' ‘vb .~ .-";. .4‘. o 1‘ r. I v -c—q. v1 w ‘ Him. I. | J to. IHESlS .[ISZWEJ'IJZJEW‘ 2 ., 2‘ '3 2’3 ' E M 5? é‘u’ ’% 34 This is to certify that the thesis entitled A Dot Matrix Printer Method For Representing Smooth Statistical Surfaces presented by William F. Johnson has been accepted towards fulfillment of the requirements for M ° A ' degree in Geography firL/aw/fiwfi Major professor Date I/Uol/Tfe/V/L/U’L :2 L; /? <5; 7/ 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution bV153I_J RETURNING MATERIALS: Place in book drop to LlBRARJEs remove this checkout from w your record. FINES will be charged if book is returned after the date stamped below. A DOT MATRIX PRINTER METHOD FOR REPRESENTING SMOOTH STATISTICAL SURFACES by William Fouracre Johnson A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Geography 1984 ABSTRACT A DOT MATRIX PRINTER METHOD FOR REPRESENTING SMOOTH STATISTICAL SURFACES by William Fouracre Johnson This research examines methods of representing statistical surfaces and problems with their use, particularly the conceptual and perceptual problems associated with conventionally'used representations of smooth statistical surfaces. Development of a symbolization model using random dot matrices is discussed prior to introducing a new method of producing that symbolization with dot matrix printers. The random dot matrix symbolization is then tested against its equivalent isarithmic symbolization in a psychophysical experiment involving the perception of surface form with smooth surface representations. The test includes semantic differential questions to measure map reader attitudes towards these two symbolizations. Two groups of map readers are tested: those familiar and those unfamiliar with the isarithmic symbolization, Results from this paired difference test show that both groups of map readers favor the isarithmic symbolization over the random dot matrix symbolization, but the difference in surface form perception between the two symbolizations is not statistically significant. It is concluded that dot matrix symbolization is as effective as isarithmic symbolization, but its application to statistical mapping may be hindered by negative map reader impressions. To Drs. Gardula, Champlin, and Barbato in the department of Geography/Earth Science at Fitchburg State College for encouraging me to pursue a post-graduate degree. ii ACKNOWLEDGMENTS I would be remiss in my responsibilities.if’I did not thank Dr. Richard Groop, my advisor, for his interest and encouragement in this thesis. Many thanks, also, to Dr. Judy Olson for her helpful suggestions and much needed testing expertise. A special and heartfelt "Thank You” goes to J. Michael Lipsey for his endless patience and willingness to help solve my many small crises. Additional thanks to Dr. Gary Manson for providing financial support through departmental assistantships during my studies. Finally, I wish to thank my family for their confidence and support, and my fiancee, Kathy Rottman, for patience and understanding while I finished this thesis. iii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER: I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . MAPPING STATISTICAL SURFACES . . . . . . . . . . . . . . . . Problems with Existing Methods of Surface Representation Continuous Tone Methods for Representing Smooth Surfaces RESEARCH PROBLEM . . . . . . . . . . . . . . . . . . . . . . II. A PROPOSED METHOD FOR REPRESENTING SMOOTH SURFACES . . . . . Technical Objectives . . . . . . . . . . . . . . . . . . The Dot Matrix Printer Method . . . . . . . . . . . . . . Other Applications of the Method . . . . . . . . . . . . III. THE EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . Method of testing . . . . . . . . . . . . . . . . . . . . Hypothesis . . . . . . . . . . . . . . . . . . . . . . . Design of the Test Maps . . . . . . . . . . . . . . . . . Test Administration . . . . . . . . . . . . . . . . . . . IV. RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . Differences in Surface Form Perception . . . . . . . . . Differences in Map Reader Preferences . . . . . . . . . . Discussion of Results . . . . . . . . . . . . . . . . . . iv Page vi vii 1H 15 16 17 23 29 29 33 33 36 H1 nu AG 52 CHAPTER: Page V. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . 55 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 55 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 57 APPENDIX: A. TEST INSTRUMENT . . . . . . . . . . . . . . . . . . . . . . 59 B. ORAL TEST INSTRUCTIONS AND DEMONSTRATION MATERIALS . . . . . 73 C. PROGRAM "DOTMATRX" AND PERIPHERAL PROGRAMS . . . . . . . . . 77 LIST OF REFERENCES 0 O O O O O O O O O O O O O O O O O O O O O O O 89 LIST OF TABLES Table Page 1. K-S test for Normality of Samples . . . . . . . . . . . . ”3 2. Paired T-test with Surface Perception Responses . . . . . ”5 3. T-test for Differences in Means Between Map Reader Groups ”6 u. Paired T-test with 8-D Responses . . . . . . . . . . . . . 48 50 BGtWGBD-GPOUDS T-tOSt for 8-D Questions 0 o o o o o o o o 50 vi Figure 9. 10. 11. LIST OF FIGURES Statistical Surface representations: a. choropleth map b. block diagram c. isarithmic map d. perspective transect model . . . . . . . . . . . . . . . Sample map from the Smith/Groop method for representing smooth statistical surfaces . . . . . . . . . Sample map using a random dot matrix method with pen plotter output . . . . . . . . . . . . . Gray-tone range with the dot matrix printer method . The density function of the dot matrix printer method Sample map showing the dot matrix printer symbology A color-encoded two variable map using the dot matrix symbology . . . . . . . . . . . . . . An example of a dot matrix LANDSAT image . . . . Corresponding dot matrix and isarithmic maps . . Sample dot matrix test map and response choices Sample isarithmic test map and response choices vii Page 10 12 18 21 2“ 26 28 35 37 38 CHAPTER I INTRODUCTION MAPPING STATISTICAL SURFACES Statistical mapping is the symbolic display of numeric data on a map to show the extent, form, and spatial characteristics of that data over two dimensional (x,y) space. The symbols used to represent the data can be thought of as giving the map a third visual dimension, that of height (or z-value) corresponding to the assignment of data values to areas on the map. The conceptual surface of data elevations is referred to as a statistical surface [Robinson, et a1, 1978, p 181, 218]. A statistical surface can take one of two basic forms. If data are collected by areas and are assumed to have uniform value throughout each area, the surface will consist of a number of steps, each having the shape of its collection area and a height proportional to the data value for that area. These are known as stepped, or discontinuous, statistical surfaces and are commonly associated with census-type data gathered by enumeration areas [Monmonier, 1977. p 23; Jenks, 1963, p 16]. Data that are sampled at points from a continuous population and are not assumed to have uniform value over areal units will lead to a smoothly undulating surface. This type of surface, called a smooth 1 2 statistical surface, has continuously changing slope, which is a measure of the relative changes in value over space. Weather data, such as temperature or air pressure, as well as many types of ratio data, are examples that can be thought of as having smooth change across the surface. Construction of a smooth surface is based on the interpolation of values between sample data points, since it is impossible to obtain values for all points in a continuous distribution [Robinson, 1961, p 51!; Jenks, 1963, p 16]. The basic decision in the statistical mapping process is the form of the statistical surface to be represented. Once decided, the secondary decision of appropriate symbol can be made. The most accurate representations of statistical surfaces are produced with symbologies which have characteristics suited to the form of the‘ surface [Jenks, 1963, p 16]. Stepped statistical surfaces should be symbolized with areal symbols that are uniform within each data collection area and show steps or discontinuities at the boundaries of units. Smooth statistical surfaces should be represented such that they have visually continuous slope over the map surface. Cartographers have at their disposal a variety of symbol types suitable for illustrating either form of statistical surface; each of these symbol types suffers from limitations which may deter their use. Stepped statistical surfaces are most commonly represented with choropleth symbology (Figure 1a), where data collection units are shaded in a graded series such that the shading for a unit is proportional in appearance to its data value or class of data values. Alternatively, block diagrams (Figure 1b) may be used which provide a perspective volumetric view with each data collection unit elevated in Stepped Statistical Surfaces ‘3 xii/la, Smooth Statistical Surfaces Figure 1. Statistical surface representations: a. choropleth map b. block diagram 0. isarithmic map d. perspective transect model [from Groop and Smith, 1982, p 1214]. u proportion to its value. Smooth statistical surfaces are most commonly represented with isarithms (Figure 1c), despite evidence suggesting that they provide less easily recognized surface representations [Phillips, et a1, 1975, p 45-6; Griffin and Locke, 1979, p 71]. Smooth surfaces may also be represented with different types of block diagrams, such as perspective transect models (Figure 1d) or "fishnet" models which use perpendicular transect lines across the data surface. Perhaps more familiar is plastic hill shading, often used to represent the land surface. Problems with Existing Methods of Surface Representation Since the purpose of representing a statistical surface is to provide an accurate visual counterpart to the conceptual data surface, there are several objectives that a successful illustration should achieve. First, the data should be accurately represented on the map so that the values of the original distribution can be retrieved. Second, the map should be planimetric, that is, the symbols on the map should be in their correct x,y position so that all data values are correctly associated with their true positions. Third, the form and configuration of the surface should be apparent; stepped statistical surfaces should appear stepped, and smooth surfaces should appear smooth and continuous [Groop and Smith, 1982, p 123-u; Robinson, 1961, p 518]. The traditional symbologies vary in the degree to which they meet these objectives. What follows is a discussion of the perceptual problems associated with surface representation using these symbologies. The choropleth method of representing stepped statistical surfaces 5 is among the most widely used cartographic symbologies. Until Tobler's introduction of "unquantized" choropleth maps in 1973, the main research questions concerning choropleth maps were appropriate class intervals for dividing the data set into generalized groupings and equal appearing tone steps for symbolizing the classes on the map. Proper class interval selection not only affects the look of the map, but largely determines the spread of error in the symbolization [Jenks, 1963, 1967, 1977]. Tobler's unclassed choropleth maps challenged the established ideas that generalized data classes are necessary for consistent map communication. Studies by Peterson [1979] and Muller [1979] confirmed the contention that the greater informational content of unclassed choropleth maps does not reduce their effectiveness. Block diagrams, an alternative to choropleth representation of stepped surfaces, offer an impression of the surface as it would appear in perspective view. The primary drawbacks to their use are loss of