Applying Math to the Study of Color 数学在色彩研究中的应用
Using mathematical equations the statistical probability and the number of individuals who are likely to have a visual anomaly within a population can be determined with a relatively high degree of accuracy. Using various demographics such as the size of a target population, the gender ratio between males and females, and the ethnic diversity of the sample population, a mathematician is able to estimate the probable number of individuals with visual anomalies.
使用数学方程，可以相对高精度地确定群体中可能存在视觉异常的统计概率和个体数量。数学家利用各种人口统计数据，如目标人群的规模、男女之间的性别比例以及样本人群的种族多样性，来估计视觉异常个体的可能数量。
Even without solving for specific variables, a basic understanding of the dominate genetic factors amongst different genders and ethnic groups allows for professional designers to quickly estimate the probability of individuals with visual anomalies that might be in an audience. This information can be important in determine an acceptable error margin for the number of people who may no be able to view specific information, make alterations to the design and colors used in a presentation, or make an appropriate number of customized documents handouts to give to individuals with various visual anomalies who may be attending the presentation. Although this might seam like a bit much for a school presentation, professional designers are constantly being held to the highest standard when creating presentations for large corporate events.
即使不解决具体变量，对不同性别和种族群体中主要遗传因素的基本了解也能让专业设计师快速估计群体中可能存在视觉异常的个人的概率。对于无法查看特定信息、更改演示文稿中使用的设计和颜色的人数，这些信息对于确定可接受的误差范围非常重要，或者制作适当数量的定制文档讲义，分发给可能参加演示的各种视觉异常的个人。虽然这可能有点像学校的演示文稿，但专业设计师在为大型企业活动制作演示文稿时，始终保持最高标准。
For example countries like Korea which has the most homogeneous population in Asia with 99.9% of its population being of Korean decent, or countries like Japan where 98.5% of its inhabitants are of Japanese decent, are both countries which have a population that is almost entirely Asian. Based on standard probabilities the instances of visual anomalies within an audience will be much lower than in European countries like Poland where 98.2% of its population is Polish (Caucasian – Northern European). Based on standard probability with Asian having a probability of 3.1% and Northern Europeans having up to 8% probability for visual anomalies, it can estimated that the probability of modifications being needed in the same presentation are 2.58 times higher when the presentation is done in Poland than in either Korea or Japan. Furthermore counties like Lesotho which has the most concentrated population of individuals with African decent with 99.7% of the population being native Sotho, and individuals of African decent having the lowest probability of having the defective X-chromosome, the probability of visual anomalies in this country is statistically the lowest in the world.
例如，亚洲人口最同质的国家如韩国，其99.9%的人口是韩国人，或日本，其98.5%的居民是日本人，这两个国家的人口几乎完全是亚洲人。根据标准概率，群体的视觉异常情况将远低于波兰等欧洲国家，波兰98.2%的人口是波兰人（高加索-北欧）。根据标准概率，亚洲人出现视觉异常的概率为3.1%，北欧人出现视觉异常的概率高达8%，可以估计，在波兰进行演示时，需要修改的概率比在韩国或日本高2.58倍。此外，莱索托等国家的非洲裔人口最为集中，其中99.7%的人口来自索托土著，非洲裔的X染色体缺陷概率最低，据统计，这个国家出现视觉异常的概率是世界上最低的。
Using Mathematical Algorithms to Create Color Simulations 利用数学算法创建颜色模拟
In 1931 the organization known as The International Commission on Illumination, or C.I.E., was established to regulate and promote the scientific study of color. The goal of the organization was to established the first scientific system of colour. C.I.E. established that there are actually 2 sets of primary colors. These are the Additive Primary colors of light and 条、the Subtractive Primary colors of matter.
