图形变换的几何化表示——论图形变换和投影的若干问题之一

Geometric Representation of Graphics Transformation

对已有文献中一般采用分离的齐次坐标矩阵的图形变换叙述方法做了比较大的改进根据仿射变换理论,从几何计算的理论和算法出发,探索了图形变换的几何化表示机制将图形变换与基本几何有机地联系在一起,用有向直线求解系列函数构筑图形变换齐次矩阵,统一了平移、旋转、错切。

This paper is focused on geometric representation of graphics transformations, and makes an improvement on the methods of transformation description, commonly given in text books with the homogenous coordinate matrix in separation. Based on affine transform theory and geometry computing theory and algorithm, geometric representation of graphics transformation is probed in the paper. By associating graphics transformation with basic geometry, various fundamental transformations, including translation, rotation, shear, symmetry and scale, are unified through a homogenous matrix constructed by a solution in terms of directed lines.