planimetry and the likelihood of obscuring at least some part of the surface by units elevated in the foreground. Further, the look of a block diagram is dependent on the view azimuth and inclination of the viewing point [Monmonier, 1977, p 2"; Groop and Smith, 1982, p 125]. The existing methods of portraying smooth surfaces vary considerably in ability to show surface form. Perspective diagrams such as the "fishnet" or surface transect models provide a good visual impression of smooth slope changes that occur with this type of surface, but like block diagrams and other perspective illustrations, the lack of planimetry and the selection of a view azimuth and inclination to minimize hidden parts of the surface are important drawbacks. A study by Rowles [1978] showed that while view angle and 6 inclination do not in themselves determine the interpretability of the surface, they may contribute to perceptual errors. View angle problems are absent from isarithmic maps, as isarithmic maps are planimetric representations of surfaces. The isarithmic symbology consists of a series of lines or isarithms formed by the intersection of horizontal planes with the surface such that isarithms are always perpendicular to slope directions. The slope characteristics of a surface are not shown directly with isarithms, but are represented by the spacing between adjacent isarithms. To facilitate slope interpretation, the isarithmic interval is usually constant on a map, but there are exceptions to this convention, especially if the surface has unusually prominent peaks. Since isarithms provide a series of sample intersections with a surface, the form of the surface can only be inferred. A further complication is that the isarithms themselves are usually based on values interpolated from a limited pool of known data values, very few of which are likely to be coincident with any of the isarithms. The isarithms are thus a "second generation" representation of the surface, and the form of the surface that must be visually'inferred from the isarithms is, in a sense, "three steps removed" from the original data surface. Because isarithms are traces of intersections with the surface at given intervals, surface representation is increasingly generalized as isarithmic interval increases. That is, as the surface is sampled at fewer levels” the amount of information suggesting surface form is deteriorating. This is analagous to data classification, where fewer classes result in greater classification error. The isarithmic model thus has a built-in generalization error which is interval dependent. 7 In addition to the problems of isarithmic generalization, there are demonstrated problems with visual interpretation of the surface. A study by Griffin and Locke [1979] identified eight types of errors in the interpretation of an isarithmic transect profile. The most dominant error was found to be slope reversal, in» the perception of a concave slope despite the isarithmic depiction of a convex slope or vice versa. Interestingly, convex slopes were found to result in consistently greater interpretation errors. The authors concluded that this was a perceptual error caused by texture gradient creating an illusion of depth, rather than a conceptual error. Other researchers have found that isarithms are useful in determining spot values, but are difficult for untrained readers to interpret, especially for visualizing surface form [Phillips, et al, 1975, p #6; Potash, et al, 1978, p 314]. The difficulty of visualizing surface form with isarithmic maps may be due to the lack of information in peripheral vision with this symbology. Interpretation of isarithmic surface representations involves focusing on a limited viewing area where the lines can be seen distinctly [Phillips, 1979, p 75]. The addition of shading tones between isarithms increases the interpretability of the map [Castner and Wheate, 1979. p 83; Potash, et al, 1978, p 3“] but creates the impression of discrete steps, an effect contradictory to the objectives in portraying smooth surfaces. Plastic hill shading does not suffer from the complex perceptual and conceptual difficulties of isarithms. With this technique, a smooth and continuous shading is applied to the map with respect to an assumed illumination direction [Yoeli, 1966; Brassel, 197”]. The surface thus depicted appears as it would with an illumination source 8 striking surfaces that face toward the light and creating shadows on surfaces that face away from the light. This provides.a realistic- looking planimetric surface portrayal, but because the illustration is modelling illumination, different points with the same elevation may not receive the same shading tone, depending on their position relative to the illumination source [Smith, 1980, p 12]. This problem limits its usefulness in representing statistical surfaces, since data values cannot generally be retrieved. In this study, an automated method for portraying smooth statistical surfaces that uses continuous tonal variation will be suggested as an alternative to existing symbologies. The effectiveness of this surface representation will be evaluated in a comparative ‘psychophysical test of surface visualization with the "continuous-tone" method and isarithmic method. Results from this experiment should show whether the continuous tone method of smooth statistical surface representation offers any significant improvement over conventional symbologies. Continuous Tone Methods for Representing Smooth Surfaces The modelling of smooth statistical surfaces with continuous tonal variation is based on the assignment of shading values scaled directly to data values at every point on the map surface. In this way, high data values receive a proportionally darker tone than low data values to create a continuously shaded surface. The gray-tone symbol is thus a continuous function of z-value. Since the symbols are related directly to individual data values, there is no classification error. Planimetry is maintained, and the form of the original data surface is 9 preserved with a minimum of information loss. A method for representing smooth statistical surfaces using continuous-appearing tonal variation was developed by Smith and Groop [Smith, 1980; Groop and Smith, 1982]. Their automated surface representation employed a lattice of finely graduated point symbols to create the visual impression of continuous gray-tone variation across the mapped surface (Figure 2). At each intersection in the lattice, a data value was represented with a point symbol graduated in size proportional to that value. The range of sizes for individual point symbols varies such that the highest data values produce symbols that fill their lattice positions and therefore create maximum tonal density. With a fine enough lattice, the visual effect is not an assemblage of graduated point symbols, but rather a continuous variation in gray-tone. Preliminary testing showed that slope direction can be accurately interpreted with this symbology [Smith, 1980, p 111]. The authors noted several advantages of modelling smooth statistical surfaces with this method. First, there is no depth illusion problem resulting from textural differences in symbol density, such as there is with isarithmic maps. Second, since there is no classification error with the model, the symbolization takes its form directly from the available data rather than from arbitrary decisions such as isarithmic interval. Third, the map remains planimetric, and all data points are accurately scaled. Finallyy the conception of continuous tonal variation is consistent with the type of statistical surface it represents [Groop and Smith, 1982, p 129]. Despite these advantages, the symbology was of limited utility SNOWFALL TOTALS Michigan's Lower Peninsula Figure 2. Sample map from the Smith/Groop method for representing smooth statistical surfaces [from Groop and Smith, 1982, p 128]. 11 because of implementation problems. To produce an impression of continuous tonal variation rather than an impression of an array of graduated point symbols, the lattice used to generate the symbols must be very fine. But since the minimum increment of standard digital plotters is not sufficiently small to produce the necessary fine graduations in point symbol size, the maps were plotted at a very large size and subsequently reduced using photographic methods. Plotting times were generally quite long and expensive, as the pen plotter drew and filled each point symbol at its appropriate size. A further problem with this symbology was the undesirable appearance of visual steps in parts of the surface where steep gradient was present. This was caused by the interpolation routine used to generate the lattice of data values, and it was a significant barrier to the application of this mapping technique [Groop and Smith, 1982, p 129]. Gray tone symbols can also be constructed using randomly placed dots. The automated use of randomly placed dots is not new to cartography. A program from the Harvard Laboratory for Computer Graphics and Spatial Analysis called DOT.MAP (later improved and renamed MIRAGE) which uses random dot placement matrices has been available since the mid-1970's [Dutton, 1978]. This program has not had wide application among the cartographic community, since the output devices, pen plotters or CRT screens, are inefficient at providing reproducible output. More recent efforts by Groop [1982] have resulted in the application of random dot placement matrices to the model for representing smooth statistical surfaces (Figure 3). This symbology used a lattice of cells, each filled with a number of randomly placed 12 dots in proportion to a data value, rather than a lattice of individual point symbols. By keeping the cell size very small relative to map size, variation in tone across the map surface appears to change in a smooth and continuous manner. Data are only generalized to the extent that a sample data point is represented with a cell of dots instead of a single point symbol. Generalization is thus a function of cell size. As cell size approaches zero, the degree of generalization also tends toward zero. Michigan Snowfall Figure 3. Sample map using a random dot matrix method with pen plotter output [Groop, 1982]. The advantages of this symbology were readily apparent. The increment in tonal variation could be reduced to a finer level than with the previous method, since the output device did not have to draw symbols in a limited range of sizes. This helped to reduce the effects 13 of unwanted visual steps in the output, as well as increase the overall "smoothness" of the surface. The practical resolution limit was instead determined by the ability of the pen in a pen plotter to consistently create small dots. Since the size of individual symbols on the surface was greatly reduced by the dot matrix method, maps did not have to be plotted at such large sizes and be drastically reduced to achieve the effect of continuous tonal variation. A more modest reduction of the original pen plotter output was sufficient to create continuous-appearing gray tone variation. The new method was limited by the technical characteristics of the output device, as pen plotters are not well suited to the task of plotting large quantities of dot symbols with consistency and reliability. The dots which form the symbology varied in size and density due to inconsistencies in the flow of ink from the pen. Ina addition, the dots could not be plotted at a size small enough to eliminate the need for photographic reduction. Further, the output was very slow, with small maps taking several hours to plot, while most maps required an "overnight" plot. In an extension of this symbology, Frohnert created unclassed choropleth maps symbolized with the dot matrix technique. While her research was aimed at effectively portraying stepped statistical surfaces, the method she used to create gray-tones is similar to the method used for smooth statistical surfaces. After experiments using random dot matrix unclassed choropleth maps to determine consistency of region generalization and pattern recall, she concluded that "...the dot matrix method holds potential as an effective mapping techniqueua' [Frohnert, 1983, p 61]. 