1931年，国际照明委员会（简称C.I.E.）成立，以规范和促进颜色的科学研究。该组织的目标是建立第一个科学的色彩系统。C.I.E.确定实际上有两套原色，光的加性原色和物质的减性原色。
In-order to scientifically study colors every possible color that could be created needed to be mathematically indexed, and a standardized reference point established. To do this A method of describing colours based on three criteria, Hue, Lightness, and Saturation (H.L.S.) was created. By mapping colors based on these three criteria a three-dimensional color map of every possible color was created. These three-dimensional color maps are known as color spaces, and the Lab Colour space was developed as a reference space that all other colour spaces are based off on. Lab colour encompasses every colour that is theoretically possible in the electromagnetic spectrum. Each Colour Space has a defined colour environment which has distinct colour characteristics and limitations. The limitation of a color space is known as its gamut. The term gamut refers to the achievable range of colour that a colour space can reproduce when compared to the full range of colours that are theoretically possible in the Lab Color Space.
为了科学地研究颜色，需要对每种可能产生的颜色进行数学索引，并建立一个标准化的参考点。为此，创建了一种基于色调、亮度和饱和度（H.L.S.）三个标准的颜色描述方法。通过基于这三个标准映射颜色，创建了每个可能颜色的三维颜色图。这些三维颜色图被称为颜色空间，实验室颜色空间被开发为所有其他颜色空间都基于的参考空间。实验室颜色包括电磁光谱中理论上可能的每种颜色。每个色彩空间都有一个明确的色彩环境，该环境具有鲜明的色彩特征和局限性。颜色空间的限制称为色域。色域是指与实验室颜色空间中理论上可能的全部颜色范围相比，颜色空间可以再现的可实现颜色范围。
The use of computer technology has allowed the study of color to advance significantly in the past few decades. Using complex computers algorithms a mathematician or computer technician can now create accurate color simulations based on the scientific study of color. For example, every color that is theoretically possible in the electromagnetic spectrum can be identified mathematically based on its H.L.S. values. By cross-referencing a colors known values to its perceived values, or the value in which it has been reproduce, the difference in the color reproduction can be calculated. By mapping the color discrepancies a custom color profile or color simulation can be created for any number of applications. These include but are not limited to simulation the output color of s specific device such as a computer monitor, projector, or printer. Color simulations can also be created to simulate chromatic visual anomalies so that individuals with normal color vision can see how a design will look by someone who has a specific visual impairment. The designer can then customize or modify their designs to maximize the visual legibility of their designs.
在过去的几十年里，计算机技术的应用使颜色的研究取得了重大进展。使用复杂的计算机算法，数学家或计算机技术人员现在可以根据对颜色的科学研究创建精确的颜色模拟。例如，电磁光谱中理论上可能的每种颜色都可以根据其H.L.S.值进行数学识别。通过将已知的颜色值交叉引用到其感知值或其已被再现的值，可以计算颜色再现中的差异。通过映射颜色差异，可以为任意数量的应用程序创建自定义颜色配置文件或颜色模拟。这些包括但不限于模拟特定设备（如计算机显示器、投影仪或打印机）的输出颜色。还可以创建颜色模拟来模拟彩色视觉异常，以便具有正常颜色视觉的个人可以看到具有特定视觉障碍的人的设计外观。然后，设计师可以定制或修改其设计，以最大限度地提高其设计的视觉易读性。
Chromatic Anomalies Color Simulation
The “Chromatic Anomalies Color Simulation” above recreates the visible light spectrum as seen by individuals with different types of visual anomalies. With the exception of Achromatopsia all other visual anomalies are able to see certain colors. By looking at the color simulation above several generalizations can be deduced. The colors blue and yellow are highly visible and can be seen by the majority of the population; however vibrant colors like magenta, orange, vivid shades of green, and red can be difficult to differentiate form one another for individuals with different visual anomalies.
