The mapping of raster images on plane isometric grid

Abstract

Drawing images on curvilinear shapes with the least distortion takes place in many design tasks. In most ways, build a grid, each elementary cell of which is painted a given color. In this problem it is necessary to solve two main problems: the first - to carry out the formation of a given curvilinear grid with elementary cells in the form of squares, which are called isometric (or isothermal); the second is to paint each cell of the curved area with the corresponding pixel color of the original raster The aim of the study is to reveal the way of displaying raster images on flat curvilinear areas represented by isometric grids, and with the help of a computer model in the Maple symbolic algebra to analyze the influence of isometric grid parameters on the position and size of displayed raster images. 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. 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 and arguments of the various isometric grids 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 and 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 and coordinate lines. It is shown the possibility of scaling a raster image that can be performed relative to the relative dimensions of an isometric grid. Since there is a correspondence between the pixel matrix of the original raster image and the - 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 coordinate lines to along the coordinate lines. Note that, the curvilinear cells of the constructed isometric grids differ somewhat from the shape of the squares because the values and of the corresponding arguments and 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.