1“ RESEARCH PROBLEM The purpose of this thesis is the development of an effective automated method for representing smooth statistical surfaces using a random dot matrix model and dot matrix printer technology. There are two primary objectives. The first involves the technical development of a continuous-tone mapping technique for representing conceptually smooth data surfaces. Technical development is focused on providing a mapping symbology that satisfies the visual/cartographic objectives for illustrating smooth statistical surfaces, as well as meeting technical requirements such as fast, high-resolution output. The second objective is to discover, through psychophysical testing of map users, whether the desired visual/cartographic characteristics are indeed present in the symbology. One of the essential characteristics of smooth statistical surfaces is continuous slope, which can be constant (linear) or, more likely, variable from concave to convex. Map readers should be able to distinguish these various slope types on the cartographic surface representations to fully understand the map. It is reasoned that if map readers can visualize slopes (and thus surface form) more easily with the proposed dot matrix representations than with the counterpart isarithmic representations, then the dot matrix mapping technique is a more appropriate cartographic symbology for illustrating the basic form of smooth statistical surfaces. CHAPTER II A PROPOSED METHOD FOR REPRESENTING SMOOTH SURFACES The evolution of a dot matrix method for portraying smooth statistical surfaces progressed to the current level on the basis of pen plotter output, a method with inherent production weaknesses. For the technique to see wide-spread application, a different method of producing hardcopy is needed. CRT screens allow fast and efficient plotting times, but do not lend themselves to hardcopy duplication. To copy an image, a photograph of the screen must be taken either directly or with a matrix camera that electronically exposes a film emulsion with the screen image. Neither option is practical for the dot matrix method, especially since the resolution of many screens is too coarse to produce continuous tone maps worthy of duplication. Dot matrix printers create images, usually alphanumeric characters, by filling a predefined print matrix cell (character space) with an appropriate combination of dots. The sports stadium scoreboard and electronic time/temperature signs found outside of many banking institutions are familiar examples of dot matrix technology. Early dot matrix printers printed only fixed character fonts, but a new generation of dot matrix printers can be used to create graphics as well as characters. With these "addressable" dot matrix printers, images of almost any description can be assembled as combinations of individual dots. The print matrix cell is not fixed on these printers, 15 16 so larger cell images may be printed in successive printing passes as the paper advances through the printer. One of the greatest attractions of these printers is their low cost and almost universal availability. Nearly every microcomputer is capable of driving one, and computer users are far more likely to have access to a dot matrix printer than other output devices such as matrix cameras or pen plotters. Technical Objectives Dot matrix printers are designed to print dot image graphics quickly, accurately, and consistently. Add to these advantages their low cost and wide availability, and it should be clear that the adaptation of the random dot matrix technique to dot matrix printer technology is a logical step. Given the limits and capabilities of dot matrix printer technology, the development of a new method for producing continuous-tone surface representations has these primary technical objectives: 1. Create a dot matrix symbology with continuous-appearing tonal variation which possesses visual/cartographic characteristics suitable for representing smooth statistical surfaces. 2. Provide fast, easy, hardcopy output which does not require subsequent photographic steps to reach final (useable) form. 3. General adaptability of the method -- use of the method should not depend on specific brands or models of computer equipment to operate successfully. The method should also be flexible enough to create random dot areal patterns for other mapping needs, such as unclassed choropleth maps similar to those investigated by 17 Frohnert. This is the least critical of the objectives, though it remains a desireable goal. The Dot Matrix Printer Method The technical development of the method is based on a family of programs written in BASIC for use with an IBM Personal Computer. Two of the programs are used for entering data and laying out the map cell structure, respectively. In addition, there is an interpolation program used to compute a matrix of data values from known control point values. These programs are essentially peripheral to the method, as they are used only to prepare input files needed to run the main program. Input files need only be prepared only once; program runs can be made as often as desired using prepared files. The heart of the method is in a program tentatively titled DOTMATRX, which computes the map pattern and drives a dot matrix printer. The dot matrix printer used to develop this technique is a GEMINI-15, which is similar’to many other currently available dot matrix printers. In order to understand how the method creates a continuous-tone symbology, it is important to consider the operation of the printer. The printer has a small print head with a single column of 9 pins spaced 1/72 inch apart. Each pin has a diameter of 1/72 inch, such that each pin is very nearly tangent to its neighbors. A printing ribbon is positioned between the print head and the paper so that when a pin is "fired" the impression of the pin head on the ribbon creates a dot on the paper with a nominal diameter of 1/72 inch. The print head is driven horizontally across the paper by a pulse motor capable of 18 moving,in increments as fine as 1/120 inch. The print head cannot move vertically, so the paper must be advanced relative to the print head. Vertical control of the platten rollers (or tractor feed sprockets) that advance the paper is accomplished with another pulse motor, this one capable of movements as fine as 1/1uu inch. The highest resolution of the printer is thus 120 by 1”” dots per square inch. At this resolution, dots overlap by 50$ vertically and “01 horizontally, effectively filling all interstices to create total ink coverage. The pin firings and pulse motor movements are controlled by a stream of codes sent to the printer from the attached computer. Generally, the print head advances across the paper, firing the pins selectively to create characters or graphics. At the end of a printing pass, the paper advances and another row is printed. But, if total ink coverage is needed, the paper must be advanced by 1/1uu inch at the end of a row to line up the print head pins with the dot interstices and print the row again. Using this strategy, the printer can create a range of dot densities from zero percent-area-inked (iee. no dots) to 100 percent-area-inked (Figure A). The continuous-appearing tone variation that this method creates is based on filling a matrix of small cells with randomly placed dots. RANGE OF TONES y;I:€-.:t tigg I4 £91.?“- . NF”. “‘5“ Maw“ ' 4- , . .- ~ -.~« g': 'i f .i V A ' ' I U I I I I O 20 4O 60 80 100 Percent of Maximum Dots Per Cell Figure A. Gray-tone range with the dot matrix printer method. 19 Each of the cells may be thought of as the graphic equivilent of a character space. Since each cell is covering a small area on the map with a relatively uniform dot density, the symbology is actually modelling a stepped statistical surface. But because the cells are quite small and the values of neighboring cells progress in a smooth manner, and since randomly placed dots do not provide clear cell edge definition, the visual effect is a smoothly changing surface. The size of individual cells used in the symbology is 1/12 inch square, or 10 dots wide by 12 dots high. Maximum dot coverage in cells of this size is thus 120 dots, and there is a corresponding maximum tonal range of 120 steps. Other cell sizes are possible, but there is a trade-off between cell size (and therefore tonal steps, as well) and coarseness of the cell matrix. If the cells are made larger, there are more possible tone steps, but this comes at the expenseeof'a coarser cell structure -- one that approaches a stepped statistical surface. The problem can also be reversed. If the cells are too small, there are few tonal steps, and the surface texture may not appear smooth across adjoining cells. The 1/12 inch cell size was chosen as a reasonable compromise for these conditions. The placement of dots in each cell is based on the data value for that cell. During computation, a 10 by 12 array is used to store the positions of dots in the cell. Dot placements are performed by a random sampling process without replacement. Since the printer must make two passes to print maximum.dot density, an entire row of cell matrices are computed before a row is printed. The first pass prints odd numbered cell matrix rows. The second pass, 1/1uu inch lower, prints the even numbered cell matrix rows. The internal memory of the 20 computer only needs the capacity to store an array with the dot pattern for a single row. Since this is seldom a large memory demand (maximum row length is fixed due to the width of the printer), the technique can be used on small microcomputers. Gray tones with the dot matrix printer symbology range in density from white to full optical density of the printing ink where maximum dot coverage is obtained. The function of optical density change associated with increasing the dot coverage per cell can be determined by measuring the reflectance densities of cells having known dot coverages. Optical reflectance density is a measure of the amount of _incident light that reflects back from a surface. When light strikes a printed page, for example, part of the light is absorbed, while the remainder is reflected. Dark areas, which have high optical densities, do not reflect as much light as light-toned areas. The ratio of the amount of light reflected from a given tone area and the amount of light reflected from a white area on the same paper is the measured optical reflectance density of that tone [Blair and Shapiro, 1980, p 5:9-10]. The density function of the dot matrix symbology was measured with a digital reflectance densitometer on an incremented set of cells with dot coverages ranging from no dots to 100% of the maximum dots per cell. The graph of this function (Figure 5) shows a nearly linear increase in optical density associated with increasing dot coverage. It is not known whether linear reflectance scaling of the dot matrix symbology results in linear perceptual response to changes in dot densities. Following the example of Stoessel [1972, p 708-713], who derived a linear perceptual scaling function for graphic arts dot screens, a perceptual scaling function could be determined for the dot 21 matrix printer symbology. 1.41 . . o >_ 1.2'l . O .‘L'.’ o m o C o 8 1.0‘ . o 8 o c 0.8" o 3 . O 2 o 15 (315‘ . m g 0.4. . - ' p O. 0 o 0.2-[ ' O l W I r I I I r 1 fi 0 20 4O 60 80 100 Percent of Maximum Dots Per Cell Figure 5. The density function of the dot matrix printer method. One of the stated design objectives of the method is to provide fast, easy, hardcopy output. Failure of previous methods to meet this objective was an important barrier to their general acceptance. This method offers significant improvements in execution speed over previous methods, due largely to the efficiency of dot matrix printers as output devices. In addition, program DOTMATRX was "streamlined" wherever possible to increase computation speed. Two program features which result in significantly reduced execution time are noteworthy. The first of these involves the random sampling method used to position dots within a cell. Each dot's position is determined by 22 sampling a random number sequence to obtain x,y cell coordinates. Since the random sample is performed without replacement (i.e. no two dots with common cell coordinates), as the number of dots in a cell approaches maximum density, the probability of randomly finding the coordinates for the remaining "empty" cell positions rapidly decreases. Program DOTMATRX avoids this problem in cells with greater than 50% dot coverage by initially assigning dots to all cell positions and subsequently deleting dots through the random sampling process. A second important feature that significantly improves program execution speed is compilation into machine language through a BASIC compiler. Uncompiled programs must be translated into machine language by an interpreter as the program executes. Repeated use of an uncompiled program requires translation each time. Compiled programs, on the other hand, are already in machine language so no translation occurs during run-time. Use of a compiled version of DOTMATRX reduces run time to about 1/6 to 1/ 10 of that required for both compilation and execution, the exact amount depending of the characteristics of the data set used. The data file needed to run DOTMATRX is a rectangular matrix of interpolated data values set up so that cells outside of the map area have null (zero) data values. The program prints a cell of random. dots for each matrix value, so non-zero values outside of the desired map area would result in unwanted printed cells. The data matrix is structured during interpolation through use of a run-encoded raster map outline file that directs the interpolation program to place zeros in cells outside of pre-defined map boundaries. The interpolation algorithm currently used in the program employs an inverse distance 23 weighting function based on the nearest six control points [Tobler, 1970]. Program output is a hardcopy map at final size printed directly on the dot matrix printer (Figure 6). The sample map shown has 2135 individual cells, corresponding to non-zero values in the interpolated data matrix. Program execution time for this map was 22 minutes, excluding the necessary preparation of the input matrix. The improvements of this method over previous dot matrix methods can be summarized briefly: 1. Improved resolution; resulting in smoother texture, fewer visible surface steps, and greater range of available grey tones. 2. Hardcopy produced directly at final size, eliminating the need for subsequent photographic reduction. 3. Increased execution speed; maps are produced in minutes, rather than hours. Other Applications of the Method The method has several other'potential applications beyond the representation of monovariate smooth statistical surfaces. One of these is the extension of the symbology to multivariate smooth statistical surfaces. Multivariate symbologies could consist of different colored dots to represent different variables. Eilertson- Rogers and Groop [1981] showed that multicolor dot maps are at least as effective as separate monovariate dot maps for representing regional data. Their maps were conventional dot maps in which each dot represents a given number of objects, but the same concept of overlaying multiple variables can be extended to the dot matrix 2h MEAN ANNUAL SNOWFALL - Michigan Figure 6. Sample map showing the dot matrix printer symbology. 25 symbology. In a similar vein, Eyton [198”] has experimented with designs for unclassed multivariate maps symbolized with continuous color gradients in complementary colors. His maps are similar in concept to the multivariate dot matrix maps suggested here. Creating a multicolor dot matrix map would be easiest with a color dot matrix printer. The author has not attempted this, due to lack of access to such a printer. In the absence of a color dot matrix printer, multicolor maps can be created by producing each statistical surface as a separate monochrome map by using the method in standard fashion. The separate maps can then be used to make photographic negatives, each one used to print a different color on a composite map. This method, though less efficient, has been used successfully to create two- variable maps of smooth statistical surfaces (Figure 7%. Another possible use of the method is unclassed choropleth mapping of stepped statistical surfaces, such as those researched by Frohnert [1983]. This would require a different structure of the input matrix; 'values would not be interpolated as for smooth statistical surfaces. Unclassed choropleth mapping has not yet been attempted with the method. An additional application of the method is nominal class mapping, where gray tones would represent different classes of features, rather than differences in value of a single phenomenon. Preliminary work in this area has been done by R. Smith and Groop [1980]. One interesting example of nominal class mapping that has potential for further research is the creation of dot matrix LANDSAT images from digital spectral reflectance data. Each LANDSAT pixel, with its spectral reflectance value, is represented as a cell of random 26 Figure 7. A color-encoded two variable map using the dot matrix symbology. 27 dots. In this way, the spectral reflectance of a scene is shown with gray tone variation. This is conceptually similar to the black and white photographic images that are commonly produced from LANDSAT data. LANDSAT scenes created with the dot matrix method are considerably magnified (Figure 8). The example shown was created from a 60 row by 60 column section of a scene imaged by LANDSAT's Thematic Mapper in band 5 (near-infrared wavelengths). Each LANDSAT TM pixel represents a 30-meter by 30-meter ground area, and is represented by a 1/12 inch square cell. The nominal scale of the image is 1:1ll,000 -- a magnification of about 53 times over the standard scale of 1:750,000. The scene shows part of the airport at Traverse City, Michigan, with buildings appearing light in tone (high reflectance) while vegetation and asphalt paved surfaces (note the runways in the lower part of the scene) appear dark. Dot matrix images of this type could prove useful as inexpensive and easily produced images of variously modified (i.e. density sliced, edge enhanced, contrast stretched, etc.) LANDSAT data sets. In summary, the dot matrix printer sybology holds potential for illustrating a variety of cartographic products. The ready availability of microcomputers and dot matrix printers necessary for producing the symbology should facilitate the use and continued experimentation of dot matrix mapping applications. The greatest attention in this thesis is placed on designing dot matrix maps to represent smooth statistical surfaces so that map readers can readily distinguish surface form. Chapter 3 deals with an evaluation of the symbology to determine if map readers can indeed use these maps to effectively visualize the surface form of smooth statistical surfaces. 28 TRAVERSE CITY AIRPORT TH band 5 - contrast stretched Figure 8. An example of a dot matrix LANDSAT image. CHAPTER III THE EXPERIMENT Preliminary testing of a dot matrix symbology was conducted by P. Smith [1980], who determined that slope direction could be accurately seen on an early version of dot matrix symbology (Figure 2). His testing was conducted using variously rotated circular maps having a linear slope profile. Subjects were asked to orient an axis through the maps identifying the direction of greatest tonal gradient. While his results were important to the continued development of an effective dot matrix symbology, they did not indicate whether subjects were able to see differences in slope form on smooth statistical surfaces. Further, the linear slopes modelled in his test maps are not characteristic of most 'real' continuous data surfaces. A more thorough evaluation of the continuous tone model can be made in a test using actual data surfaces and determining if map users can visualize the essential form of the surface. Method of Testing Much has been published in the cartographic literature pertaining to test designs for cartographic research. Investigators warn that the validity of many testing procedures hinges upon careful selection of test instruments and testing instructions. Shortridge and Welch [1980, p 22] determined that slight changes in emphasis within testing 29 30 instructions produce markedly different results. They also advise cartographic researchers to acknowledge the fact that map reading involves not only perception but a variety of non-perceptual factors such as the readers' expectations. The degree of task specificity in psychophysical test instructions can also affect test results. Cole [1980, p 65] noted that as test instructions become increasingly task- specific, there is a decline in the amount of response error. The issue of designing experiments with the perspective of the map user was also discussed by McCleary [1975, p 2118]. He warns that inappropriate or mis-applied techniques are often the result of overlooking the motivation of the map reader. Experience, too, becomes a factor in test results. Test subjects in cartographic testing may perform differently on a test if they are given task-specific training prior to the test. Olson [1975] performed psychophysical tests involving map comparisons to discover that a small amount of task-specific reader training clarified the test concept and led to greater response accuracy. Finally, psychologists Thorndyke and Stasz [1980] cataloged learning strategies for knowledge acquisition from maps, and found that successful learners relied on a structured procedure to encode map information. This suggests that cartographic tests should provide instructions that facilitate this structured strategy. In light of these findings, it is clear that testing instructions and administration procedures, as well as test instruments, must be thoughtfully designed if test results are to be meaningful and valid. The testing method used in this study is modelled, in part, after a technique used by Griffin and Locke [1979], who addressed the visualization of slope form on isarithmic maps by asking map readers to 31 match the slope of surface transects with one of five graphic profile choices. Surface form may be described as the nature of the surface, including slope characteristics (convexities and concavities), smoothness, and complexity of gradient changes. For the present study, a paired difference test was used to compare the effectiveness of the random dot matrix representations of smooth statistical surfaces with corresponding isarithmic surface representations. The paired difference test employs responses for both.map types from each test subject to facilitate a direct comparison of the difference between these paired responses. Perception of surface form was tested by asking map readers to compare transect lines drawn on test maps with a selection of graphic surface profiles. Additional