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ART 314 - Material Culture: Light and Color

Page history last edited by williamCromar 8 years, 1 month ago

Fig 1 James Turrell, Afrum I (White), 1967


This reference resource is linked to Visual + Theoretical References in ART 314 - Environments, and will provide a basic historical-theoretical backdrop for this course.


Toward a Philosophy of Digital Modeling Part II

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...all material in nature—it being, as I said before, the mountains and the streams and the air and weare made of light which has been spent. And this crumpled mass called material casts a shadow. And the shadow belongs to light. So light is really the source of all being.

— Louis Kahn[1]


The ancient Greeks believed that the perception of reality occurred with the coincidence of two lights: one that projected from our own eyes and one that projected from the heavens. The convergence of the two lights upon objects was a precondition, to them, for the perception of the material world. We know now that light only comes from a source external to the body, but as artists we can still find a useful metaphor in the light of the eye... the mind's eye... bringing new form into the light.


Sunlight is perceived as essentially a radiant "white" color. Yet, even though it is only a small sliver of the entire electromagnetic spectrum, this light is a container for any color the human eye can perceive. When we see the world, we are not actually looking at material. Rather, we are observing the macroscopic result of a complex microscopic dance. Material absorbs certain frequencies of light, and allows others to reflect back out to our eye. We don't see stuff... we see the light stuff allows us to see.


Renderers use an algorithmic process that effectively models this process... and at a fundamental level, all your modeling efforts are aimed at manipulating this model of light. Although the process it models is almost infinitely more complex than any processor can handle, we'll see how certain light models are now creating images that are, at the resolution of human perception, almost indistinguishable from the reality they represent.

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Light is reflected into our eye, but this is only one among many interactions light has with material. The "spent light" of Kahn crumples into mass which can refract, diffuse and redirect light. The source, color cast, intensity and order of the light on that material greatly affects the way things appear in nature... and in your model.


Light and Meaning

Of all those variables, a simple change in the ordering of light energy, such as its direction, can fundamentally and dramatically change the content of a work. Margaret French Cresson recounts a famous example in the story of how Daniel Chester French, her father and the sculptor for the statue of Abraham Lincoln in the famous memorial in Washington, dealt with the problem of unfortunate lighting in the installation of the work.


Fig 2 Daniel Chester French, Abraham Lincoln, 1921. One of the first deliberate uses of artificial lighting by a sculptor, French maintains his intended narrative of a strong, confident Lincoln at left, using downlighting which imitated the light of the studio where he carved the work. When the sculpture was originally installed in the monument, Lincoln exhibited the frightened look at right, due to sunlight reflecting up off the floor. Light changes meaning!


The position of light also changes perception of form. Raked light... light which is directed from the side... emphasizes material texture and depth, more clearly articulating 3D form (Figure 2 at left). Frontal light, seen at right in the illustration, flattens the features and emphasizes outline or shape over mass. Baroque painters, sculptors and architects are among the most facile artists manipulating the dramatic possibilities of a light source. Francesco Borromini was a master of manipulating the hidden light source in a church, bouncing light off textures and layers to achieve high drama (Figures 3-4). Caravaggio (Figure 5) was accomplished at achieving light dramatics through the use of a technique he dubbed tenebrism, or night-effects. Light, for Caravaggio, was a means toward generating compositional hierarchy.


Fig 3 above left Sebastiano Giannini, section drawing of Church of San Carlo alle Quattro Fontane, ca. 1730. Drawn a century after church's completion.


Fig 4 above Francesco Borromini, Church of San Carlo alle Quattro Fontane, 1638-41. View of dome.


Fig 5 left Caravaggio, Supper at Emmaus, 1601-02


The period of the Enlightenment ushered in unprecedented scientific discoveries. By the 19th Century, the true nature of light began to be understood, and the advent of technologies like photography compelled the Impressionists to begin painting in an entirely new way. Interested in the camera and the scientific study of optics, Claude Monet (Figure 6) developed a style he called "optical realism" ... it wasn't about painting things, it was about painting light. The misperception of critics at the time was that Impressionists were sloppy, sketchy painters. The nature of their exploration... capturing the chromatic and optical effects of light... demanded a rapid, plein-air approach to craftsmanship.


