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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

 

 

 

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?

Through the use of curvilinear perspective  visionary landscape paintings are created to situate the viewers in an expanded sense of time and space. This curvilinear perspective approach to painting relies both on the Renaissance foundation of linear perspective and the modernist’s abstraction of pictorial time and space. This curving pictorial mode of imagery deals with a fresh approach to the fundamental problems of representing a three-dimensional world on a flat surface. Although this new approach is often overlooked it is becoming more common among contemporary painters. The results of this effort could become an accepted resolution of the postmodern antithetical split between the formalists need to abstract and the realists need to capture a concrete world.


BACKGROUND ON CURVILINEAR PERSPECTIVE

WHY STRAIGHT OBJECTS CAN BE DEPICTED WITH CURVED LINES

Within our normal peripheral vision objects, which are straight such as roads or buildings, can be depicted as such with straight lines in pictures. However, the act of viewing straight objects beyond our normal peripheral vision requires that we remember more than we can see at any one instant and therby we need to mentaly stitch together these multiple views. Also in the act of seeing beyond our normal peripheral vision we rotate, tilt, and twist our heads as we look around the scene. When depicting such an experience of the wider view, the combination of moving our heads and of stitching together multiple views is what creates the curved look of straight objects. For visual demonstration of this effect see the home page of the web site, brandenbergerfineart.com, or view the DVD in this packet.

A BRIEF HISTORICAL ACCOUNT OF THE SIGNIFICANCE OF BRANDENBERGER’S CURVED SPACE IN PAINTING

A PREVIEW SYNOPSIS

The Middle Ages strived to see a spiritual realm in its pictorial creations. It transported us to an abstract space and time through the use of dazzling materials like gold leaf and ceramics as well as through the use of abstract elements in line, shape and color. It did not use pictorial techniques to show a physical world.

The Renaissance needed to capture concrete reality. A major pictorial development towards this end was the creation of linear perspective as an illusion of three dimensions on a flat surface. The Renaissance abandoned the abstractions of the Middle Ages.

Modern Art was preoccupied with a formalistic ‘art for arts sake’ approach of pure vision in painting. Abstract qualities of painting ruled as a way of enhancing the design elements and compositions of the material on the surface of the paintings. Any illusion to the three dimensional world was considered  superfilous to the autonomy of pure vision. The techniques of linear perspective were deemphasized.

Postmodern Art has changed the strict abstract approach to painting that prevailed in Modern Art, by loosely applying its basic formalistic premise of emphasizing the qualities of design principles and elements in figurative imagery that satisfied the needs of the mass culture. Postmodern artists also have rebelled against Modern art by employing the illusion of traditional linear perspective. Postmodern art uses either abstract or traditional representational approaches to painting or combinations of these two. But Postmodern artists have not created a new form of spatial compsoition.

Brandenberger’s art is designed to find a resolution to the postmodern bifurcation in painting of abstract versus representational space. His solution is to employ curvilinear perspective in a way that includes the use of temporal and spatial imagery that works with both realistic and abstract aspects of painting.


HISTORICAL SIGNIFICANCE

MIDDLE AGES – SPIRITUAL TIME AND SPACE

During the Middle Ages a prevailing attitude was that man should strive for an omnipresent godly understanding of his place in a spiritual world. The art of the Middle Ages was less concerned with how the physical world looks to any one person and more concerned with the scheme of the non-physical spiritual universe. ‘How many angels can dance on the head of a pin?’ points to this kind of abstract thinking. The art of the Middle Ages attended to the beauties of the abstract art by employing the use of such shimmering materials as gold leaf and ceramic surfaces and by employing the abstract order of lines, shapes, patterns and color. The depiction of physical realities including the recession of deep space was neglected or ignored.

