Bitmap rotation, raster shear, and block diagram construction

Abstract This paper describes the mathematical theory required to construct block diagrams on a personal computer and presents output of a working Macintosh program written by the author. As is common in graphics-intensive applications, efficiency of computation is more important than succinct solution of equations. When applied to thousands of pixels, traditional methods of calculation are much too slow to permit interactive control of bitmapped images. Instead, the images on the sides of a block must be obtained by deformation. Despite appearances, no orthogonal rotation tensors are employed; instead, images are manipulated by shear displacement of rows or columns of pixels. This process has implications for strain studies; oblique superposition of simple shear zones of the same sense may lead to highly rotational deformation states with very little distortion.