上面的“颜色异常模拟”表呈现了具有不同类型视觉异常的个体所看到的可见光谱。除色盲外，所有其他视觉异常都能看到某些颜色。通过观察颜色模拟，可以推断出以上几种概括。蓝色和黄色非常显眼，大多数人都能看到；然而，对于具有不同视觉异常的个体来说，洋红、橙色、绿色和红色等鲜艳的颜色很难相互区分。
Tonal Progression 色调级
All colors can be thought of as a tone within a tonal progression from black to white. It is often difficult to think of colors as a tone and not of the color we see; however understanding a colors tonal value is an important aspect when analyzing how much contrast there is between two different colors in a design. Look at the tonal scale below:
所有颜色都可以被认为是从黑到白的色调过程中的一种色调。通常很难将颜色视为一种色调，而不是我们所看到的颜色；然而，在分析设计中两种不同颜色之间的对比度时，了解颜色的色调值是一个重要方面。请看下面的色调阶：
Now think about the different colors shown in the color spectrum. Where would colors such as yellow and blue be place on this scale if we consider the colors tonality? Is there a large difference in tonality between these two colors? If we use these two colors together in a design will we have good contrast and legibility? What about colors such as crimson and azure, or orange and olive?
现在想想光谱中显示的不同颜色。如果我们考虑色调，黄色和蓝色的颜色会放在什么地方呢？这两种颜色的色调有很大差别吗？如果我们在设计中同时使用这两种颜色，我们会有良好的对比度和易读性吗？像深红色和蓝色，或者橙色和橄榄色这样的颜色呢？
Tonal Matrix 色调阵
The tonal matrix below show the legibility of different tonal combinations based on contrast values. Ideally a minimum contrast ratio of 50% is desirable; however lower contrast ratios can be seen with some difficulty. The larger the contrast ratio is between two colors the easier it will be to see the different elements in a design.
下面的音调矩阵显示了基于对比度值的不同音调组合的易读性。理想情况下，50%的最小对比度是理想的；然而，较低的对比度是有一定难度的。两种颜色之间的对比度越大，越容易看到设计中的不同元素。
Note: Although this matrix is in black and white only, any color can be substituted for any tonal value. For example blue has a tonal value of about 80% while yellow has a tonal value of about 20%. The contrast ratio between the two is a difference of 60% and will be legible even to individuals with chromatic visual anomalies.
注：尽管该矩阵仅为黑白，但任何颜色都可以替换。例如，蓝色的色调值约为80%，而黄色的色调值约为20%。两者之间的对比度相差60%，即使是有色觉视觉异常的个体也能清晰地看到。
Colors in Design 设计中的颜色
Colors can imply many different types of emotions. Used effectively color can be a strong design element.
颜色可以表明许多不同类型的情感。有效使用的颜色可以是一个强大的设计元素。
The theory of psychological color effect is used in many different creative fields. Graphic designers use color theory when choosing colors and color combinations that they will use in a document. Corporate marketing agents will use color theory when designing corporate identities and promotional materials for their clients. Movie directors will use color theory when lighting a movie set in-order to create a particular mood for a scene. Even if we do not notice the specific applications of color and are completely unaware of its affects on our subconscious, the use of color influences every aspect of our daily lives. Every product that we buy, to every ad we see has had its colors carefully chosen by a professional designer based on the subconscious effects and emotions that will be experienced by the final viewer.
心理色彩效应理论被应用于许多不同的创作领域。图形设计师在选择文档中使用的颜色和颜色组合时使用颜色理论。公司营销代理在为客户设计公司标识和促销材料时将使用颜色理论。电影导演在为电影布景照明时会使用色彩理论，以便为场景营造特定的气氛。即使我们没有注意到颜色的具体应用，也完全没有意识到它对我们潜意识的影响，颜色的使用影响着我们日常生活的方方面面。我们购买的每一件产品，看到的每一个广告，都有专业设计师根据最终观众的潜意识效果和情感精心挑选的颜色。
Although colors can portray many different emotions, the effective use of color in creative fields is more complicated than just simply using the color. Context is very important in understanding the effective uses of color in design. Many colors can portray many different emotions depending on the surrounding context and cultural perceptions of the target market.
