THE MAPPING OF RASTER IMAGES ON PLANE ISOMETRIC GRID

Abstract

The mapping of images onto curvilinear forms with minimal distortion takes place in many design tasks. A method of conformal mapping of arbitrary raster images onto plane curvilinear region is proposed, which are represented by isometric (also called isothermal) grids. Using the developed computer model in the Maple symbolic environment, the effect of the isometric grid parameters on the position and size of the mapped raster images is analyzed. When performing the research, the capabilities of the powerful ImageTools library are used. The formation of flat isometric grids is carried out with the help of the author of the library of designing functions of isometric grids with different initial conditions. The essence of the proposed method is as follows. Any raster image, for example, digital photography in jpg format, is characterized by the dimensions N×M – the number of pixels in width and height. In addition, each pixel has a color and brightness, which are arranged in rows and columns. To apply a raster image to a curvilinear region, it is also necessary to divide the curvilinear domain into N×M, the number of elementary squares, each of which is assigned the corresponding color from the raster. The influence [ .. ] 1 2 u = u u and [ .. ] 1 2 v= v v arguments of the various isometric grids R(u,v) constructed on the sizes and positions of an arbitrary raster image are investigated in the article. It is shown how the isometric grid, depending on u and v localizes the raster image − it can be located both within the limits of the isometric grid coordinate lines and beyond it, can also be oriented in different directions with respect to the u and v coordinate lines. The possibility of scaling a raster image that can be performed relative to the dimensions of an isometric grid is shown. Since there is a correspondence between the pixel matrix of the original raster image and the u,v - cells of the isometric grid, the rotation of the image will affect its position in the isometric grid. For example, rotating the original bitmap image at an angle 90 degrees will change its location on a plane isometric grids – from along the u coordinate lines to along the v coordinate lines. Note that, the curvilinear cells of the constructed isometric grids differ somewhat from the shape of the squares because the values du and dv of the corresponding arguments u and v of their coordinate lines were taken somewhat too large. Otherwise, cells would degenerate into points and the corresponding grid image would not be so clear.