prepared as case studies to demonstrate the effectiveness of the proposed method.

本文提出了一种新颖的方法，用于将要加工的纹理映射到自由曲面上。当在2D平面上设计的纹理简单地投影到自由曲面上时，该纹理会沿着曲面的曲率在投影方向上变形。因此，需要一种抑制这种失真的方法。本文提出的算法可快速生成一个点云，该点云表示简单连接的参数曲面上变形较少的纹理。具体来说，提出了四个表示局部几何约束的方程，而不是传统的参数化方法，以减少点云上相邻点之间的失真。求解这些方程式可以在自由曲面上生成晶粒纹理。