insights to the perception of surface form were obtained by asking subjects to compare spot elevations on the maps and to identify the "landform" (hill, valley, eth at selected points. In addition to the transect/profile matching and point questions, a short series of semantic differential questions was asked of each subject for both the isarithmic and dot matrix.maps. The semantic differential (S-D) procedure consists of a series of questions or statements, each followed by a bipolar word pair'(ime. good/bad, interesting/boring, etc.) separated by a scale bar. Subjects respond to each question by placing a mark on the scale bar between the word pair to indicate their relative evaluation of the map on the quality indicated. For example: The effectiveness of the maps at showing overall surface form: excellent I I I 1+1 I I I poor 32 A response mark in this position on the line indicates that a map reader is neutral in judgement of the effectiveness of the maps for showing surface form. Responses are quantified by assigning numeric values to segments of the line. A mark in the center segment is scored as '0', while segments closer to "excellent" are scored as '1', '2', and '3', respectively. Segments in the direction of "poor" are scored with negative values. S-D word pairing has gained acceptance in cartographic research as a quantitative tool for measuring subjective responses of maps as whole entities [Petchenik, 197A; Dent, 1975; Gilmartin, 1978; Olson, 1981]. The S-D questions used in this test were aimed at evaluating the difficulty of the experimental task and the overall effectiveness of the two different symbolizations at communicating the form of smooth statistical surfaces. Five S-D questions were used. The same set of questions followed both the dot matrix maps and the isarithmic maps in each test so that subjects indicated attitudes about both.map types. The five S-D questions used were: 1. The ease of matching the transect lines to the profiles: easy/difficult 2. The ease of comparing spot elevations on the maps: easy/difficult 3. The effectiveness of the maps at showing overall surface form: excellent/poor u. The aesthetic appeal of the map symbolization: very nice/awful 5. The texture of the map symbolization: smooth/coarse 33 S—D questions are an effective tool for measuring attitudes and subjective responses, but test subjects may feel strongly about some aspect of a test that the S-D questions do not address. To overcome this, the test used in this study ended with a page for subjects to write comments. mmothesis It is hypothesised that map readers can distinguish surface form of conceptually smooth surfaces more effectively with the proposed dot matrix symbology than with the corresponding isarithmic symbology. ‘The hypothesis will be supported if the difference in paired responses is significantly different from zero, in the direction favoring the dot matrix maps. The null hypothesis, to be accepted or rejected in the statistical analyses, states that the difference in means of paired responses is equal to zero. The significance level for acceptance or rejection is (L95, indicating that there is only a 51 chance of rejecting the null hypothesis if it is indeed true (idh, of "accepting" the working hypothesis when it is false). Design of the Test Maps Five different pairs of dot matrix and corresponding isarithmic test maps were produced for the testing experiment. The maps portrayed a variety of surface configurations to reduce the possibility of the test results being map-specific or surface-specific. Real data sets, such as the percentage of cropland used for corn in Michigan or population density in Washington state, were used so that the test would simulate normal map reading conditions. Corresponding isarithmic 3h maps were matched as closely as possible to their random dot matrix counterparts by using the same data control points to create similarly interpolated data matrices, and by producing the maps with the SURFACE II computer mapping package. A pair of corresponding test maps is shown in Figure 9. Test maps were constructed using a H inch square format which :allowed the corresponding pairs to be rotated relative to each other so that test subjects would be less likely to recognize the map patterns. Titles, scales, legends, and other peripheral map information were omitted from the maps to help maintain test subjects'lattention on the map symbolizations. Random letter codes were affixed to each different test map so that no order was implied in the sequence of'maps in the test booklets” Each test map included two transects with labelled end- points and three labelled spot elevation points. Labels for the transects and spot elevations were typeset and printed on the maps with white "casing" surrounding each label to improve legibility. Transect lines and labelled points were drawn with red transparent ink to add contrast to the black printed map symbolization and to allow the symbolization to "show through". Profile choices for the transect/profile matching were constructed by systematically reversing the slope characteristics of the correct profile. For example, the profile choices for a linear slope transect would include a convex and a concave profile choice. The true profile choices were determined by graphing the values of all known or interpolated values along a transect. Labelled points for the "landformP identification questions were placed on the maps in locations selected to avoid ambiguities. The test questions and response choices for each pair of corresponding ‘Qn ,4 )‘r 555 ’92.». ._ x ‘.v r} Figure 9. Corresponding dot matrix and isarithmic maps. 36 maps were identical so that each test subject responded to the same questions on both map symbolizations (Figures 10 and 11). Test Administration The test was conducted on sample groups of students enrolled in undergraduate Geography and English classes at Michigan State University. Two general groups of map readers were targeted in the experiment: those who were familiar with isarithmic map reading and those who were unfamiliar with it. The two separate groups were not identified before the testing, but were instead identified by including a question in the test booklets asking if they had used maps like those in the test. Responses from these two general groups of map readers were separated to determine whether familiarity with isarithmic mapping affects the difference in surface form perception between the two mapping symbologies. A preliminary version of the test was conducted with four subjects to aid in determining the final format of the test. Results of the preliminary test showed that the experiment took too long (approximately 25 - 30 minutes) and that the physical size and thickness of the test booklets intimidated some test subjects. To overcome these problems, the test was shortened and the test booklets were reduced to half-page format. Five pairs of test maps were still used in the test, but instead of placing all five pairs in each test booklet, five different combinations of three map pairs were used. Each test booklet began with a series of three dot matrix or isarithmic maps, each with the transect/profile matching questions, spot elevation comparisons, and "landform" identification questions. The maps were Part I Match each transect line on the map to the profile that most Mark closely resembles the form of the surface along that transect. ion in the space provided. your select a “i Transect A - A' \I ) e b E g Transect B - B' Q m. A_ ' ts on the map for these questions. in Part II Refer to the numbered po #3 is situated a) on a "ridge" b) in a "valley" c) can't determine Point point #2. #1 is a) higher than Point b) lower than c) same elevation as Sample dot matrix test map and response choices. Figure 10. 38 Part I Match each transect line on the map to the profile that most closely resembles the form of the surface along that transect. Mark your selection in the space provided. Transect A - A':___ a) \\\~“~__-_- b) —-“‘\‘-- Transect B - B':_ a) A b) A c)-/\ d) \ e) /\ Part II Refer to the numbered points on the map for these questions. Point #1 is ___ point #2. Point #3 is situated a) higher than a) on a "ridge" b) lower than b) in a "valley" c) same elevation as c) can't determine Figure 11. Sample isarithmic test map and response choices. 39 followed by the series of five S-D questions. Then another set of three maps corresponding to the first three, but rotated to prevent recognition, appeared with identical questions, followed by another set of S-D questions. Finally a page for comments was included at the end of the booklet. Test booklets were distributed to test subjects from a colated stack arranged so that each booklet contained a combination of maps different from the booklets preceding and following it. Further, half of the test booklets began with three dot matrix maps, while the remainder began with isarithmic maps. In total, ten permutations of test booklets were used: five combination of three maps, isarithmic or dot matrix appearing first. Test subjects were given a brief introduction prior to the experiment to familiarize them with the experimental tasks. An example of a statistical surface representation was shown to them on an overhead projector, and the transect/profile matching exercise was demonstrated. The map shown to them did not resemble any of the experimental maps. A sample S-D question was then shown to them on another overhead transparency and the proper response method was demonstrated. After the introductory demonstrations, subjects were given test booklets and asked to begin the test. No time limit was imposed, but subjects were advised every two minutes that they should be advancing to the next map. The test took an average of fifteen minutes to complete. Since it was impossible to predict beforehand how many test subjects in a given group would claim familiarity with isarithmic maps, the test was conducted on several small groups which had reasonably H0 predictable ratios of experienced vs. inexperienced map readers. Thus it was possible to obtain a total sample with roughly half of the respondents familiar with isarithmic map reading. A total of 109 test subjects participated in the experiment. One test booklet was removed from the sample due to incomplete responses, leaving an adjusted sample of 108: 62 familiar with isarithmic maps, and H6 unfamiliar with isarithmic maps. CHAPTER IV RESULTS Responses from the profile/transect matching, spot elevation comparisons, and "landform" identification questions were scored on the basis of correct responses. Response totals were paired from each test booklet by scoring the dot matrix and the isarithmic maps separately. S-D responses were also paired for each test booklet. Paired responses were tabulated separately for experienced vs. inexperienced isarithmic map readers. In total, twelve paired samples were tabulated: two for differences in surface form perception (experienced and inexperienced with isarithms), and five sets of S-D questions for both experienced and inexperienced isarithmic map readers. Data analysis for paired samples involves the determination of differences between pairs. Each sample has parameters that describe the data population from which it was drawn. In paired sample analysis, these parameters can be used to generate statistics which inferentially indicate whether the paired samples belong to the same population or were drawn from different populations. Paired sampling has the advantage of reducing the influences of extraneous variables, especially the effect of subject-to-subject variability [Nie, et al, 1975, p 270]. In this study, we are interested in determining if the responses for the dot matrix maps are significantly