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Six-Point Perspective and Beyond as Examples of Integral Art
When I say that "curvilinear perspective is an example of Integral art," I'm not suggesting that all Integral art should be based on curvilinear perspective but only pointing out that this technique represents a significant departure from linear or rectilinear perspective. It accomplishes this by providing an expanded perception of space and time that is not normally accessible to the visual field. On the other hand, depicting people using curvilinear perspective may be undesirable as that could stretch the morphology of humans to something cartoon-like, unrecognizable, and weird. I think that it is used primarily to depict natural or non-human scenes.
As I understand it, curvilinear perspective is also known as "five and six point perspective." However, beginning at four point perspective, perspective is no longer based on straight angles or lines but on lines that are bent from an an oval-like grid across a picture plane canvas. This four-point perspective is utilized primarily by architects for designing tall buildings above the visual field with multiple vanishing points. I do not think that four-point perspective is curvilinear, which I believe applies only to five, six, and possibly zero point perspective.
In five-point perspective, the canvas or grid becomes spherical in shape permitting the depiction of a full 180 degree hemispheric scene. Unless one is a fish, this is beyond the normal scope of vision. Beyond that, it is purely speculative for me as I am certainly no artist by any stretch of the imagination. My primary interest is generic patterns of any kind, whether visual or non. However, based on everything that I've read, seen, and heard, one to five point perspectives refer to objects in front of the visual field. Beyond the six point or sixth-person perspective, the spherical canvas becomes a moving and transparent sphericity of clear light. The purpose for the transparency and movement being to view objects behind the visual field for a 360 degree panoramic view. How is this possible? Because movement is not necessary in the viewer, the passive receptical: only in the artist who creates the scene who can successfully bring the full panoramic view in clear light before the viewer, and in the moving sphere. Thus, agency, creativity, and a bit of autonomy are required in an artist at six point perspective or higher. Very few artists ever attempt it, although it has been done.
"I become a transparent eyeball. I am nothing, I see all. . . ." --Emerson
| If you were to put a transparent ball on your head and float out into the middle of a pond with trees around its edges and copy onto the inside of the ball what you see this is what Termes thinks it would look like. All up and down trunks of trees would reflect to a point on the bottom of the ball. The motion in the water would create an opposite pattern. It would create concentric circles aiming toward the bottom of the sphere. Source: http://www.termespheres.com/gallery1.html
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And beyond six-point perspective? Perhaps to 'see through' the innards or interiority of people as well in transparency.




For more information on multiple point perspective, click here:
http://www.2d-digital-art-guide.com/multiple-point-perspective.html
On second thought--I don't know whether curvilinear perspective or transparency is even considered "Integral" art so never mind...
I came here initially to add another image but upon typing "On second thought--" above, had a change of heart. I almost deleted the entire post. But now that I've typed the disclaimer above, I suppose that I'll leave everything down below "as is," for whatever it is worth.
The article below, "Curvilinear Perspective as Synthesis Art," provides a brief history of Western art and claims that curvilinear perspective is "beyond postmodern" and is a synthesis of multiple perspectives in a single glance, resulting in the widening of peripheral vision beyond 180 degrees and the curvature of space by time. It is a synthesis (or integration, if you will) of all present and all prior artistic techniques in Western art involving representation, abstraction, and perspective. By all accounts, it appears to an example of what Jean Gebser refers to as "aperspectival-integral" art in that it is integrating, is concerned with temporics, is spherical in nature, and transcends three-dimensionality by manipulating space and time. It is thus multiperspectval, yet transcends the pluralism and relativism of postmodern art. Is it a return to the modernism of Picasso and Cezanne? Some may think so; certainly Gebser regards those artists as "integral" and I don't think there's been any Integral artist to champion them to date. I will return with some sample images of this art form to add to this post from different artists using this particular technique. Here is the url for the artist's personal example (click image), where s/he provides an excellent description of curvilinear perspective:

Curvilinear Perspective
Source: http://www.cheeseman-meyer.com/techniques/curvilinear.html
Curvilinear Perspective
Curvilinear perspective allows much greater field of vision than traditional rectilinear perspective. In the image below, we are able to see boxes from all 6 directions, and draw them well beyond the vanishing points, while allowing them to still look like boxes. In rectilinear 3-point perspective, the boxes beyond the vanishing points distort severely.