A century later, James Turrel continues artistic fascination with the phenomenology of light in his large scale, immersive environments. More akin to the grandeur of ancient architectural monuments than anything else, he sculpts light into mass in Afrum 1 (White) (Figure 1 above) and makes the volume of a space "disappear" in Night Passage (Figure 7), all through the careful arrangement of light and material.


Fig 6 above Claude Monet, Poplars on the Epte, 1900

Fig 7 above right James Turrell, Night Passage, 1987


Today, Raphael Lozano-Hemmer generates surreal encounters through manipulations of projected light levels in interactive, public works such as Under Scan (Figure 8). The video with interview gives a full understanding of the phenomenon he creates (Figure 9).




Fig 8 left Raphael Lozano-Hemmer, Under Scan, 2008. Installation in Trafalgar Square, London


Fig 9 below Video documentation of Under Scan and interview with the artist. 

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Light and Material: a Spectrum of Properties

Because what we see is the interaction of light with material, it is important to understand that physical properties of material allow or restrict the movement of light. The spectrum of properties from opaque through translucent to transparent is illustrated in Figure 10.





Fig 10 A spectrum of physical properties of a material interacting with light. Behind each mass is a star:


1. Opacity, where the material allows no light to pass through its mass, so the star is unseen.


2. Translucency, where the material allows light to pass but diffuses it (see below) such that a clear view of the star that lies beyond the mass is not permitted.


3. Transparency, where the material allows light to pass through with a minimum of interference (see below), allowing full or near-full optical transmission of the star. 

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Opaque materials are rarer than one thinks. Generally, metals and very dense, matte materials are considered opaque. The misperception is that dark materials are opaque (Figure 11), but dark things can be, and often are, translucent. Darkness is not a characteristic indicator of opacity. Because they reflect a lot of light, mirrored surfaces, which typically use polished metals or foil-lined glass for reflection, are not thought of as opaque, but indeed they are (Figure 12).




Fig 11 Carbon black is obviously recognized as an opaque material... 


Fig 12 ... but a mirror is also opaque!

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Translucency is more common than we perceive. It is more a matter of degree than the poles of opacity or transparency... it is a manifestation of diffuse reflection of light under the material surface (Figure 13). One of the effects that generates the highest sense of realism in rendering (Figure 14) is the modeling of translucency. As we study material texture, we'll encounter a surprising number of materials that we think are opaque, but are in fact translucent (Figures 15-17).


Fig 13 left Diffuse reflection scattering light


Fig 14 middle left Henrik Wann Jensen and Juan Buhler, A Rapid Hierarchical Rendering Technique for Translucent Materials, 2002


Fig 15 middle right Light propagating through a human hand


Fig 16 below left Gordon Bunshaft with SOM, Beinecke Rare Book and Manuscript Library, 1963. The glowing walls are thin, translucent marble.


Fig 17 below right Translucent concrete (!) uses ground glass as an aggregate instead of stone 

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Like the other properties, we carry false generalizations about transparent materials. While transparent materials allow light to pass through, that doesn't mean the material doesn't affect the light. The thickness, density and surface topology of the material refracts the light path... bending the direction (Figure 18). Some materials, like water, are assumed to affect light color... the horrible stereotype of blue water is debunked in Figure 19. Other, nearly fully-transparent materials are really just ultra-translucent. That is, we assume they are colorless when in fact they have a tint, absorbing slight amounts of a broad spectrum wavelength (Figure 20). When modeling transparent materials, don't assume... observe!




Fig 18 above The straw in the water (dyed blue) appears broken due to refraction .


Fig 19 above right The color of water is completely dependent upon context... no blue here...


Fig 20 below right ... while seemingly colorless glass reveals a tint when observed carefully, especially at the edge. Even "clear" glass allows less than 90% of light to pass through. 

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Light and Maya


Light Models and Rendering

Light enters an environment and bounces around like an infinite quantity of crazed super-balls that refuse to lose momentum until either absorbed by something or bouncing back out. Each super-ball is a metaphor for a photon vector. Simple light models calculate one vector path for a given super-ball... the vector enters a room and bounces off a surface one time in a direction aimed at the eye (Figure 21 at left). These kind of direct illumination models give a sense of light and surface color, but they appear unnaturally flat. To achieve a higher fidelity with the real world, light models have been developed which bounce the light around a bit before it enters the camera. To be sure, the number of photons bouncing around in a real room is incalculable, so these models as a practical matter are restricted. While they fall far short of processing the full complexity of reality, they come very close to generating images that satisfy our perception of real-world light conditions (Figure 21 at right).