different from the responses for the isarithmic maps. A comparison of paired sample means ’41 #2 using the T-test is appropriate for this analysis. The paired T-test is used to calculate the probability that the difference in sample means is equal to zero. If the difference in paired sample means is significantly different from zero, then it can be inferred that the samples were not drawn from a common population. The T-test in this analysis is two-tailed. That is, if the difference in paired sample means is significantly different from zero, we would like to know in which direction the difference differs from zero. This information can be used to determine which symbology leads to significantly "better" results. An important assumption of the T-test is that sample data are normally distributed. Failure to use normally distributed data may lead to spurious results, since the T-test computes the probability of a normally distributed sample -- the difference in sample means for a paired T-test -- belonging to a normally distributed population. To check the sample data for normality, a Kolmogorov-Smirnov (K-S) goodness-of-fit test was used. This non-parametric test compares the sample distribution with a theoretical normal distribution and computes the probability of the sample being;normally'distributed. Table 1 summarizes the results of K-S tests for the twenty-four individual samples (paired samples were split for the K-S tests). The null hypothesis for the K-S test is that the sample distributions are normally distributed. The surface form perception questions -- profile/transect matching, spot elevation comparisons, and "landformP identification -- for both symbologies with both experienced and inexperienced isarithmic map readers were within acceptable normality limits. Several of the samples for S-D responses with experienced Table 1. "3 K—S test for Nermality of Samples H0: Sample distribution = Nbrmal distribution Significance = 0.05 Sample Sample Two-tailed Data Size Probability Decision 1. Respondents experienced with isarithmic mapping: A. Dot Matrix symbology: Surface Form perception 62 0.070 Accept Ho S-D question #1 59 0.015 “Reject H0 S-D question #2 59 0.009 “Reject HO S-D question #3 59 0.075 Accept H0 S-D question #u 59 0.038 “Reject H0 S-D question #5 58 0.08” Accept H0 B. Isarithmic symbology: Surface Form perception 62 0.389 Accept Ho S-D question #1 59 0.052 Accept Ho S-D question #2 59 0.000 “Reject Ho S—D question #3 59 0.000 “Reject H0 S-D question #H 59 0.030 “Reject H0 S-D question #5 58 0.025 “Reject H0 II. Respondents inexperienced with isarithmic mapping: A. Dot Matrix symbology: Surface Form perception 46 0.172 Accept Ho S-D question #1 45 0.059 Accept H0 S-D question #2 "5 0.068 Accept H0 S-D question #3 “5 0.275 Accept Ho S-D question #M "5 0.096 Accept Ho S-D question #5 ”5 0.319 Accept Ho B. Isarithmic symbology: Surface Form perception #6 0.661 Accept Ho S-D question #1 H5 0.3uu Accept Ho S-D question #2 “5 0.198 Accept Ho S-D question #3 H5 0.069 Accept Ho S-D question #M #5 0.0H0 “Reject Ho S-D question #5 #5 0.198 Accept H0 llll isarithmic map readers differed significantly'fromznormality; The remaining S-D samples were acceptably normal. Differences in Surface Fer-.Perception The responses to the transect/profile matching, spot elevation comparisons, and "landform" identification questions were used in this study to measure surface form perception with the two symbologies. To test the hypothesis that one of the symbologies leads to fewer errors in surface form perception, and thus provides the average map reader with a more effective surface representation, a paired T-test was used on the differences between paired responses. The difference in paired responses was found by subtracting the number of correct responses on the isarithmic maps from the number of correct responses___/ b)-\ V Part II Refer to the numbered points on the map for these questions. Point #7 is ___ point #8. a) higher than b) lower than 0) same elevation as Point #9 is situated a) on a steep slope b) on a flat area c) can't determine Part I Match each transect line on the map to the profile that most closely resembles the form of the surface along that transect. Mark your selection in the space provided. Transect G - G': a) b) X c) A a) /\ e) )ll |(l> Transect H - H': a) b) _ _ c) c , a) ——\ '3) Part II Refer to the numbered points on the map for these questions. Point #10 is point #11. Point #12 is situated a) higher than a) on a "ridge" b) lower than b) in a "valley" c) same elevation as 0) can't determine E Part I Match each transect line on the map to the profile that most closely resembles the form of the surface along that transect. your selection in the space provided. a)-“‘\\//”" d)\/ Transect I - I': QM Transect .) - J': a)‘~c~‘~‘—”// 0),\/ d) A Mark b)/\ e)W ”\f e) A Part II Refer to the numbered points on the map for these questions. Point #13 is point #14. a) higher than b) lower than c) same elevation as Point #15 is situated a) on a "hill" b) in a "lowland" 0) can't determine Part III: After you have completed the questions for the preceeding three maps, respond to the following statements by placing a mark on the line between each word pairs Base each response on your initial reaction. 1. The ease of matching the transect lines to the profiles: easy I I I I I I I I difficult 2. The ease of comparing spot elevation on the maps: easy I I I I I I I I difficult 3. The effectiveness of the maps at showing overall surface form: excellent I I I I I I I I poor 4. The aesthetic appeal of the map symbolization: very nice I I I I I I I I awful 5. The texture of the map symbolization: smooth I I I I I I I I coarse .Have you used maps like these before (yes/no)? Use the space below to make any comments about the maps or the test. “““““ Thank you for your help! “““““ APPENDIX B ORAL TEST INSTRUCTIONS AND DEMONSTRATION MATERIALS APPENDIX B ORAL TEST INSTRUCTIONS AND DEMONSTRATION MATERIALS [read aloud to test subjects prior to testing] I'm doing my Master's thesis research on the effectiveness of two types of map symbolizations. To do this, I need to know how people perceive the information shown on maps. The symbolizations I'm testing are used to represent something called Statistical Surfaces. [show top half of first overhead] A statistical surface is an abstraction -- it shows the height of data values over an area. This example shows annual snowfall data for Michigan's lower penninsula. We can see, for example, that it snows the most in the northwestern part of the state. The test consists of 6 maps; 3 of one type, and 3 more of another type. There is no particular order to the maps in each test booklet. You'll be matching transect lines on the maps with profiles [show bottom half] like these. Each map has two transect lines on it. [read intructions from overhead] Each map also has several numbered points [show on overhead] like these. There will be questions like: '18 point #1 higher or lower than point #27'. If you're not sure about an answer; just guess, but don't skip any questions or leave anything blank. 0K? After the the first 3 maps, you'll come to a short series of Impression Questions [show second overhead]. There will be another set of questions like these after the second set of 3 maps. These 73 74 questions apply only to the 3 maps that precede them. Answer these questions by making a single vertical mark on the line [show on overhead]. Mark the line with your FIRST IMPRESSION. You shouldn't spend much time on these questions, just read them and quickly mark your responses. In this example, IHve responded to the statement 'The color scheme of this overhead' by making a mark between 'neutral' (the middle of the line) and 'beautiful'. Are we clear on this? The last page of the test asks for any comments about the test or the maps. I encourage you to write down your comments. [begin passing out the test booklets] As soon as everyone has a test booklet, you may begin. There's no fixed time limit, but I'll help you pace yourself by telling you approximately when you should be starting the next map. Don't panic if you're a bit behind, just pick up the pace and try to catch up with everyone else. If you're COMPLETELY confused about the whole thing, raise your hand and I'll come over to you -- otherwise don't ask any questions during the test. Bring your test booklet up here when you're finished. [when everyone has a test booklet] 0K, please begin. [at 2 minute intervals] You should now be finishing up the (first, second, etc) map and starting on the next one. If youuw: behind, don't panic and don't skip any questions, just try to pick up the pace. 75 " IIC'IGAN SNOUFALL' \ Wound X'X“ C” — «>\~)'\_ c)\/ d)_/\.9‘——— 75 10¢ch a finsecf 7‘5 aprafiye, /aol(' 41‘ fit an, e/oy fie fiance!“ lu'oe and firma menial line]: of fit an, Svrfice 4/011] Haf line. 77¢)! Chose fl: prof”: flef Mosf Cbse/y ankles your mafia/1309:. (dn'k your answer in He 306:: FW’I'éJ. Overhead transparency #1 for test instructions. 76 w 3 “ion 0:: i he a: .. shrf'sen'es of fesféus fil/oui} eec‘ ref of 3 liars; ’aesf/ous ”I, 3 “at. 3 #1,: OMLI’. .. lurk fie In Ive been and pair of M: “will, 7'. your FIK‘T REACT/0A! 1'0 fie sfahamct for “up“: TA: Color Sela-e of “is Overland Far/mcy : “WV" '-—#+—-|—-I—t—t——I Wyatt") «fire! (cafe? 0' I“) a he" ‘01:.“20h3 “a! I “At fie «(or “have i: 'prdfy ”I ' -' pf may, “1" hirer “an urfhl. Overhead transparency #2 for test instructions. APPENDIX C PROGRAM "DOTMATRX" AND PERIPHERAL PROGRAMS APPENDIX C PROGRAM "DOTMATRX" AND PERIPHERAL PROGRAMS Program.“DOTMmTRX' 10 20 30 4O 50 60 70 80 90 100 110 120 130 mo 150 160 170 180 190 200 210 REM This program prints a "random dot matrix - smooth symbology" map on a dot matix printer. The map will show a smooth gradation in grey tone, consistent with the notion of a smooth statistical surface. REM The input data is a matrix of values interpolated from known "control point" values. The output is a matrix of cells, each containing randomly placed dots in proportion to a data value. REM This program uses graphics printing codes for a GEMINI-15 printer. The resolution (dots/cell) is either 10 x 12 (high res.) or 5 x 6 (low res.). The cell size is the same (1/12" square) in either case. REM Program stored as "DOTMATRX.WFJ" in ASCII code. Program written for compatability with BASIC compiler. Compiling the program greatly increases the speed of execution. Written 3—29-84 by Bill Johnson. REM—--= ——— ___— REM Initialize variables, set constants, prompt inputs CLEAR: PRINT: PRINT "Turn printer 0N" 'clear memory, printer message LPRINT CHR$(27);"€" 'initialize printer mode WIDTH "LPT1:",255 'initialize width of printout FOR 11:1 TO 24: PRINT: NEXT 'scroll to clear screen OPTION BASE 1 'minimum array subscript=1 LMARGIN$=0: NONZERO=0 PRINT "This program will produce a random dot matrix map. The output is a" PRINT "matrix of grid cells, each one containing randomly placed dots in" PRINT "proportion to a data value. The output can be produced in either" PRINT "high or low resolution. High resolution (120 x 144 dots/sq. in.)" PRINT "looks better than low resolution (60 x 72 dots/sq. in.) but takes" PRINT "about two and a half times longer to produce.": PRINT INPUT "Do you want the output in high (1) or low (2) resolution";RES: PRINT IF RES=1 OR RES=2 THEN 210 ELSE 190 INPUT "Enter the maximum blackness of a cell (20-1001):",MAXBLK 77 220 230 240 250 260 270 280 290 300 310 320 330 3H0 Q: 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 78 IF MAXBLK>100 OR MAXBLK<20 THEN 210 PRINT: INPUT "Do you want to set a new left margin on printer (Y/N)";Y$ IF Y$="n" OR Y$="N" THEN 270 PRINT: INPUT "Enter new left margin for printer (0 - 6 inches): ",INCHES IF INCHES (0 OR INCHES>6 THEN 250 