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 HiGraf - Graphics Plot Routines [BGI]  John Farrell 13.11.1989

Набор программ, демонстрирующих методы построения графиков в линейных и логарифмических координатах. Для запуска требуется драйвер EGAVGA.BGI v2.0.
A set of high level graphics routines in Turbo Pascal 5.x that can be used for scientific graphics. Four demo programs demonstrates a cursor and crosshairs, plotting data and curves with log or linear axes by contour lines in color and a "color contour" plot. egavga.bgi v2.0 required.



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HiGraf Graphics Routines John Farrell and D. B. Holtkamp All of these routines (except the contour plotting routines) are copyrighted (1989) by John Farrell and David B. Holtkamp, Los Alamos, New Mexico. The contour plotting routines are copyrighted (1988) by Neil Judell, Optimal Systems, Laboratory,Plainfield, NJ. These routines are released to the Public Domain and may be freely distributed. They may not be resold by anyone (besides us, of course!). These routines are a set of high level graphics routines in Turbo Pascal (version 5.x) that can be used for scientific graphics. The header of the unit is appended to this writeup. Four demo programs are included that demonstrates many of the routines. The first (GRAFTEST.PAS) demonstrates the core routines of plotting data and curves with log or linear axes. There is a contour plotting demo (CONTEST.PAS) that synthesizes some data and plots it in contour plots of three different types: contour lines in color, contour lines in monochrome, and a "color contour" plot. The other two routines demonstrate the cursor (CRSRTEST.PAS) and crosshairs (CRHRTEST.PAS) packages in HiGraf. First, a couple of words about graphics directories and hardware. If the "TPDirectory" compiler directive is defined at the top of HIGRAF.PAS, the BGI routines will automatically detect the graphics hardware present in your machine and load a graphics driver from a directory "C:\TP" (this directory is defined in a procedure named Initialize_Graph in HiGraf). If the "DefaultDirectory" compiler directive is defined, then InitGraph will look for the BGI drivers in the default directory. If you wish to force the BGI routines to run in a particular graphics mode (i.e. the IBM8514 or ATT400 mode on a Compaq) or use the AutoMode detect function in InitGraph, choose the desired compiler directive to suit your taste. The program calling the HiGraf routines must use two data types defined in HIGRAF: TYPE FLOAT = EXTENDED; LINLOG = (lin,log); These are used in the routines along with more familiar data types. The basic sequence for using the HiGraf routines is to : Initialize_Graph; {sets up hardware} Setup_Graph(....); {sets up software variables, etc} Axes(...) or Frame(...); {displays axes} Label_Axes(...); {labels axes} TopTitle(...); {labels the top of the plot} XAxisTitle(...) and YAxisTitle(...); {axes labels} (do plotting commands: PlotData(...) or PlotPoint(...) or combinations of Move(...) and Draw(...) or somesuch) Then Pause somehow... CloseGraph; {BGI closout of graphics} That's all there is to it. Take a look at the demo program (GRAFTEST.PAS) for more complete details and examples. This short example program displays two plots with linear and log axes, data points, and other features. The following is a listing of the routines in the HIGRAF.PAS unit. A couple of definitions are in order first: World Coordinates: this coordinate system is the one usually used for the plot data; these are FLOAT variables describing the data values: i.e. x=1.27,y=1.366E-4, etc. Screen Coordinates: these are the INTEGER numbers describing the pixel addresses of each pixel; the upper left corner of the physical screen is (0,0) in screen coordinates. Additional Routines in SCALING.PAS Another useful procedure is in SCALING.PAS; often in producing plots, you have an array of data (with or without error bars) that must be autoscaled. Scale_Axis (in SCALING.PAS) takes pointers to these arrays, the type of array it is (Byte, Word, etc), the number of values, and the type of plot the axis is (Log or Linear). It returns "nice" values for the minimum and maximum limits on the axis to be plotted and a nice value for the axis labeling interval. One way to use it is: Scale_Axis(XData,NIL,Byte_Array,100,XWorldMin,XWorldMax, XLabelArg,Lin); Scale_Axis(YData,NIL,Byte_Array,100, YWorldMin,YWorldMax,YLabelArg,Lin Setup_Graph(XWorldMin,XWorldMax,YWorldMin,YWorldMax, 15,90,15,85,Lin,Lin); Axes(0,0,XLabelArg/5,YLabelArg/5,5,5,FALSE); Frame(XLabelArg/5,YLabelArg/5,5,5,FALSE); Label_Axes(XLabelArg,YLabelArg); This