Roll mouse over image to see rectilinear version (give time for both images to load) [should rectilinear version fail to load, click link above --b]:
Curviliear Perspective as Synthesis Art
WHY CURVILINEAR PERSPECTIVE COULD BE SYNTHESIS ART?
Joining the traditions of Giotto, Bruenelleschi and Masaccio and in the traditions of Cezanne, Picasso and Warhol seems promising. Focusing on the spatial/temporal traditions of painting does have the advantage of attending to a significant artistic problem that many postmodern artists have overlooked. This effort could prove to be valuable because of the fundamental nature of the problem. History shows that solutions to this very problem have had a monumental effect on the history of art. Brandenberger is hard at work to perfect a curvilinear solution to extending the temporal/spatial qualities of painting. |
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6-point perspective & interest in generic patterns.
Posted March 15th, 2009 by barbi hammondI've added a note and some speculative thoughts about 4, 5, and 6-point perspective and transparency/clear light to my post. It is located above the original post above the horizontal separator bar.
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A brief summary of 1 to 6 point perspective (with images)
Posted March 15th, 2009 by barbi hammondSource: http://www.termespheres.com/perspective.html
One Point Perspective | |||
One point perspective takes one of the three sets of parallel lines of the cube and projects them to a point, a VANISHING POINT. We will say this is the North direction. The other two sets of lines of the cube continue to run parallel and unaltered. This vanishing point can also be considered where your eye is located in relation to objects found on this page. This location of the eye or (vanishing point) becomes the place where cubes shift across in space to show their opposite side, from right to left and from above you to below you. | ![]() | ||
Two Point Perspective | |||
Two point perspective uses two of these three sets of parallel lines of the cube. It projects one set of parallel lines to the North point and the second set of parallel lines to the East vanishing point. In two point perspective, the third set of lines continues to run parallel. In this case, they run straight up and down. Notice the two points we are using, North and East, are 90 degrees of our horizon. This HORIZON LINE is also the EYE LEVEL LINE. The eye is better to use because if you are underground or in outer space there is no such thing as a horizon but there is always a location of your eyes (eye level). | click on picture to print out your own two point grid | ||
Three Point Perspective | |||
Three point perspective uses all three sets of parallel lines of the cube. Similar to two point perspective, one of the sets of parallel lines aims toward the North point and the other set aims toward the East point. The third set of lines projects toward the Nadir point (below you) or the Zenish point (above you). Either Zenith or Nadir can be used with the same grid by spinning the three point perspective grid 180 degrees. You can project all of these lines with a straight edge. | ![]() | ||
Four Point Perspective | |||
Four point perspective can be thought of in a couple of different ways. First, we use the same logic it takes to get to three point perspective. But if the cube we are looking at is very tall and projects above you and also goes below your eye level, these up and down lines must project toward two points. Not only does the cube look fat in the middle, it also seems to get smaller as it goes above and below your eye level. These lines, which used to be the up and down parallel lines of the cube, are now curving in like a football coming together at the Zenith and Nadir points. If you were on the twentieth floor of a skyscraper, looking out the window at another skycscraper, forty stories high, you would see this type of effect. | ![]() | ||
Five Point Perspective | |||
This system of perspective, using five points, creates a circle on a piece of paper or canvas. You now can illustrate 180 degrees of visual space around you. It captures everything from North to South and from Nadir to Zenith. Think of yourself inside a really exciting visual environment like St. Peter's Basilica in Rome. You bring a transparent hemisphere with you. When you find a spot in the Basilica where any direction you look is visually exciting, you put the hemisphere in front of your face and copy what you see on the inside of it. The hemisphere shows five vanishing points, north, on the left, east in the middle and south on the right. There is also a point above your head and another below your chin. One hundred and eighty degrees of the total environment can be drawn in this hemisphere. Think of how this would look on the flat surface. You would have to rely on five point grid system on the flat page to do the same thing, but it really will work. | ![]() | ||
Six Point Perspective | |||
The sixth (South) point is missing from five point perspective drawings. Within five point we get half, or a hemisphere, of the visual world around us. To get the rest of the picture, the the whole picture that is, you must add that last vanishing point. You would have to turn around and look at the room BEHIND you to see the rest of the room and to find that last point. If you were in the transparent sphere in St. Peter's Basilica you would have to copy not only what you see in front of you, but everything behind you as well. A good way to do this on flat paper is to draw the last vanishing point on the back side of the first drawing. Yes, I mean on the back side of your first drawing. The same grid will help you finish the total picture on this back side. When the rest of this picture is drawn you have a 360 degree picture in all directions. | ![]() | ||
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click on picture to print out your own two point grid



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Keith's article doesn't address the space and time relationship to...