RENAISSANCE – CONCRETE TIME AND SPACE

During the early Italian Renaissance the a new humanistic attitude evolved that promoted the idea that God gave each person the ability to reason on his own, therefore each person should use his God given abilities to reason from his own personal experiences of the world. The term ‘Renaissance Man’ refers to the ability of individuals such as Leonardo da Vince to rely on his own observations of the world to solve a myriad of problems in all kinds of disciplines. Giotto di Bondone (c, 1267-1337) used this new attitude in his paintings to depict how the physical world looks from a single person’s point of view. He has been credited as the first artist since the ancient world to create on a flat surface the appearance of three-dimensional forms. The great early Italian Renaissance architect, Filippo Bruenelleschi (1377-1446) continued this tradition of depicting three dimensions on a flat surface by creating the first consistent system of one point perspective. This form of linear perspective is based on a rational geometric system of straight lines that guide the artist in accurately depicting the recession of space according to size and position of objects as they appear from one point of view at any one instant. With this approach both time and space were considered absolute in that both time and space were unaffected by objects or their motion. Within this cultural context of needing to see the physical world the invention of linear perspective was so valued that it has dominated the art world for at least three hundred years and continues today as one of the most generally accepted artistic tools for depicting three-dimensional space on a flat surface.


MODERN WORLD – FORMAL TIME AND SPACE

As the Western culture evolved it became less reliant on direct observation of the concrete to develop its understanding of the world. After all, diseases were now thought to be caused by micro organisms and the solidity of mass itself seemed to evaporate into an invisible structure of subatomic particles. The “Renaissance Man” faded with the onslaught of the specialists formally trained in their respective disciplines. Yes, even the artists immersed into the esoteric world of formalistic art as they began to emphasize the arrangement of lines, shapes, colors and textures while deemphasizing the three dimensional qualities of shaded modeling and linear perspective. The Postimpressionist, Paul Cezanne, was the first to break the Renaissance bonds of seeing only one view at one instant and began to experiment with showing a scene with multiple views in one image. In this way he introduces a new sense of time in painting because one cannot be in two places at once. Further, Cezanne introduces a new relationship with pictorial space and energy. He employs patches of colors and broken lines which emphasized the formal abstract qualities of arranging shifting pictorial planes in a dynamic spatial composition of a scene. These images suggest that energy; matter, time and space are affected by one another as if the forces of an invisible relativistic realm are being revealed. Pablo Picasso continued to develop this multiview approach with the creation of Cubism. With Cubism the artists had stepped over the threshold of a new form of creativity by freeing themselves from referencing the world of the concrete. They transformed the multiple views into shapes, lines, colors and textures then reassembled them into pure visions beyond anything that could be seen in the ‘real’ world. Modern artists in their zeal to develop their formal discipline of art based on a pure visual aesthetic, separated themselves from the common man’s everyday view of the three dimensional world. This Formal art is based on the idea that the integrity of visual art is diluted when it pretends to be stories, illustrations or windows into other worlds because this violates the inherent flatness of a painting. Further no other media such as literature, music or architecture offers this quality of flatness. The work of the Abstract Expressionist painter, Jackson Pollack, is an example of such art that no longer refers to the illusion of a space and time of a three dimensional world but is an example of painting where material on a flat surface creates a visual simulation of a purely abstract swirling realm of its own space and time.

POSTMODERN WORLD – A  FORMALISTIC CULTURAL TIME AND SPACE

As the ‘modern artists’ achieved at least in their own minds the high status of the avant-garde above the common throngs, a new form of art immerged which appealed to the masses need to see realistic images as well as their need to affirm the popularity of their mass culture. Pop Art was borne. With it came all kinds of commercial and popular images that continued or adapted the modern abstract approach to painting such as in the work of Andy Warhol, Roy Lichtenstein, and Jasper Johns, Also during this postmodern phase a rebellion surfaces against formalistic tenets of modern Art with the advent of realistic paintings. Realistic paintings of the everyday world as can be seen in  Richard Estes, which returned to the use of linear perspective just as it had been perfected during the Renaissance. 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. The contemporary painting world seems bifurcated into accepting either the formalistic attitudes of the modern painters which emphasize material and design elements over depicting a three dimensional world or accepting the traditional techniques of linear perspective as established in the Italian Renaissance. The condition of postmodern painting is one of returning to and revising its own already established cultural achievements of expressing time and space in painting. In this sense contemporary painting is ‘retro’ which is generally considered to be one of the prevailing characteristics of the postmodern world.