would give you "nice" axes with 5 minor tick marks between axis labels in both X and Y. Rapid Contour Plots By Bilinear Patch by Neil Judell, Optimal Systems Laboratory, Plainfield, NJ In this technique, the points of the original data array are viewed as being samples of a function that is continuous, with piecewise continuous partial derivatives. This function is presumed to be bilinear within the squares delineated by the data points. In order to prepare the contour plot of the entire region, we merely prepare a contour plot of each square "patch" delineated by four adjacent data points. There is one potential problem with this method, and that is if a contour value is exactly equal to one of the data values (one of the values exactly on the corner of a patch), then the plot becomes ill-conditioned. In the software example provided, this is readily prevented. The data values take on only integer values, while the contour levels are floating point. We simply prevent any contour value from taking on an exact integer value by adding a small number (constant called epsilon) if we determine that the contour value is an exact integer. Once this conditioning problem is resolved, it may readily be seen that within a single patch, for a specified contour level, exactly three possibilities exist: no contour line crosses the patch, determined if the contour level is either less than the minimum of the four corner values or greater than the maximum of the corner values; one contour line crosses the patch; or two contour lines cross the patch. In the case where one contour line crosses the patch, the bilinear equation is solved for the endpoints of the contour line and the line is plotted. In the case where two contour lines cross the patch, we determine the four endpoints, and then must decide which pairs of endpoints to match to draw the appropriate contour lines. Define the bilinear coefficients for the patch in a coordinate system local to the patch, so that the x value ranges from 0 to 1 and the y value ranges from 0 to 1, and let the bilinear equation be: value(x,y) = ax + by + cxy +d. If we now attempt to parametrize the contour line in x in terms of y we find: x = (value - contour level - by - d)/(a + cy). We then see, that because of the nature of the local coordinate system, one of the contour lines must have the y value of both of its endpoints greater than -a/c, and the other contour line must have both of its endpoints less than -a/c. (It should be noted that because of the non-integral nature of the contour level, we cannot have two contour lines in a patch when c=0). This means that if we simply sort the four endpoints in increasing value of their y- values, that the two endpoints with the lowest y-values form a pair for one contour line and the two endpoints with the highest y-values form a pair for the other contour line. In the software example provided, contour lines are approximated by drawing straight lines from one edge of the bilinear patch to the other. In cases where the number of data points are large relative to the screen pixel density (say 20 x 20 data points for an EGA display), this is adequate for reasonable contour plots. If the data are sparse, it may be desirable to plot the contour line more accurately within the patch, using the parametrized equation above. The software example provided contains the definitions used for the contour plotting software, and the pointers to the data array and the contour level array. The procedure for allocating memory to these arrays must be user provided. The data array pointer is called data_array_pointer, which points to longint data points, via: data=data_array_pointer^[x]^[y], with 1<=x<max_x_size and 1<=y<max_y_size. The contour level array points to type float , and is accessed via: contour level = contours[i], with 1<=i<max_contours. The only procedure available for external calling is Contour_Plot, which performs the entire plot function. The test program, CONTEST.PAS, is a skeleton of a general user program employing the contour plot modules. It performs the operations minimally necessary for operation. First, it allocates storage. Then, it fills the data array. In this example, the data array consists of a sum of two two- dimensional Gaussians plus noise. The contour level array is then filled with values (which should be in ascending order). Initialize_Graph is called to set the display to graphics mode, Contour_Plot is called to perform the plot, and finally CloseGraph is called to return the display to text mode.