The simplest light models, such as scanline rendering, geometrically project an object in the scene to an image plane. The more complex raytracing adds optical laws of reflection intensity, shadow casting, diffusion, refraction and other optical effects to build a more realistic image. Like the Greek idea of light emanating from the eye, raytracing calculates an image by extending vectors, or rays, from the camera point into the scene (Figure 22). Of course, raytracing is more processor intensive than scanline rendering, making it better for pre-rendered situations like still images or movies and poorly suited for the real-time situations found in games.


Radiosity is added to the model to achieve the "super-ball" effect described above, using an algorithm that processes a selected number of times light reflects diffusely around in a scene. The higher the number of bounces, the higher fidelity the image. Radiosity can account for such variables as the area of the light source... take a look at your shadow in the sun and you'll see the edge of the shadow diffuses, because the sun (or any other light source) does not project light from a single geometric point. Through all these viewpoint-independent calculations, radiosity creates the diffuse light and shadow edges we encounter in the real world, yielding the highest fidelity images among the rendering models you'll encounter in Maya. Of course, it comes at a price: radiosity modeling takes the most time to generate.




Fig 21 above The bouncing light of the radiosity algorithm generates a more realistic effect  


Fig 22 left Diagram of the raytracing algorithm, building an image by extending rays into a scene 

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Atmospheric Perspective

Diffusion can also occur as a function of the atmosphere. Painters have long used atmospheric perspective to achieve a sense of pictorial depth. Hudson River School painter Asher Durand (Figure 24) illustrates the effect: particles in the atmosphere reduce detail, colors become desaturated, values become lighter, and longer wavelengths of light are blocked, causing all colors to shift to the blue-violet end of the light spectrum.


Fig 23 above Darrin Krumweide's illustration of the use of Simple Fog in a Maya rendering


Fig 24 left Asher B. Durand, Kindred Spirits, 1849 


One way Maya can emulate the effect atmosphere has on light is by using an environment effect known as fog (Figure 23). Simple Fog is one of Maya's Volumetric Materials, and is applied differently depending on whether you use Maya Software renderer or mental ray. In Maya Software, apply the fog material in the Render Settings window under the Maya Software tab>Render Options>Post Processing parameters... you'll click on the checkerboard icon to browse for and select Simple Fog. In mental ray, you apply fog using a Global Volume Shader which is assigned by heading for the Volume Shader attribute in the mental ray section of your selected camera’s Attribute Editor. A quick tutorial is available at the Gnomon Workshop that will demonstrate the parametric adjustment of fog.


They are a lot of fun, but over-use of environmental effects are often seen as a hallmark of newbie poor practice. Be discriminating in your use of an effect, and base it, as you do other decisions about light, on observation of real-world phenomena. Your portfolio should include use of fog only when it's appropriate, not just to show off.

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Fig 25 One Million Colors. When viewed at full resolution (1000 pixels wide and high), the image contains one million pixels. By changing values incrementally for red, green and blue, each pixel contains a unique color value. The human eye is sensitive enough to detect about 10 million colors, although the number of colors possible is theoretically infinite. See the full resolution version at this link.


Color is a property of light. Our eyes have the ability to perceive and distinguish different wavelengths of light, which we categorize by name as red, green, blue and other hues. Color is associated with material as well as light source, and color is generated by physical properties of material such as light absorption, reflection, diffusion, and other optical properties discussed above. The nature of physical optics was revealed by Sir Isaac Newton in Opticks (Figure 26), one of the primary documents in the history of science. His experiments with prismatic dispersion of light into the spectrum associated with the rainbow (Figure 27) led to the development of understanding one aspect of light as a wave phenomenon, with longer frequency waves yielding human sensations of reds, shorter yielding violets (Figure 28).




Fig 26 above Isaac Newton, Opticks , 1704


Fig 27 above right A prism dispersing light...