THE SYNTHESIS

One of the subtleties of considering spatial aspects of painting is that time is often over looked as an inherent feature of its imagery. For example a one-point-linear-perspective image requires that time is momentarily frozen as it shows one point of view at one instant. Whereas the imagery of Paul Cezanne’s paintings suggests that time is slightly extended beyond an instant as multiple views of the same objects implies a shifting of positions during the viewing. Likewise, curvilinear perspective that Brandenberger uses has its temporal qualities because of the time it takes to scan a scene with multiple views and then intuitively stitch these views together from memory or imagination.

In Brandenberger’s curvilinear paintings, a case can be made that this creative method is fundamentally the same as the cubistic approach begun by Cezanne and continued by Picasso. Firstly, both the cubistic approach and Brandenberger’s curvilinear approach employ a combining of multiple views in an act of creating worlds that cannot just simply be observed. Secondly, Both approaches affirm the hallmark of modern art that the artist must above all be creative i.e. create their own worlds not imitate it. Clearly when straight objects are depicted with curved lines, the viewer will consciously or unconsciously become aware that the artist is using a pictorial devise to create an image that is not imitating the world as we normally see it. In this sense both the multiple viewing and the curving of space are transcending reference to the ‘real’ three-dimensional world because the artist is manipulating space and time while creating his own visions.

On the other hand Brandenberger’s work in curvilinear perspective is much like the traditional Renaissance perspective. During the Italian Renaissance there was a need to capture reality by rationalizing understandings of the real world. In this cultural context linear perspective was created as a rational pictorial device to imitate that real world. It was based on straight-lined, geometric law-like regularity in the depiction of objects and their relative sizes as they receded in space. The result was a very consistent unbroken illusion of natural space. Brandenberger’s use of curvilinear perspective actually uses this very same unbroken consistent perspective technique when applied to images that are included within the range of normal peripheral vision. In this sense he is like all the other artists since the Italian painter Masaccio (1401-1428) that have used linear perspective. In this way Brandenberger’s work is part of one of the longest traditions of depicting the natural world by using a consistent law like method of showing the recession of natural space in paintings.

What places Brandenberger outside the tradition of simply repeating the same established tenets of linear perspective is that his perspective is radically different when it depicts objects that extend beyond the limits of our normal peripheral vision. When he depicts a scene that extends beyond normal peripheral vision, space bends and time is extended. These are opposite features from traditional perspective where guidelines are straight and time is shrunk into an instant. However, the curving and temporally expansive qualities of his curvilinear perspective become more like the cubistic approach of the early modern artists where the creative liberties of expressing pictorial time and space were exalted. The temporal/spatial aspects of his curvilinear perspective owe a great deal to both the Renaissance ideal of attending to the natural world and to the Modern Cubistic ideal those artists create their own worlds. He is synthesizing both the traditional approach to linear perspective and the cubists approach to formal space with his approach to curvilinear perspective.


Others have also explored of the spatial/temporal aspects of curvilinear perspective. The contemporary realists Clive Head one such painter. A special note goes to Rackstraw Downes with is panoramic curvilinear realists works.  The artist M. C, Escher (1898-1969?) focused on curvilinear representation of space earlier than either of these two painters. In his lithograph titled ‘High and Low’ Escher creates a visual curvilinear world in which a viewer seems to wrap around himself because he is simultaneously in two different places at the same time looking at himself.  Escher creates curvilinear worlds that stretch rationality to the point of absurdity. 

 

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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Keith's article doesn't address the space and time relationship to...

As 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.

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6-point perspective & interest in generic patterns.

I'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)

Source: 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.