虽然颜色可以描绘许多不同的情感，但在创意领域有效使用颜色比仅仅使用颜色更复杂。语境对于理解色彩在设计中的有效运用非常重要。根据目标市场的周围环境和文化感知，许多颜色可以描绘许多不同的情感。
Red is an example of a color which has two very different associated emotions. In one context the color red might be used to portray love, while in a different situation the color red might portray hate or anger. The English expression “red with anger” is commonly illustrated in Western cartoons where a villains face will become bright red when they are angry that one of their evil plans has failed. What other examples can you think of where the color red is used to convey an emotion? Can you think of any other idiom that uses color to portray meaning such as the phrase “green with envy”?
以红色为例，它有两种截然不同的关联情感。在一种情况下，红色可能用来表示爱，而在另一种情况下，红色可能表示仇恨或愤怒。英语表达“愤怒的红色”通常在西方漫画中出现，当恶棍们对他们的一个邪恶计划失败感到愤怒时，他们的脸会变得鲜红。你能想到哪些例子里红色是用来表达情感的？你能想到其他用颜色来表达意思的习语吗，比如“嫉妒的绿色”？
Color Meanings in Design 设计中的颜色含义
| Yellow | 黄色 | Attention Cheerful Childish (Naive) Optimism | 注意 愉悦 天真（幼稚） 乐观 |
| Orange | 橙色 | Attraction Stand Out (Unique) Wealth Youthfulness | 吸引 突出（独特） 财富 年轻 |
| Pink | 粉红色 | Caring Empathy Love Sympathetic (Tenderness) | 关爱 同情 爱心 怜悯（亲切） |
| Red | 红色 | Anger Energy Hunger Love (Passion) | 愤怒 能量 饥饿 热爱（激情） |
| Purple | 紫色 | Arrogant or Childish Luxury (Royal) Mysterious Sadness | 自大或幼稚 奢侈（贵族） 神秘 伤感 |
| Blue | 蓝色 | Calm Faith (Trust) Smart and Stable Power | 镇定 信念（信任） 聪颖和稳定 力量 |
| Green | 绿色 | Soothing Eco-Friendly Envy Jealousy | 温和 环保 羡慕 嫉妒 |
| Black | 黑色 | Bold Evil Rich, Powerful, Elegant Strength | 大胆 邪恶 富有，权利，优雅 力气 |
Describing Color 描述颜色
The following is a list of terminology which is specific to the study of color.
以下是专门用于颜色研究的术语列表。
| Additive Color | 加色 | A color system where colors will become brighter when they are mixed together. | 当颜色混合在一起时会变得更亮的颜色系统。 |
| Ambient Light Effect | 环境光效应 | An illusion where the color characteristics of an image seem to have different tonality and hue when viewed under a different light sources. Example: a change in the perceived color of an image when it is viewed under daylight and then tungsten light. | 一种错觉，在不同光源下观察时，图像颜色特征具有不同的色调和色调。示例：在日光和钨光下观看图像时，图像的感知颜色发生变化。 |
| Saturation | 饱和 | The intensity of color. | 颜色的强度。 |
| Complement | 补充色 | A color opposite in hue. Example: a color located on the opposite side of the color wheel. | 色调相反的颜色。示例：位于色轮另一侧的颜色 |
| Contrast | 对比度 | The visual attribute that allows colors to be distinguished from one another. This is a function of a difference in the tonal value between colors. | 允许颜色彼此区分的视觉属性。这是颜色之间色调值差异的函数。 |
| Dynamic Range | 动态范围 | The amount of contrast between the lightest and darkest points in an image. Also used to describe the maximum recording limit of a medium such as film. | 图像中最亮点和最暗点之间的对比度。也用于描述介质（如胶片）的最大记录极限。 |
| Fluorescence | 荧光 | A phenomenon where a substance changes ultraviolet light into visible white light. This makes the color appear brighter than its surroundings. | 一种物质将紫外线变为可见白光的现象。这使颜色看起来比周围环境更亮。 |
| Hue | 色调 | A difference in color along the visible light spectrum. | 沿可见光光谱的颜色差异。 |
| Secondary Color | 次生色，混合色 | A color which is made as a result of mixing two primary colors together. | 由两种原色混合而成的颜色。 |