Fig 28 below ...shown in schematic animation


The terms and definitions used to describe color can often be contradictory and confusing, probably because perception of color is an intuitive and subjective condition. Terms are often used without great precision, yet even when they are precisely defined, their specific use depends on the color model being used. A color model is an abstract, mathematical description of the components of a color. Multiple color models exist, not because they compete with one another, but because each has their proper use in a certain context. In our work, we will discuss three kinds of models: the additive model, the subtractive model and a model known as HSV, based on the three properties of color known as hue, saturation and value. Before we explore the models, let's define those three terms.

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Hue is the property that gives color its color... the degree to which one color wavelength can be distinguished by name from another. The International Commission on Illumination (abbreviated CIE for its French name, Commission internationale de l'éclairage) defines hue as “the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, green, blue, and yellow." These are colors that have been described as psychological primaries or unique hues which humans perceive to be irreducible. Other hues on the spectrum have names, to be sure... orange, violet... but they are perceived as hues built from other hues.

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Saturation is the property that describes the amount or intensity of a hue present in a color. Other rough synonyms in various color models include colorfulness, chroma, purity... the idea is intuitively understandable. A red's red contains the brightest possible hue at the narrowest possible wavelength with no presence of a value bias... that is, no white (tint) to pink it up, gray (tone) to dull it or black (shade) to darken it down.

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The final property of color is Value, defined by the relative perceived lightness or darkness of a color. Depending on the kind of color model one uses, this property is also known by the synonyms lightness or tone. Photoshop uses the term brightness. The term shading is also used, usually to describe subtle manipulations of value in a drawing. When the value property is assessed under pure white light with no hue bias, it essentially becomes a spectrum of gray values from white to black, seen in Figure 29. This is known as a a grayscale. Note the interesting property of relativity demonstrated by using the middle value gray, perceived as midway between black and white, as a frame.


Fig 29 The frame surrounding the value scale is a uniform middle value gray. Having equal amounts of black and white, the frame seems to change value, an optical illusion based on the relativity of color.

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The Problem of Primaries

While discussing hue, the odd phrase psychological primaries was mentioned. We are all familiar with the idea of primary colors... red, yellow, blue, right? The so-called secondary colors are considered mixtures of the primaries, with red and blue mixing to achieve violet, blue with yellow to get green, and yellow with red to find orange. If we bend a spectrum around to create a circle and stitch violet to red, we get the color wheel.


This is the historical color model known as RYB, or Red-Yellow-Blue, and we recognize it in the traditional color wheel in Figure 30 that we've seen since grade school. It should be regarded somewhat as dogma, and with respect to modern color science it is as fatally flawed as the concept of a flat earth!


First, we must understand that the primary color concept is not a fundamental physical property of light. Rather, it is based on the physiological response of our eyes to light. Human sight is trichromatic. That is, we have receptors in our eyes that absorb light in three different frequency ranges, which combine to create the millions of colors we can perceive. The spectrum of hues is not itself made of mixtures, but are pure, discrete wavelengths. Primaries are biology, not physics.


Because we mix three colors in our eye, we psychologically react to colors with the sense that some are irreducible. Now, while the choice of any three primary colors is arbitrary, some colors mix better as primaries than others. The mixture of primaries creates what is known as a gamut... a useful, wide range of mixable colors. The larger the gamut, the more useful the set of primaries. The RYB model is not a terribly useful set of primaries, because the gamut it creates is fairly limited.


So, how do we determine a good set of primaries? There are two ways we know color mixes in the material world. We can mix colors by projecting or illuminating colored lights, and we can mix them by mashing compounds like ink or paint together...


Fig 30 Traditional RYB model 

Fig 31 Additive RGB model 

Fig 32 Subtractive CMY model

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Additive and Subtractive Color Models

When colored lights are combined, they mix to form the perception of new color. When enough of the right colors of light are added together, they combine to form pure, white light. A color model using light mixture is therefore known as an Additive color model. In an additive color model, the primaries that yield the largest gamut are red, green and blue (Figure 31), making up the model known as RGB.


When pigments such as inks or paints are mixed, they form the perception of new color as well. But as more pigments are combined, they subtract the amount of light that would be reflected off of the white surface upon which they are mixed. A color model using pigment mixture is therefore known as a Subtractive color model. The largest gamut achieved in a subtractive color model is generated by cyan, magenta, and yellow (Figure 32), and we call it a CMY model.


