Affine transformations for digitized spatial data in geology

Affine transformations are among the most basic and useful geometrical operations in computer applications in geology. Homogeneous coordinates extend their applicability. The methods are essential in handling digitized Iocafional data and are applicable widely in other graphical applications such as calibrating data sets for plotting, and in shape comparison and spatial analysis. Affine transformations alter the length of lines and the angles between them, whereas straight lines remain straight, parallel lines remain parallel, and the ratio in which a point divides a line remains the same. Their geometrical significance indicates that they can he visualized readily, and the corresponding operations in matrix algebra provide a straightforward method of computer implementation. A transformation matrix is calculated from four calibration points, the coordinates of which are known before and after transformation. Multiplication of coordinates in the initial frame of reference by the transformation matrix converts them to coordinates in the new frame of reference. A listing of relevant FORTRAN programs is given, with examples.