PRINT:PRINT "Disk containing data matrix should now be in drive 'a'.":PRINT INPUT "What diskfile contains your data matrix (a: .mtx)";N$ Q=LEN(N$): IF Q<= -8 THEN 300 ELSE PRINT "Name mustm m5 characters or less.": GOTO 280 P$="a:": 83:".mtx": A$:P$+N$+S$: 'concatenate string (fn) PRINT: INPUT"How many ROWS in your data matrix";NROWS5 PRINT: INPUT "How many COLUMNS in your data matrix";NCOLS5 PRINT: INPUT "What is your map title (up to 50 characters)";H$ LEN(H$): IF Q<=50 THEN 350 IF RES=1 THEN R$="High resolution mode (120 x 144 dots/sq. in.)" ELSE R$="Low resolution graphics mode (60 x 72 dots/sq. in.)" FOR 15:1 TO 24: PRINT: NEXT: PRINT "You have selected ";R$;"." PRINT "Your data set (";A$;"), has";NROWS5;"rows and"; NCOLS5;"columns." PRINT "Maximun cell blackness=";MAXBLK;"5. Left margin="; INCHES;"inches. PRINT "Your map title is '";H$;"'." PRINT: INPUT "Is this correct (Y/N)";Y$: PRINT IF Y$="n" 0R Y$="N" THEN 190 IF RES=1 THEN LMARGIN5=CINT(INCHES“120) ELSE LMARGIN5=CINT(INCHES“60) IF RES=1 THEN NTONES5=CINT(120“(MAXBLK/100)) ELSE NTONES5=CINT(30“(MAXBLK/100)) T$="00:00:00": TIME$=T$ IF RES: 1 THEN CELLCOLS5= NCOLS5'10 ELSE CELLCOLS5=NCOLS5'5 N15: (LMARGIN5+CELLCOLS5) MOD 256: N25: INT((LMARGIN5+CELLCOLS5)/256) REM ------------- REM Find range of data values, compute scaling factor for number of tones PRINT "Finding ranges of data set -- Please be patient" MINVAL=9.000001E+09 MAXVAL=-9.000001E+09 OPEN A$ FOR INPUT AS #1 'open diskfile to read data FOR ROW5=1 TO NROWS5 FOR COL5=1 TO NCOLS5 INPUT #1,VALUE IF VALUE>MAXVAL THEN MAXVAL=VALUE ELSE 570 IF VALUEO THEN NONZERO=NONZERO+I ELSE 590 NEXT NEXT CLOSE#1 IF MINVAL>0 THEN RANGE=MAXVAL ELSE RANGE=MAXVAL-MINVAL FACTOR=NTONES5/RANGE 'compute scaling factor REM=— _ ___ = 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 79 REM Print title on map (8.5 cpi, double-strike), centered over map area LM5=INCHES“10+(NCOLS5/2“8.5/12)-(Q/2“8.5/10): IF LM5<1 THEN LM5=1 LPRINT CHR$(27);CHR$(77);CHR$(LM5) 'set left margin: center title LPRINT CHR$(15):CHR$(14);CHR$(27);CHR$(71); 'set to 8.5 cpi, double-strike LPRINT H$: LPRINT: LPRINT: LPRINT REM-- — —- REM Compute number of random dots for each cell IF RES:1 THEN MINUTES:CINT((NONZERO/120)+.5) ELSE MINUTES:CINT((NONZERO/300)+.5) FOR 15:1 TO 24: PRINT: NEXT 'scroll to clear screen PRINT "Computing dot pattern for each cell. Please wait for printout." PRINT: PRINT "This map should take about";MINUTES;"minute(s) to print." PRINT "Do not handle paper while printer is in operation. Slight gaps" PRINT "will show on your output if the paper is moved during printout." OPEN A$ FOR INPUT AS #1 IF RES=2 THEN 1380 REMaaeaassereensaaeeeseeeeaa HIGH RESOLUTION reassessersnanaeeaaeaa DIM MATRXROW(12,1200) 'row storage array for dot pattern LPRINT CHR$(27);" ";CHR$(27):CHR$(51);CHR$(1) 'set carriage return: 1/144" FOR ROW$=1 TO NROWS5 'rows in data matrix FOR COL$:1 TO NCOLS5 'columns in data matrix INPUT #1,VALUE NDOTS5=CINT(VALUE“FACTOR) 'compute # of dots for cell IF NDOTS5>60 THEN 880 ELSE 1020 NDOTS5=120-NDOTS5 FOR I$:1 TO 12 'fill cell array with 1's FOR J5=1 TO 10 MATRXROW(I5.((COL5-1)“10+J5)):1 NEXT NEXT RANDOMIZE (ROW5“COL5) 'reseed random # generator FOR DOT5:1 TO NDOTS5 'find random dots for a cell: ndots>60 X5:CINT((RND(DOT5)“12)+.5) Y5=CINT((RND(DOT5)“10)+.5) IF MATRXROW(X5,((COL5-l)‘10+Y5))=0 THEN 960 MATRXROW(X5,((COL5-1)’10+Y5))=0 NEXT GOTO 1090 RANDOMIZE (ROW5“COL5) 'reseed random # generator FOR DOT5:1 T0 NDOTS5 'find random dots for a cell: ndots<60 X5:CINT((RND(DOT5)“12)+.5) Y5:CINT((RND(DOT5)'10)+.5) IF MATRXROW(X5,((COL5-1)‘10+Y5))=l THEN 1040 MATRXROW(X5,((COL5-1)'10+Y5))=1 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 80 NEXT NEXT COL5 REM ———— — REM Print out row in two passes FOR PASS5=1 TO 2 'loop for two printing passes LPRINT CHR$(10);CHR$(27);CHR$(76);CHR$(N1$); CHR$(N25); 'graphics FOR BLANK$:1 TO LMARGIN5 'move to left margin LPRINT CHR$(0); NEXT FOR SPACE5:1 TO CELLCOLS5 PIN1$:0: PIN25:0: PIN3$:0: PIN4$:O: PIN55=0: PIN65=0 IF MATRXROW(PASS5,SPACE5):1 THEN PIN1$=128 IF MATRXROW(PASS5+2,SPACE5):1 THEN PIN25:64 IF MATRXROW(PASS5+4,SPACE5):1 THEN PIN35=32 IF MATRXROW(PASS5+6,SPACE5):1 THEN PIN45:16 IF MATRXROW(PASS5+8,SPACE5)=1 THEN PIN55=8 IF MATRXROW(PASS5+10,SPACE5):1 THEN PIN65:4 LPRINT CHR$(PIN1$+PIN2$+PIN3$+PIN4$+PIN55 +PIN65); NEXT NEXT LPRINT: LPRINT: LPRINT: LPRINT: LPRINT 'carriage return for LPRINT: LPRINT: LPRINT: LPRINT: LPRINT: LPRINT 'next row (9 x 1/144") FOR 11:1 TO 12 'reset row storage array to zeros FOR J5:1 TO CELLCOLS5 MATRXROW(I5,J5):0 NEXT NEXT NEXT ROW5 CLOSE #1 GOTO 1920 RgMaaeaereassesseaaeaeeeaees LOW RESOLUTION nasaeeeuaeeaaeesearean DIM MATRXCEL(6,5) 'cell storage array for dot pattern LPRINT CHR$(27);" ";CHR$(27):CHR$(65);CHR$(6) 'set carriage return: 6/72" ROW5=1= COL5=1: BLANK5=1: 15:1: J5=1: DOT5:1: SPACE5=1 FOR ROW5:1 TO NROWS5 'rows in data matrix LPRINT CHR$(27);CHR$(75);CHR$(N15);CHR$(N25); 'low res. graphics FOR BLANK5:1 T0 LMARGIN5 'move to left margin LPRINT cnas(o): NEXT FOR COL5:1 TO NCOLS5 'columns in data matrix INPUT #1,VALUE NDOTS$:CINT(VALUE“FACTOR) 'compute # of dots for cell IF NDOTS5>15 THEN 1510 ELSE 1650 NDOTS5=30-NDOTS5 FOR 11:1 TO 6 'fill cell array with 1's FOR J5=1 TO 5 MATRXCEL(I5,J5):1 81 1550 NEXT 1560 NEXT 1570 RANDOMIZE (ROW5'COL5) 'reseed random # generator 1580 FOR DOT5:1 TO NDOTS5 'find random dots for cell: ndots>15 1590 X5:CINT((RND(DOT5)“6)+.5) 1600 Y5:CINT((RND(DOT5)“5)+.5) 1610 IF MATRXCEL(X5,Y5):O THEN 1590 1620 MATRXCEL(X5,Y5)=0 1630 NEXT 1640 GOTO 1720 1650 RANDOMIZE (ROW5“COL5) 'reseed random # generator 1660 FOR DOTS=1 TO NDOTS$ 'find random dots for cell: ndots<15 1670 X5:CINT((RND(DOT5)“6)+.5) 1680 Y5:CINT((RND(DOT5)“5)+.5) 1690 IF MATRXCEL(X5,Y5)=1 THEN 1670 1700 MATRXCEL(X5,Y5)=1 1710 NEXT 1720 REM _ 1730 REM Print cell with random dots 1740 FOR SPACE5:1 TO 5 1750 PIN15:0: PIN25:0: PIN35=0: PIN45=0: PIN55=03 PIN65=0 1760 IF MATRXCEL(1,SPACE5)=1 THEN PIN15:128 1770 IF MATRXCEL(2,SPACE5)=1 THEN PIN25=64 1780 IF MATRXCEL(3,SPACE5):1 THEN PIN35:32 1790 IF MATRXCEL(4,SPACE5)=1 THEN PIN45:16 1800 IF MATRXCEL(5,SPACE5):1 THEN PIN55=3 1810 IF MATRXCEL(6,SPACE5)=1 THEN PIN65=4 1820 LPRINT CHR$(PINl5+PIN25+PIN35+PIN45+PIN55 +PIN65); 1830 NEXT 1840 FOR 15:1 TO 6 'reset cell storage array to zeros 1850 FOR J5:1 T0 5 1860 MATRXCEL(I5,J5):0 1870 NEXT 1880 NEXT 1890 NEXT COL5 1900 LPRINT 'carriage return for next row (6/72") 1910 NEXT ROW5 1920 REM 1930 REM Restore printer mode, and program execution 1940 CLOSE #1 1950 LPRINT CHR$(27);"€": WIDTH "LPT1:",80 'restore printer mode 1960 LPRINT: LPRINT: LPRINT: LPRINT 1970 PRINT: PRINT: PRINT "Program execution completed.": PRINT 1980 V$:TIME$: PRINT "Total time of program execution: ";V$ 1990 END 82 Program 'INTERP' 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 REM Program to interpolate values into a grid from scattered control points. REM The interpolation is done with Tobler's algorithm (value at a point "P" is based on the values of the nearest 6 control points, each weighted by the inverse of their distance from "P"). REM The input data is a set of scattered control points, identified by their position (row,col) in a rectangular gridcell matrix. The empty positions in the matrix will be filled with interpolated values. REM Also input is a data set to clip non-map areas from the matrix. This suppresses interpolation of values outside of the map area. These non-map areas are given values of zero in the matrix. REM The matrix is partitioned during the search for the nearest 6 control points to save search time. Partitioning is based on a box (1/3 number of rows x 1/3 number of columns) surrounding the current matrix position. REM The completed grid of values is written to a diskfile. REM Program stored as "INTERP.WFJ" in ASCII code. Program written for compatability with BASIC compiler. Compiling the program greatly increases the speed of execution. Written 3-31-84 by Bill Johnson. REM= —===== — - — —— —— —— — REM Initialize variables, prompt inputs, dimension arrays, Open diskfiles CLEAR: PRINT OPTION BASE 1 'minimum array subscript : 1 DIM R5(110),C5(110),VALUE(110),MATRIX(110,110),NEARDIST(6), PTDIST(6) PRINT "This program will interpolate values into a grid from scattered control points." PRINT "The interpolation is done with Tobler's algorithm (value at a point" PRINT "is based on the values of the nearest 6 control points, each" PRINT "weighted by the inverse of their distance from that point)." PRINT " The completed data grid will be written to a diskfile.": PRINT PRINT "Disk containing data files should now be in drive 'a'." PRINT: INPUT "What file contains your control points (a: .dat)";N$ Q=LEN(N$): IF Q<:8 THEN 210 ELSE PRINT "Name must be 8 characters or less": GOTO 190 P$:"a:": S$:".dat": A$=P$+N$+S$ 'concatenate string (filename) PRINT: INPUT "How many control points in your file";NPOINTS5 PRINT: INPUT "What file contains your map outline data (a: .dat)";0$ Q=LEN(O$): IF Q<=8 THEN 250 ELSE PRINT "Name must be 8 characters or less": GOTO 230 PRINT: INPUT "How many ROWS in your matrix";NROWS5 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 N10 420 430 uuo 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 83 PRINT: INPUT "How many COLUMNS in your matrix";NCOLS5 PRINT: INPUT "What name for your output diskfile (a: .mtx)";M$ Q:LEN(M$): IF Q<:8 THEN 290 ELSE PRINT "Name must be 8 characters or less": GOTO 270 B$=P$+O$+S$: T$:".mtx": C$:P$+M$+T$ 'concatenate strings (filename) PRINT: PRINT"You will be interpolating a";NROW85;”rows by";NCOLS5;"columns" PRINT "matrix from";NPOINTS$;"control points. Your control points will be" PRINT "read from file '";A$;"'. Your map outline data will be read from" PRINT "file '";B$;"'. Your matrix will be written to file 1n;c$;n1.n PRINT: INPUT "Is this correct (Y/N)";Y$ IF Y$="n" 0R Y$="N" THEN 190 OPEN A$ FOR INPUT AS #1 'open file for control points OPEN B$ FOR INPUT AS #2 'open file for map outline OPEN C$ FOR OUTPUT AS #3 'open file to write matrix data T$:"00:00:00": TIME$=T$ 'initialize timer REM — REM interpolate grid PRINT: PRINT "Interpolation begins. . . ." FOR 15:1 TO NPOINTS5 'input control points (v,r,c) INPUT #1,VALUE(I5),R5(I5),C5(I5) NEXT CLOSE #1 COUNT5:0 FOR ROW5=1 TO NROWS5 'rows in matrix V$=TIME$z PRINT PRINT "=- -— ","Time so far: ";V$ PRINT "Row","Column","Value",NROWS5;"rows,";NCOLSS;"columns in matrix" INPUT #2,BLANKCELLS5 COL5=1 'initialize column counter FOR COL5=COL5 TO ((COL5-1)+BLANKCELLS5) 'assign zeros to non- map areas MATRIX(ROW5,COL5)=0 WRITE #3,MATRIX(ROW5.COL5) 'write value to diskfile PRINT ROW5,COL5,MATRIX(ROW5,COL5) NEXT IF BLANKCELLS5=NCOLS5 THEN 1040 'if row is blank go to next row INPUT #2,MAPCELLS5 FOR COL5:COL5 TO ((COL5-1)+MAPCELLS5) 'interpolate values in map area FOR NEAR5:1 TO 6 'initialize nearest 6 distance NEARDIST(NEAR5)=9000! PTDIST(NEAR5)=O NEXT FOR SEARCH5:1 T0 NPOINTS$ 'search for nearest 6 points IF NPOINTS5<20 on (NCOLS5<20 AND Naowsfi<20) 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 84 THEN 700 IF R5(SEARCH5)>(ROW5+NROWS5/3) 0R R5(SEARCH5)<(ROW5-NROWS5/3) THEN 860 IF C5(SEARCH5)>(COL5+NCOLS5/3) OR C5(SEARCH5)<(COL5-NCOLS5/3) THEN 860 PTNUM5:SEARCH5 IF ROW5<>R5(SEARCH5) OR COL5<>C5(SEARCH5) THEN 760 MATRIX(ROW5.COL5):VALUE(SEARCH5) 'control point value WRITE #3,MATRIX(ROW5,COL5) 'write to diskfile PRINT ROW5,COL5,MATRIX(ROW5,COL5) GOTO 960 DIST:SQR((ROW5-R5(SEARCH5))“2+ (COL5-C5(SEARCH5))“2) FOR NEAR5=1 TO 6 'sort nearest 6 points IF DIST>NEARDIST(NEAR5) THEN 850 SHORTDIST:NEARDIST(NEAR5) NEARDIST(NEAR5):DIST DIST:SHORTDIST PTDIST1=PTDIST(NEAR5) PTDIST(NEAR5)=PTNUM5 PTNUM5:PTDIST1 NEXT NEXT SEARCH5 v1=0: v2=0 FOR NEAR$=1 T0 6 'weight values by distance V1:V1+VALUE(PTDIST(NEAR5))/ (NEARDIST(NEAR5))“1.5 V2:V2+1/(NEARDIST(NEAR5))“1.5 NEXT MATRIX(ROW5,COL5):V1/V2 'interpolated matrix value WRITE #3,MATRIX(ROW5,COL5) 'write value to diskfile PRINT ROW5,COL5,MATRIX(ROW5,COL5) COUNT5:COUNT5+1 NEXT COL5 INPUT #2,BLANKCELLS5 IF BLANKCELLS5>0 THEN 540 FOR COL5=COL5 TO NCOLS5 'assign zeros to non-map areas MATRIX(ROW5,COL5)=0 WRITE #3,MATRIX(ROW5,COL5) 'write value to diskfile PRINT ROW5,COL5,MATRIX(ROW5,COL5) NEXT NEXT ROW5 CLOSE #2: CLOSE #3 PRINT "End of program execution." PRINT COUNT5;" values interpolated from ";NPOINTS5;" control points." TOTAL5=COUNT5+NPOINTS5z PRINT "Matrix has";TOTAL5;"values." V$=TIME$: PRINT "Total time of program execution: ";V$ END 85 Program "CELLGRID' 10 20 30 40 50 REM This program prints a grid cell matrix for the dot matrix map symbology. REM The output is printed on the GEMINI-15 printer at whatever size is desired. The matrix cells are 1/12" square, and are used for both the low and high resolution versions of the dot matrix smooth symbology. REM Program stored as "CELLGRID.WFJ" in ASCII code. Program written for compatability with BASIC compiler. Compiling the program greatly increases the speed of execution. Written 3-28—84 by Bill Johnson. REM-—— ___ __ REM Initialize variables, prompt inputs 60 CLEAR: PRINT 70 LPRINT CHR$(27);"€" 'initialize printer mode 80 WIDTH "LPT1:",255 'initialize width of printout 90 PRINT "This program will print a cell grid of 1/12 in. square cells." 