It's possible with very pure pigments or filters to achieve a black, but in most color mixing, an undertone of black pigment makes color mixing easier and more economical. This adjusted model is known as CMYK, with K standing for Key Black, because in the four-color printing process the black printing plate is the one used to register, or key, the other plates.


An Integrated Color Wheel

A careful observer will note that, when the primaries of the additive color model are mixed, they create secondary colors which are none other than the primaries for the subtractive model, and vice versa! Additive red and green mix to form yellow (weird, right?), green and blue make cyan, and blue and red wavelengths create magenta. Subtractive cyan and magenta combine to make blue, magenta and yellow make red, and yellow and cyan generate green.


This reciprocity among the two models makes it easy to combine them into an integrated color wheel (Figure 33), replacing the traditional and limited RYB wheel. So when we shift our orientation from one color model to the other, we simply shift the identity of primary and secondary triads. In our new color wheel, observe sets of numbers that show you the mixture of values in the respective color models. In CMYK, these numbers are expressed as percentages. In RGB, they are expressed in increments from 0 (no illumination) to 255 (maximum illumination), typical of how monitors, televisions and projectors process information. The third set of "numbers" is known as the hexadecimal system, which encode standard RGB values for use web page design... F is the highest value (equivalent to 16 in a base 10 system) and 0 is the lowest.


Fig 33 Integrated RGB-CMY color wheel


The integrated color wheel gives us a standard set of hues that works in tactile color mixing as well as across computer applications, from Photoshop to Maya to Premier. The new wheel acts like the traditional color wheel, but some old relationships need to be reassessed... complementary colors are shifted (the complement for red is cyan, not green, for example).


With hues well-defined in accordance with modern optical science, we can turn our attention to particularly useful color model.

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HSV Color Model

One limitation of a color wheel is its ability to model all of the properties of color. As a flat plane it has area area, and can therefore show two variables. For example, one can create a wheel that shows all the hues as one variable, and the saturation level as another. Or, one can show hue and value... or saturation and value. But it's impossible to show all 3 variables without turning to a 3 coordinate system. Imagine trying to describe 3D space while only using an XY coordinate system...


Hence, color standards have been developed that are known as color spaces. One common cartesian-based, 3-coordinate color space uses RGB as values along the 3 axes and is computationally very useful, but the resulting RGB color space makes it difficult to visualize neutral gray tones in a graphic way (the gray values run along a diagonal bisector of the RGB color cube). The HSV color space reorients the geometry of the RGB space to solve these perceptual deficiencies.


HSV stands for Hue-Saturaton-Value, as you might already have guessed. In some applications (like Photoshop) it is called HSB, where value is replaced with the synonym brightness, but they are equivalent. The HSV model creates an abstract, cylindrical "space" that can be conceptualized as containing all "possible" colors in the gamut. The cylinder is useful because we can recognize the color wheel as the hue values march around one set of degree coordinates. We can perceive saturation as intense at the skin of the cylinder and totally desaturated at the center. Finally, we can see the grayscale of value from black at the bottom to white at the top. The brightness of a pure color in the HSV model is equivalent to the brightness of white (other models, like the HSL model, create different value-based equivalencies... make sure you are clear on the definitions in a given model!). Explore the components of the HSV color cylinder in Figure 34 below.


Fig 34 A color cylinder used to describe HSV color space. B. The unwrapped "skin" of the cylinder describes the high saturation (S) of all hues (H) and values (V) together, with S values on a decimal scale from 0 (no color) to 1 (full color). C. A horizontal section of the cylinder describes all hues and saturations present for a given value, here a middle value gray, with V quantified from 0 to 1. D. A vertical section describes all values and saturations for a given hue pole, here a red-cyan pole... demonstrating that red and cyan are complements in the integrated RGB-CMY color model. H values are typically described as degrees, with 0 being red, 60 yellow, 120 green, 180 cyan, 240 blue and 300 magenta.


The HSV cylinder aspect used in color pickers such as we see in Photoshop (Figures 35) was specifically developed for computer applications, but it is very intuitive for artists and not difficult to understand once it is visualized as a "space." In the Maya material color picker, you can change the selector from an RGB cube to an HSV cylinder at the lower right drop-down (Figures 36-37).