Posted March 14th, 2009 by barbi hammondAs the author above notes,
The postmodern art world has seen many gifted painters searching and finding new exciting psychological, social, technical, and multimedia solutions to problems of painting, but few are directly attending to that perennial problem of finding new ways of depicting deep space on a flat surface like Giotto or Cezanne once attempted.
Perhaps equally important, if not more important, than "subjective" or "objective" from an artistic standpoint is the space and time constitution of the structures. Each structure of consciousness has a unique way of relating to space and time, and this space-time relationship is reflected in the arts. Without addressing the important relationship of space and time to the structures, we are essentially left without a way of following three-dimensional perspectival art from the Rennaissance (which is three-dimensional, spatial, and temporically frozen) to its logical conclusion; nor with any way of discriminating what is "new" from what is "old" insofar as technique. While very useful in a very general sense, the descriptions below and the article that it came from doesn't really address what is novel or integral in art in terms of technique or what to "look for," for example, in integral art; nor offers any examples.
The stages above are not in themselves "structures" in the Gebserian sense but are general cultural movements and art movements. I wouldn't even call Postmodernism an art movement as such, but rather a philosophy and a cultural term that did not produce any new techniques in art per se other than pop-art.
Whereas historically or time-wise, the first three belong in the three-dimensional mental-rational structure (orange and green), the last art movement, if it exists, Integralism, refers to the four dimensional aperspectival-integral structure (teal and above). Yet even in the mental-rational structure of Modernism, there are inceptions of the four-dimensional aperspectival-integral art in the artwork of Picasso, Cezanne, Georges Braque, Paul Klee, Dali, and many other avant-garde artists--all of whom transcend the boundaries of linear perspective and duality by incorporating the time element into their artwork. In other words, they had a new perception of the world and a brand new technique for depicting the world that differs from that of linear perspective. This cannot be said of Postmodernism as it is a hodge-podge of prior movements (including Modernism) and pop-art (which many do not even consider to be art). What does "Integralism" have insofar as technique, more specifically, that is beyond that of Modernism? I seem to run across the same issue in 20th century music as well.
Because of the basic approach of modern art--that of incorporating the fourth dimension, time, into three-dimensional space--it represents a whole new perception of the world from that of linear perspective. As a consequence, modern art will naturally take on a less "objective" look and may appear more surreal, more subjective, and less culturally (or viewer) "accessible" compared to, say, Realism, which is "obvious and given" or to Postmodernism, which is attuned to pop culture. The seeming inaccessibility, incommunicability, and subjectivity of Modernism is perhaps the time element in art which bends space and opens it up more so than on the infallibility of "subjective truth."
To my knowledge, Modernism is really the most advanced art form that we have to date insofar as perspectival technique but of course I could be mistaken. For instance, even though curvilinear perspective is possibly "integral," it isn't really "new" since Cezanne and many others were already employing "sphericity" in the early 20th century.
Under "The Meaning of Art Is" for "Integralism," "What the culture allows" doesn't really make a great deal of sense to me as a requirement of integral art since "culture" doesn't even allow for or appreciate modern art (hence the replacement of "high art" with the pop-art and mediocrity of Postmodern art). The author of that article (forgot name, sorry) doesn't really define "what the culture allows"; yet seems to suggest that culture does not like postmodern art. But nor does mainstream culture care for modern art. So I'm not really sure what the culture allows for.