| Shade | 阴影 | A darker variation of a color as a resulting from the addition of a black pigment. | 因添加黑色颜料而引起的颜色的较暗变化。 |
| Spectrum | 光谱 | The progression of visible light from red through violet. | 可见光从红色到紫色的过程。 |
| Subtractive Color | 减色 | A system of color where colors become darker when they are mixed together. | 当颜色混合在一起时会变暗的一种颜色系统。 |
| Tint | 淡色彩 | A lighter variant of a color as a resulting from the addition of a white pigment. | 一种颜色的较浅变体，由于添加了白色颜料而产生。 |
| Value | 色值 | The range of a colors tonality ranging from bright shades to dark tones, where white and black are the two extreme values. 颜色 | 色调的范围从明暗色调到暗色调，其中白色和黑色是两个极端值。 |
Color Schemes
| Accent color | 重点色 | A color that is added to a composition which does not belong to any particular color combination and is used to add visual interest or a focal point to the image. | 添加到构图中的一种颜色，不属于任何特定的颜色组合，用于给图像增加视觉趣味或焦点。 |
| Double Complement | 双重补色 | The combinations of two adjacent colors (including different values of the color) in the color star. | 色星中两种相邻颜色（包括颜色的不同值）的组合。 |
| Monochrome | 单色 | A color scheme using varying values of only one color. | 仅使用一种颜色的不同值的配色方案。 |
| Split Complement | 分裂补色 | A Color scheme consisting of an accent color and the two colors to either side of its complement on the color wheel. | 一种配色方案，由一种强调色和两种颜色组成，分别位于色轮补色的两侧。 |
| Triad | 三色 | Color combinations that are made from mixing colors from either the additive or subtractive color primaries. | 由加色或减色原色混合而成的颜色组合 |
| Wide Analogous | 宽类比 | Color combinations which encompass a wide range of adjacent colors and may include up to half of the hues and tones in the color wheel. | 组合颜色包括范围广泛的相邻颜色，并可能包括色轮中多达一半的色调和色调。 |
Design Terminology 设计术语
| Busy Background | 复杂背景 | A background image with many design elements. This makes identifying the main object or focal point difficult. Since busy backgrounds reduce the legibility of key elements and content, they are typically considered as a bad design choice. | 具有许多设计元素的背景图像。这使得识别主要对象或焦点变得困难。由于复杂的背景会降低关键元素和内容的易读性，因此它们通常被视为糟糕的设计选择。 |
| Dominant Element (Focal Point) | 主导元素（焦点） | The most significant object in a design which draws the viewers attention. | 吸引观众注意力的设计中最重要的对象。 |
| Legibility | 清晰度 | The ability to clearly see and discern the difference between the elements of a design. | 能够清楚地看到和辨别设计元素之间的差异 |
| Vanishing Boundaries | 消失边界 | The inability to discern adjacent elements from one another because the two colors are similar in value. This results in the two elements blending into one another making them look like a single element. | 由于两种颜色的值相似而无法区分相邻元素。这导致两个元素相互混合，使它们看起来像一个元素。 |
| Varying Backgrounds | 变化背景 | A surface which has a gradation between two or more colors or shades. | 在两种或两种以上颜色或色调之间具有渐变的表面。 |
| Vibrating Boundaries | 振动边界 | A phenomena which causes visual irritation to the viewer when two adjacent elements in a design are identical in value but are significantly different in hue. This phenomena makes it appear is if the colors are vibrating but is actually a result of eye fatigue. | 当一个设计中的两个相邻元素的值相同，但色调明显不同时，会对观看者造成视觉刺激的一种现象。如果颜色在振动，但实际上是眼睛疲劳的结果，这种现象就会出现。 |
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