Fig 35 left The Photoshop Color Picker presents a vertical half-section of the HSV cylinder alongside the brightest portion of the "skin." H values are quantified by degree, S and B (an alternate for V) as percentages. 


Fig 36 lower left The Maya material color selector, set to choose HSV values. Compare to the Photoshop picker, and to the Maya selector set to RGB in Fig xx. 


Fig 37 below The Maya selector, set to RGB. 


Color is a fascinating topic which we've only been able to scratch the surface of in this title. If you wish to go in greater depth, visit David Briggs' comprehensive website The Dimensions of Colour.

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Color and Space

Color is stereotyped as a purely graphic or surface phenomenon, but as color begins to interact it begins to suggest spatial relationships both actual and illusionistic. One way that color generates a sense of space is through the juxtaposition of warm and cool colors. Although not a hard and fast rule, warm colors (based on magentas, reds and yellows) tend to advance visually in most contexts, while cool ones (based on greens, cyans and blues) tend to recede (Figure 38).



Fig 38 left Yellow HSV values are 60-1-1, blue 240-1-1. They represent warm colors (colors that visually advance) and cool (colors that visually recede) at their most extreme, seen here on a neutral, middle-value gray (HSV = X-0-0.5) field.






Fig 39 left Joseph Albers, Homage to the Square: On an Early Sky, 1964


The color-based geometric abstraction of Josef Albers presents us with a sense of layered space through color interaction and an illusion of transparency fostered by color relationships. In Figure 39, we first see three squares: on top a high-saturation lighter red, in the middle a high-saturation darker shade orange (a.k.a. brown) and lastly a high-saturation middle-value cyan-blue. As we observe, a strange phenomenon begins to take place: the brown, containing a high level of red, begins to associate with the top square, while at the same time, its darker value begins to associate with the cyan-blue. We start to see the cyan-blue as a transparent filter, laying on top of a red square sitting behind it, with a hole... the smallest square... opening to it. Not only has Albers made three squares become two, and made one square feel like a hole, he's made the "advancing" warm color appear to sit behind the "receding" cool one. Even more astounding, he's made the dark orange (technically a warm color) feel like it contains cyan-blue... its complement! These are byproducts of color interaction and phenomenal transparency techniques, of which Albers was the acknowledged master.


Other color relationships begin to generate a sense of pictorial space, but they can also be used to manipulate actual space in a 3D model. Among the many are these:


  • Monochrome palette (Figure 40): uses tints, tones and shades based on the same or nearly the same wavelength of light. These palettes tend to create a sense of color unity that binds and camouflages form, compresses space and create a psychological sense of relative stability.


  • Analogous palette (Figure 41): uses hues adjacent to a dominant color to create variety, hierarchy, balance, focal points and other visual phenomena. Analogous colors create more distinct form but maintain a sense of spatial and pictorial unity, since the colors on either side of the dominant color tend to be, at some level, a mixture containing some aspect of the dominant color.


  • Complementary palette (Figure 42): creates stronger figure-ground relationships that tend to develop uniqueness, contrast and spatial depth. Interesting situations can develop with complementary palettes whereby a hot color rendered on a far-away object can tend to shoot forward in a cool environment, creating a strong sense of spatial tension and ambiguity.


Fig 40 below James Whistler, Nocturne: Blue and Silver - Cremorne Lights, 1872. An example of a monochrome color palette based on shades of blue.


Fig 41 right Paul Cezanne, Houses in Provence, 1883. A painting with an analogous color scheme centered on green, with yellows and cyans to either side.


Fig 42 below right Henri Matisse, La Danse (1), 1909. An example of a complementary color palette... orange and a bright blue-cyan.


As the use of these various palettes establishes spatial relationships for the artist, we begin to better understand how form and color interact to manipulate visual phenomena in complex ways. Revisiting the illustration from our discussion of asymmetrical balance (Figure 43), we can perhaps better appreciate how the "rules" can be overturned by the perceptual changes color brings to the compositional mix.


Fig 43 Recalling our earlier discussion of asymmetrical balance...

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This reference resource is linked to Visual + Theoretical References in ART 314 - Environments, and will provide a basic historical-theoretical backdrop for this course.