100 PRINT: INPUT "Enter the desired WIDTH of the cell grid (1-12 in.):",HOWWIDE 110 IF HOWWIDE<1 OR HOWWIDE>12 THEN GOTO 100 ELSE 120 120 INPUT "Enter the desired LENGTH of the cell grid (1-30 in.):",HOWLONG 130 IF HOWLONG<1 OR HOWLONG>30 THEN GOTO 120 ELSE 140 140 WIDE5:CINT(12“HOWWIDE): LONG5:CINT(12“HOWLONG) 150 M5:(WIDE5“5)+1: N15:M5 MOD 256: N25=INT(M5/256) 'graphics parameters 160 REM - — —— 170 REM Print grid 180 PRINT: PRINT "Please wait for printout. This may take several minutes." 190 PRINT "Do not handle the paper while printer is in operation." 200 LPRINT "Matrix cell grid (":LONG5;"rows x";WIDE5;"columns) for dot matrix" 210 LPRINT "smooth symbology. Each cell is 1/12 inch square.": LPRINT: LPRINT 220 LPRINT CHR$(27);"A";CHR$(6) 'set carriage return to 6/72" 230 ROW5:1: COL5:1: SPACE5:1 240 FOR ROW5:1 TO LONG5+1 250 LPRINT CHR$(27);CHR$(75);CHR$(N15);CHR$(N25); 'low res. graphics mode 260 IF ROW5:LONG5+1 THEN 360 270 FOR COL5:1 TO WIDE5 280 LPRINT CHR$(252); 'print vert. line (6 pins) 290 FOR SPACE$=1 TO 4 'print horiz. line (top pin) 300 LPRINT CHR$(128); 310 NEXT SPACE5 320 NEXT COL5 330 LPRINT CHR$(252); 'finish last column (6 pins) 340 LPRINT 'carriage return for next row 350 360 370 380 390 400 410 420 86 NEXT ROW5 FOR SPACE5:1 TO M5 'finish last row (top pin) LPRINT CHR$(128); NEXT SPACE5 LPRINT LPRINT CHR$(27);" ":WIDTH "LPT1:",80: LPRINT 'restore printer mode PRINT: PRINT "Program execution completed." END Program "INPUT" 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 REM Program to write data to a file from keyboard input. REM Stored as "INPUT.WFJ". Written 3-28-84 by Bill Johnson. CLEAR: CLS PRINT "This program is used to write data to a diskfile from keyboard" PRINT "entry. Data will be sent to the disk in drive 'a' and will be" PRINT "given the name suffix '.dat'. ie.(a: .dat)." PRINT: INPUT "What name do you want for your file";N$ A:LEN(N$): IF A>8 THEN 90 ELSE 100 PRINT "The file name must be 8 characters or less.": GOTO 70 PRINT: PRINT "Your data file will be named '";N$;"'." PRINT: INPUT "Is this correct? (Y/N)";Y$ IF Y$:"n" OR Y$="N" THEN 70 P$="a:": S$:".dat": A$=P$+N$+S$ OPEN A$ FOR OUTPUT AS #1 PRINT: PRINT "What type of data will you be entering?": PRINT INPUT "Enter (1) for numeric data or (2) for character data:",T IF T:1 OR T:2 THEN 180 ELSE 150 IF T:1 THEN T$:"numeric" ELSE T$:"character" PRINT: PRINT "You will be entering ";T$;" data. "; INPUT "Is this correct (Y/N)";Y$: PRINT IF Y$:"n" OR Y$="N" THEN 160 CLS: PRINT "You may now enter data after each prompt (7)." PRINT "If you make a mistake, backspace and correct it before entering it." PRINT "You can also edit your data set after data entry is completed." IF T:2 THEN 280 PRINT: PRINT "Enter '999' when finished.": PRINT GOTO 290 PRINT: PRINT "Enter 'end' when finished.": PRINT COUNT=O IF T:2 THEN 390 DIM D(1000) FOR I:1 TO 1000 PRINT 1;" "; INPUT D(I) IF D(I)=999 THEN 460 COUNT:COUNT+1 370 380 390 400 410 420 430 uuo 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 87 NEXT I GOTO 460 DIM D$(1000) FOR I:1 TO 1000 PRINT 1;" "; INPUT D$(I) IF D$(I):"end" OR D$(I):"END" THEN 460 COUNT:COUNT+1 NEXT I PRINT "End of data entry. You can now list your data set to check for" PRINT "errors. Each data value will be listed with a number. Note the" PRINT "numbers of data values to be corrected. You can halt the listing" PRINT "by pressing CTRL + NUM LOCK. Listing will resume when any key is" PRINT "pressed.": PRINT INPUT "Press RETURN to list your data on the screen",R$: CLS IF T:2 THEN 570 FOR I:1 T0 COUNT PRINT 1;" ";D(I) NEXT I: PRINT GOTO 600 FOR I:1 TO COUNT PRINT 1;" ";D$(I) NEXT I INPUT "Do you want to make any corrections (Y/N)";Y$ IF Y$:"n" OR Y$="N" THEN 800 PRINT: GOTO 650 INPUT "Another correction (Y/N)";Y$ IF Y$="n" OR Y$:"N" THEN 770 IF T:2 THEN 680 INPUT "Enter the number of a data value to be corrected: ";I GOTO 690 INPUT "Enter the number of a character string to be corrected: ";I IF I>COUNT OR I<1 THEN 660 IF T:2 THEN 740 PRINT "Current value:";D(I) INPUT "Enter the new data value: ";D(I) GOTO 630 PRINT "Current string :";D$(I) INPUT "Enter the new character string: ",D$(I) GOTO 630 PRINT: INPUT "Do you want to list your data set again (Y/N)";Y$ IF Y$:"y" OR Y$:"Y" THEN 790 ELSE 800 IF T:1 THEN 530 ELSE 570 CLS: PRINT "Data are now being sent to diskfile '";N$;"'." PRINT "NOte: identifier numbers are not included in your data file." IF T:2 THEN 870 FOR I:1 T0 COUNT WRITE #1,D(I) 850 860 870 880 890 900 910 920 930 9140 950 960 970 980 88 NEXT I GOTO 900 FOR I:1 TO COUNT WRITE #1,D$(I) NEXT I CLOSE #1 IF T:2 THEN 940 ERASE D GOTO 950 ERASE D$ CLS: INPUT "Do you want to enter another data set (Y/N)";Y$ IF Y$="y" OR Y$="Y" THEN 30 PRINT: PRINT "End of program run." END LIST OF REFERENCES LIST OF REFERENCES Blair, Raymond and Charles Shapiro, editors, The Lithographers Manual, The Graphic Arts Technical Foundation, 1980, pp. 5:8-5:13. Brassel, Kurt E., "A Model for Automatic Hill Shading", The American Cartggrapher, Vol. 1, No. 1, (1974), pp. 15-27. Brassel, Kurt E. and Jack J. Utano, "Design Strategies for Continuous- tone Area Mapping", The American Cartographer, Vol. 6, No. 1, (1979), Pp. 39-50. Castner, Henry W. and Roger Wheate, "Re-assessing the Role Played by Shaded Relief in Topographic Scale Maps", The Cartpgraphic Cole, Daniel 6., "Recall vs. Recognition and Task Specificity in Cartographic Psychophysical Testing", The American Cartographer, V01. 8, NO. 1’ (1981), pp. 55-66. Dent, Borden D., "Communication Aspects of Value-by Area Cartograms", The American Cartogpapher,Vol. 2, NO. 2, (1975), pp. 154-168. Dutton, Geoffrey, "Experiments in Contouring and Shading: A Dot Map Portfolio", Laboratory for Computer Graphics and Spatial Analysis, Harvard University, Unnumbered Report, July, 1978. Eilertson-Rogers, Jill P. and Richard E. Groop, "Regional Portrayal with Multi-Pattern Color Dot Maps", Cartographica, Vol. 18, No. 4. (1981). Pp. 51-64. Eyton, Ronald J., "Complementary Color, Two-Variable Maps", Annals, Association of American Geographers, Vol. 74, No. 3, (1984), pp 477-490. Frohnert, Kathryn 6., "An Evaluation of Unclassed Choropleth Dot Matrix Mapping", Unpublished M.A. Thesis, Michigan State University, 1983. Gilmartin, Patricia P., "Evaluation of Thematic Maps Using the Semantic Differential Test", The American Cartogpapher, Vol. 5, No. 2, (1978), pp. 133-139. Griffin, T. L. C. and B. F. Locke, "The Perceptual Problem in Contour Interpretation", The Cartographic Journal, Vol. 16, NO. 2, (1979), pp. 61-71. 89 90 Groop. Richard E., BASIC Algorithm for Random Dot Matrix Model, Unpublished, Michigan State University, 1982. Groop, Richard E. and Paul Smith, "A Dot Matrix Method of Portraying Continuous Statistical Surfaces", The American Cartographer, Vol. 9, NO. 2, (1982), pp. 123-130. Jenks, George F., "The Data Model Concept in Statistical Mapping", International Yearbook pf Carto ra h , Vol. 7, (1967), pp. 182- 188. Jenks, George F., "Generalization in Statistical Mapping", Annals, Association of American Geographers, Vol. 53, NO. 1, (1963), pp. 15-2607 Jenks, George F., "Optimal Data Classification for Choropleth Maps", Occasional Paper No. 2, Department of Geography, University of Kansas, 1977. McCleary, George F., "In Pursuit of the Map User", Auto-Carto II, Proceedings of the International Symposium on Computer-Assisted Cartography, September, 1975, pp. 238-250. Monmonier, Mark 8., "Maps, Distortion, and Meaning", Association of American Geographers, Resource Paper No. 75-4, 1977. Muller, Jean-Claude, "Visual Comparison of Continuously Shaded Maps", Cartographica, Vol. 17, No. 1, (1980), pp. 40-52. Nie, NOrman H., C. Hadlai Hull, Jean J. Jenkins, Karin Steinbrenner, and Dale H. Bent, SPSS Statistical Packagg for the Social Sciences, 2nd Edition, New York: McGraw-Hill, 1975, pp 267-275. Olson, Judy M., "Experience and the Improvement of Cartographic Communication", The Cartpgraphic Journal, Vol. 12, (1975), pp. 94-108. Olson, Judy M., "Spectrally Encoded Two-Variable Maps", Annals, Association of American Geographers, Vol. 71, No. 2, (1981), pp. 259-2760 Petchenik, Barbara Bartz, "A Verbal Approach to Characterizing the Look of Maps", The American Cartographer, Vol. 1, No. 1, (1974), pp. 63-71. Peterson, Michael P., "An Evaluation of Unclassed Crossed-Line Choropleth Mapping", The American Cartoggapher, Vol. 16, No. 1, (1979), pp. 21-37. Phillips, Richard J., "An Experiment With Contour Lines", The Cartographic Journal, Vol. 16, (1979). pp. 72-76. 91 Phillips, Richard J., Alan DeLucia, and Nicholas Skelton, "Some Objective Tests of the Legibility of Relief Maps", The Cartographic Journal, Vol. 12, (1975), pp. 39-46. Potash, L. M., J. P. Farrell, and T. Jeffrey, "A Technique for Assessing Map Relief Legibility", The Cartographic Journal, Vol. 15, NO. 1, (1978), Pp. 28-35. Robinson, Arthur, H., "Cartographic Representation of the Statistical Surface", International Yearbook pf Cartoggaphy, Vol. 1, (1961), pp. 53-61. Robinson, Arthur, H., Randall Sale, and Joel Morrison, Elements 2: Cartography, 4th Edition, New York: John Wiley and Sons, 1978. Rowles, Ruth A., "Perception of Perspective Block Diagrams", The American Cartographer, Vol. 5, No. 1, (1978), pp. 31-44. Shortridge, Barbara G. and Robert B. Welch, "Are We Asking the Right Questions?", The American Cartograpper, Vol. 7, No. 1, (1980), pp. 19-23. Smith, Paul, "Representing the Statistical Surface Using Continuous- Appearing Grey-Tone Variation", Unpublished M.A. Thesis Draft, Michigan State University, 1980. Smith, Richard M. and Richard E. Groop, "Producing NOminal Maps with Matrix Line Printers", Revista Cartographica, Instituto Panamericano de Geografia e Historia, NO. 37, (1980), pp. 89-96. Stoessel, Otto C., "Standard Printing Color & Screen Tint Systems for Department of Defense (DOD) Mapping, Charting & Geodesy Services (MC&G)", Proceedings 9: the Fall Convention, American Congress on Surveying and Mapping, Columbus, Ohio, 1972, pp. 91-149. Thorndyke, Perry W. and Cathleen Stasz, "Individual Differences in Procedures for Knowledge Acquisition from Maps", Cogpitive Psychology, Vol. 12, (1980), pp. 137-175. Tobler, Waldo R., "Choropleth Maps Without Class Intervals?", Geographical Analysis, Vol. 5, (1973), pp. 262-265. Tobler, Waldo R., Selected Copputer Programs, Department of Geography, University of Michigan, 1970. Yoeli, P., "Analytical Hillshading and Density", Surveying and Mapping, V01. 26’ NO. 2’ (1966), pp. 253-259. llllllllllll 3