2.7.1 Fuzzy logic
The principle of vagueness is common in spoken language. While describing a certain object, the exact attributes and parameters become substituted by vague expressions (fig. 16), which indicate only the real-world data. However, they still have to describe the degree of membership, especially when using them in mathematical analyses (Kruse et al. 1994, 2). Since there are fewer rules, the system is seen as quite intuitive (Cox 1994, 7). Due to imperfect data it becomes even less complex (Kruse et al. 1994, 1). The core element is the fuzzy sets, which describe the degree of membership. The degree is represented by an interval of [0, 1] (Cox 1994, 2; Dubois and Prade 1988, 14). Therefore, it becomes highly suitable for representing uncertainty (Klir and Yuan 1995, 4). Crisp sets (fig. 16) describe the opposite and are either 0 or 1. Instead of numbers, the Boolean
operators “true” and “false” can also be used. This sharp distinction of data might work only in theoretical models. The real world usually does not build up on this system (Klir and Yuan 1995, 4 and 220).
Figure 16: Comparison between a fuzzy dataset (a) and a crisp dataset (b). The graphs clearly indicate that fuzzy sets have no sharp boundaries and can flow smoothly into another one. The single value, here temperature, can be perceived over a longer range. In contrast, crisp sets allow only the assignment of a temperature to predefined intervals (Klir and Yuan 1995, 15).
50 The membership function of the fuzzy logic describes the degree of membership of an individual object to a subject. Hereby, each object is assigned an own value (Klir and Yuan 1995, 4). A similar approach is provided by the probability theory (Klir and Yuan 1995, 187). By contrast, the probability theory deals mainly with random distribution, while fuzzy logic uses actual data (Cox 1994, 19; Nicolucci and Hermon 2010, 30). Consequently, fuzzy systems can describe real-world behaviors in most cases best (Klir and Yuan 1995, 15). Transferring the idea of fuzzy systems to an archaeological context, the membership function indicates to what extent a piece of evidence might prove or disprove a certain theory, which results in a degree of uncertainty. A crisp set would represent perfect data, which would make each investigation unnecessary (Klir and Yuan 1995, 177), while fuzzy data might represent the best data from archaeological research and should be used as a leading method (Sifniotis et al 2006, 1; Nicolucci and Hermon 2010, 28). While fuzzy logic is completely based on mathematical principles, colors seem to be more subjective. However, the theory indicates soon that also the colors are based on static rules.
2.7.2 Colors
Colors are a major factor in design and serve in many cases as information transmitters (Wäger 2017, 15). However, the reception and interpretation of colors are heavily dependent on the society. Changes over time and from one geographical region to another are not uncommon (Wäger 2017, 64). The primary colors cannot be created by mixing (Wäger 2017, 81). Therefore, secondary colors emerge when two primary colors are mixed in a ratio of 1:1 (Wäger 2017, 82f). Primary and secondary colors are rare in the natural environment. Most natural colors are from tertiary nature (Wäger 2017, 84). The actual colors depend on the blending mode and can be separated in additive (light) and subtractive (particles) nodes (Wäger 2017, 81). Black, white and grey are defined as achromatic colors since their emergence is slightly different from the other ones (Wäger 2017, 86). Technically, colors are usually described with the RGB or HEX code for digital end products. Other codes would be CYMK, lab and the grayscale used in photography or printing. Each of them indicates the amount of primary color that has to be added to obtain a certain color (Wäger 2017, 94). Nevertheless, it should be noted that up to 8% of the male population has an eye malfunction, which might result in color blindness or shift (Wäger 2017, 142).