Toward a Philosophy of Digital Modeling Part II


Return to Exercises at the main page for ART 314 - Environments

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Credits + References



Fig 1. http://www.guggenheim.org/new-york/collections/collection-online/show-full/piece/?search=James%20Turrell&page=1&f=People&cr=3 

Fig 2. http://media.photobucket.com/image/lincoln%20memorial%20light/sasims1112/lincoln.jpg

Fig 3. http://commons.wikimedia.org/wiki/File:Borromini_Drawing_02.jpg modified by the author

Fig 4. http://commons.wikimedia.org/wiki/File:InteriorDomeSanCarlo4Fontane1.JPG modified by the author

Fig 5. http://www.wga.hu/frames-e.html?/html/c/caravagg/06/index.html

Fig 6. http://en.wikipedia.org/wiki/File:Claude_Monet_040.jpg

Fig 7. http://www.guggenheim.org/new-york/collections/collection-online/show-full/piece/?search=James%20Turrell&page=1&f=People&cr=3

Fig 8. http://www.tate.org.uk/intermediaart/underscan.htm

Fig 9. http://www.tate.org.uk/intermediaart/underscan.htm

Fig 10.http://en.wikipedia.org/wiki/File:Opacity_Translucency_Transparency.svg modified by the author

Fig 11. http://commons.wikimedia.org/wiki/File:Carbon_black.jpg

Fig 12. http://en.wikipedia.org/wiki/Mirror

Fig 13. http://en.wikipedia.org/wiki/Diffuse_reflection

Fig 14. http://graphics.ucsd.edu/~henrik/papers/fast_bssrdf/

Fig 15. http://sites.google.com/site/dosiatbli/what-is-dosi-

Fig 16. http://en.wikipedia.org/wiki/Beinecke_Rare_Book_and_Manuscript_Library

Fig 17. http://www.lewism.org/2005/07/29/translucent-concrete/

Fig 18. http://en.wikipedia.org/wiki/Refraction

Fig 19. http://commons.wikimedia.org/wiki/File:Glass-of-water.jpg

Fig 20. http://riderglassit.glassinchina.com/product/showpro_327699.html

Fig 21. http://en.wikipedia.org/wiki/Radiosity_%283D_computer_graphics%29

Fig 22. http://en.wikipedia.org/wiki/Ray_tracing_%28graphics%29

Fig 23. http://www.thegnomonworkshop.com/tutorials/simple_fog/simple_fog.html

Fig 24. http://www.artlex.com/ArtLex/n/nature.html

Fig 25. http://en.wikipedia.org/wiki/File:1Mcolors.png

Fig 26. http://en.wikipedia.org/wiki/Opticks

Fig 27. http://en.wikipedia.org/wiki/Prism_%28optics%29

Fig 28. http://en.wikipedia.org/wiki/File:Light_dispersion_conceptual_waves.gif

Fig 29. Illustration by the author

Fig 30. http://en.wikipedia.org/wiki/RYB_color_model modified by the author

Fig 31. http://en.wikipedia.org/wiki/RGB_color_model modified by the author

Fig 32. http://en.wikipedia.org/wiki/CMYK_color_model

Fig 33. Illustration by the author

Fig 34. http://en.wikipedia.org/wiki/HSL_and_HSV modified by the author

Fig 35. Illustration by the author

Fig 36. Illustration by the author

Fig 37. Illustration by the author

Fig 38. Illustration by the author

Fig 39. http://artsearch.nga.gov.au/Detail-LRG.cfm?View=LRG&IRN=32424&PICTAUS=True 

Fig 40. http://www.tate.org.uk/tateetc/issue3/riverofdreams.htm

Fig 41. http://www.nga.gov/press/exh/194/index.shtm 

Fig 42. http://en.wikipedia.org/wiki/File:La_danse_%28I%29_by_Matisse.jpg

Fig 43. Illustration by the author



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Twombly, Robert, ed. Louis Kahn: essential texts. W. W. Norton. 2003. p. 275.


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  1. Kahn, Louis. "Lecture at Pratt Institute (1973)." In Twombly, Robert, ed. Louis Kahn: essential texts. W. W. Norton. 2003. p. 275.

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