vplotraster - A guide to using raster plotting commands in vplot graphics
Despite the name vplot (where the `v' once stood for `vector') the vplot metalanguage includes raster plotting capability. This document describes more detailed aspects of raster plotting than are included in the vplot manual page.
A raster is a rectangular array of bytes. The value stored in each byte
determines the number of the color that is to be displayed at the
corresponding location in the raster. The mapping of array values to colors
is set up by the programmer by calling the
vp_coltab() routine, which may be found in libvplot.a.
To define a color using vp_coltab(),
the red, green, and blue components of the color are each specified as
floats from 0. to 1., with 1. being fully on and 0. being fully off. The
corresponding `grey level' for grey-scale devices is given by the formula
floor((4 * green + 2 * red + blue + 6)/7).
Each device has a number of settable colors (call this number N). Calling vp_coltab() for colors 0 through N-1 will redefine the desired color. If you attempt to define a color X outside of the range 0 through N-1, vplot will pick the color number in the range 0 through N-1 that is closest to color X in color and map all requests for color X to that color number. Whenever any color in the range 0 through N-1 is changed, all the mappings will be recalculated (although of course what is already drawn cannot be changed). Note that color 0 is the background color. Other colors will be mapped to color 0 only if the match is exact.
As an example, consider the common case where an eight bit per pixel raster is to be displayed using a grey scale, ranging from black to white, and various colors are to be used to display labels on the plot. The calling program should call vp_coltab to allocate the first few color numbers to the label colors, then fill the remainder of the lower half of the color scale (up to color 255) with the needed grey scale colors. Because different devices have different numbers of settable colors, it is important to order the grey scale colors so that the most important ones such as black (0, 0, 0), white (1, 1, 1), and medium grey (.5, .5, .5) come first. Then whatever the number of settable colors, the raster reproduction will be as good as possible. More explicitly, the calling program should repeatedly cover the 0 to 1 range with a decreasing step size, taking care not to repeat colors, i.e., (0, 0, 0), (1, 1, 1), (.5, .5, .5), (.25, .25, .25), (.75, .75, .75), (.125, .125, .125), (.375, .375, .375), etc. Then in the upper half of the color scale (colors 256 through 511), the calling program can define the grey scale colors corresponding to the raster array values, setting, for example, color 256 to (0, 0, 0), color 257 to (1./255., 1./255., 1./255.), color 258 to (2./255., 2./255., 2./255.),..., and color 511 to (1, 1, 1). (This is all a bit tricky to implement, of course, so we have written a libvplot utility to help you do this: vp_rascoltab().) The .B offset parameter in vp_raster is used to reference these colors. For this example, offset=256 would be the appropriate specification. Then for each value in the raster array, vplot adds 256 to it to find the grey scale color defined for that value, then (using the mapping to available colors) uses the available color that best matches the requested color to plot that raster element.
Monochrome devices such as plotters are unable to give a good representation of grey rasters because of the lack of definable colors. For such devices, vplot can dither the image to simulate a grey or continuous-tone image. Briefly, dithering methods represent a continuous-tone image on a bilevel display by varying the threshold value that determines whether a given output pixel is set to `on' or `off' given its value on input. Consider the above example of an eight bit per pixel raster. This means that, on an appropriate graphics display, each pixel can take on any of 256 different intensity levels. The task of dithering is to represent such an image on a device that has only two different intensity levels. A crude way of transforming from continuous-tone to bilevel form would be to divide the continuous-tone intensity range in half, and set input intensities 0-.5 to `off' and .5-1 to `on'. But this would neglect most of the continuous-tone information. Vplot has four better ways of performing this transformation built in.
Random dither randomly selects a threshold value for determining whether a given output pixel is set to `on' or `off'. This preserves much of the continuous-tone information, but gives a rather `noisy' image, since within a constant-intensity region of the raster, some pixels will be set to both `on' and `off' due to the random thresholds.
Ordered dither applies a sixteen by sixteen matrix of threshold values to the input image in checkerboard fashion. This gives a much more regular appearance on output.
The minimized average error method or Floyd-Steinberg algorithm takes the `error' in converting a single pixel to bilevel form into account when converting neighbors, with the goal of minimizing the difference between the continuous-tone and bilevel images. This method generally produces the best representation of the original image, though it is the slowest of the four algorithms.
Digital halftoning is an ordered-dither scheme that is designed for images that are going to be reproduced photographically. The high-frequency alternation of black and white samples that is used to produce grey levels in ordered dither is not reproduced faithfully by photocopiers. This algorithm uses lower-frequency alternation of samples to produce the same grey level. While the resulting image has a coarser texture, it will be reproduced accurately. This method is especially recommended for images that will be reproduced photographically.
The dithering method can be selected by use of the dither parameter with any pen filter. The available dithering methods are:
0 No dither (0=off, anything else=on)
1 Random Dither
2 Ordered Dither
3 Minimized Average Error Method
4 Digital Halftoning
Dithered output can be displayed on polytone or color devices by specifying mono=y in the .B pen filter call.
On a typical graphics display, a linear grey scale has a nonlinear appearance. The transition from black to white is more rapid than expected, leaving the scale clipped at both ends. This perceived nonlinearity is due to the characteristics of the human eye, which sees a linear change in brightness as a logarithmic change, as well as to the display characteristics of the device being used. When a grey scale is displayed on paper using the dithering methods described above, the nonlinearity is no longer present. Such images seem to have a washed out appearance because of the relative scarcity of pure black and white shades. The nonlinearity of display devices seems to be a useful feature that one might wish to duplicate on paper. The pen filter parameter greyc (short for `grey correction') modifies the grey scale used to display a raster to simulate the nonlinearity of displays. The grey scale is multiplied by a cubic polynomial with greyc determining the exact shape of the polynomial. The function has been constructed such that the ends and middle of the grey scale are left undisturbed, but on either side of the middle the grey scale is skewed towards the end of the scale (black or white). Greyc=1. leaves the grey scale undisturbed, and values smaller than 1. skew the scale as described above. We have found greyc=-0.5 to yield plots on our Imagen laser printer that are very similar to images displayed on our Rastertek graphics display. Some experimentation is undoubtedly required for other devices. Once a desirable value has been obtained for a particular device, that value should be made the default for the particular device.
A further complication with plotting raster images is the dot size used by the plotter. In displaying a linear grey scale on our laser printer, we found the result to be much darker than expected, especially in the darker half of the scale. Our hypothesis is that the plotter causes adjacent dots to overlap. When the image is mostly white (as in the white end of the grey scale), this overlap is not very important, since it is rare that a given empty spot is surrounded by black dots. However, in the black half of the grey scale, white places in the plotted image are usually surrounded by black dots, and the overlap causes the white space to be much smaller than expected. Hence the plot is darker than expected.
From this hypothesis, we have constructed a function that alters the grey scale to compensate for dot or pixel overlap. The pixc (short for `pixel correction') parameter controls this alteration of the grey scale. Pixc=1. leaves the grey scale undisturbed. Values smaller than 1. shift all the grey values toward white in such a way as to compensate for the darkening that results from pixel overlap. The shift is larger for the dark half of the grey scale, since (from the above discussion) it is more seriously affected by pixel overlap. We have found pixc=0.6 to be an appropriate value for our Imagen laser printer. This value gives accurate reproduction of a linear grey scale.
As with the greyc parameter, once a suitable value has been obtained for a particular printer, the appropriate value should be made the default for that device.
The Vplot source code is copyrighted. Please read the copyright notice which can be found in the Vplot manual page.
The vplothacker doc
Joe Dellinger and Steve Cole
graphics/vplot