Various rule sets have been established over time to give the color combinations a meaningful interpretation. Most of them are known as contrast (tab. 3) and harmony theories (tab. 4). Firstly, there is the dark and bright contrast. This contrast is mainly used
51 to differentiate between a foreground and background. The highest contrast that can be achieved in achromatic colors is black (0%) and white (100%), while blue (20%) and yellow (80%) represent the highest dark and bright contrast in chromatic colors (Wäger 2017, 254). Secondly, there is the color contrast. The color contrast contains assorted colors. The saturation and brightness might vary between pallets. The contrast itself is determined by the distance of the colors on the color wheel. However, all kinds of contrasts can be combined and mixed. Moreover, manipulated or mixed primary colors are usually more suitable for scientific representation since they are more pleasant to observe (Wäger 2017, 256). Thirdly, there are complementary contrasts, in which two opposite colors on the color wheel are used to express a high contrast between two datasets (Wäger 2017, 258). Fourthly, one has to consider warm and cold contrast, whereby the color wheel is rotated slightly so that blue is on the top and red at the bottom. This enables an easy categorization in warm and cold colors (Wäger 2017, 260). Fifthly, there is the saturation contrast, which is small rather than high (Wäger 2017, 262). Sixthly, the chromatic and achromatic color contrast is similar to the previous one, but with a higher contrast in total since it also includes all the black and white tones. Therefore, achromatic color can further emphasize chromatic colors when chosen correctly (Wäger 2017, 264). Finally, there is the area contrast, which is highly subjective and consequently less in use (Wäger 2017, 268).
Table 3: Colored examples of the various contrast theories. The examples are just a combination of countless possibilities (after Wäger 2017, 252-266 and http://paletton.com)
Contrast Dark and bright Color
Complementary Warm/cold Saturation
Chromatic and achromatic
The color harmonies (tab. 4) can have similarities to the contrast. They relate to the combination of several colors with a pleasing color palette as outcome matches (Wäger 2017, 268). The harmonic triad uses three colors with the same contrast at the color wheel. When using primary colors, it is advisable to slightly manipulate the brightness, tint or hint to take away some of their prominence (Wäger 2017, 270). Similar to that is
52 the tetrad harmony, which has four colors instead of three (Wäger 2017, 272). The complementary color harmony shows the complementary contrast by using two opposing colors from the color wheel. It can represent opposite opinions (Wäger 2017, 274). The analogous harmony bears a resemblance to a gradient. It combines neighboring colors on the color wheel and represents the opposite of the complementary harmony. The former harmonies can be interpreted mainly intuitively (Wäger 2017, 280). Lastly, we have the monochromatic color harmony. Hereby, the same color is used with different saturations and brightness (Wäger 2017, 284), which makes it suitable to display related data. Table 4: Colored examples of various harmony theories. The examples are just a few of countless combinations (after Wäger 2017, 268-287 and http://paletton.com)
Harmony triad tetrad complementary analogous monochromatic
Pbr-shaders are related to the color theory, but are not based upon the same principles. In contrast to the previously described theory, they encode another kind of information. Rather than showing harmonies, they encode information about light behaviors during the rendering process. The exact functionality and possible use for archaeology is explained in the next section.
2.7.3 Physically-based rendering
Physically Based Rendering (PBR) is an upcoming technology in the virtual reality world rather than a standard. In the process of pbr rendering, render information about light behavior is encoded in different kinds of texture maps (fig. 17). The main aim is to improve the behavior and the approach to reality (McDermott, 2f). This can be created by oneself or purchased on specialized websites, such as http://poliigon.com/ or http://textures.com. One set of maps usually includes a diffuse, albedo, ambient occlusion, normal, displacement, reflection and gloss texture map of the same object. Each texture map encodes a different kind of information for the lighting behavior (http://poliigon.helpscoutdocs.com/).
53 Figure 17: Texture maps of a material. The figure represents only a selection of the most common ones. From left to right: Diffuse map (+ ambient occlusion), displacement map, normal map and the rendered model (textures from/ after http://poliigon.com/).
Accordingly to Allegorithmic, the company that provides software to create and edit this
data, one major advantage is that it “provide[s] a workflow for creating consistent artwork, even between different artists”. Consequently, each map describes a different attribute of the same object (McDermott, 3). And a standard between several users is established.
In this case it might describe the behavior of light and manipulate geometry, but would it not be possible to transfer this concept to our problem and use distinct texture maps to encode various kinds of uncertainty directly upon the object? It might be even possible to use this form of data enrichment as base for conditional rendering.