In Human history both clear glass and linear perspective are new inventions, both appearing in the last 600 to 700 years. They worked in concert. With clear glass we got lenses, clear windows and vivid mirrors. All three were adapted by artists as tools to make more believable space in their pictures.
By the 15th century artists were mastered linear perspective and aimed lenses at their subjects through camera obscuras. Their observations astounded them. Glass windows and mirrors added multiple layers to reality. Reflections on glass distorted according surface curvature. Reflections on window glass obscured and confused the subject behind them. Artists were first attracted to the distortions of curvature as new motif in the 17th century. But, they would wait for architecture and design innovations of the 20th century to begin to wrestle with layers of reflections on glass co-mingled with the motif behind the window.
In the 18th century halls of mirrors not only filled royal palaces with light (Versailles) they also expanded the feeling of space. England’s Crystal Palace of 1850 filled its giant interior space with light as well as, showed vast fields of sparkle and reflections to the exterior world. These effects were not lost on artists.
By the 1920s the German Bauhaus art and design school changed architecture by rethinking the use of glass. They wanted more of it (see W. Gropius). They wanted long lines of it, walls of it. Within a few years architects like Jean Prouve were designing Bauhaus like homes featuring walls of glass (example 1). He relied on simple linear perspective in his design work . You can see the evidence in his 3D model here.
example 1. Prouve house from 1930s.

By mid 20th century the fashions of painting had turned away from the apparent rigidity of linear perspective in favor of the physical gestures of abstract expressionism. But, as that fashion faded artists returned to linear perspective and the distortions of transparent and reflective glass. In the last half of the 20th century artists found delight in ambiguities of reflections found on glass and the world seen through it. Photography fed us ideas here.
But our brain works differently than a camera. We can look at the same 2D surface and recognize a variety of patterns because of our ability to selectively focus and, our ability to select different patterns from the same reflective surface. These are zones of attention which can be manipulated at will. A photograph of myriad glass reflections were reconstructed in paint by artists of the late 20th century, especially a group identified as photo realists. One prominent example is the artist Richard Estes (example 2). He uses convincing linear perspective and the ambiguities of glass to create an inside/outside world.
example 2. Richard Estes, Columbus Circle.

Because our focus is directed to intersections, especially “T” intersections, we delight in columned architecture. Our eye’s attention is primarily directed at the nexus of the vertical and the cross bar. We spend less attention on the column. Example 3 traces eye fixations while looking at a column with overhead crossbar (G.T.Buswell 1931). See where we direct our foveal saccades.
Example 3. Cornea tracing of eye fixations.

If you are making a picture with columns/verticals and rhythmic variations of the intersecting overhead cross bars then you can anticipate where the viewer will look. Intersections attract our attention.. The glass reflections create layers of ambiguity which enhance a feeling of dynamic (motion evoking) 3D space.
Consider this linear perspective diagram of DaVinci’s last supper (example 4) then, notice how an offset overlay of the same diagram on itself creates a stronger feeling of stereopsis (example 5).
example 4. Perspective design of Last Supper painting.

example 5. Perspective design with faux stereopsis.

For my following painting examples I wandered through New York finding complex glass reflection patterns coupled to opportunities for linear perspective. I discovered deviously ambiguous images to confuse or enhance our sense of deep space. In example 6 I explored the glass walled foyer of the new Whitney museum of American Art in NYC. In example 7 I began the same subject in a square format; this is step one. Example 8 represents a later step of the same painting. I placed shadows on the floor on a bias to casually intersect with the vertical columns and people. In example 9 I have the ricocheting reflections of glass along Madison Avenue. In example 10 you see the first step in trying a squared version of the same subject. Example 11 presents the same painting in a later stage.
example 6. Foyer of New Whitney Museum

example 7. Step one of Squared version

example 8. Step two of the Square version.

example 9. Horizontal of Glass on Madison.

example 10. Step one of Squared version of Glass on Madison.

example 11. Step two of Squared Version of Glass on Madison.

On November 8, I welcome you to a late afternoon lecture, Art and Architecture, how they similarly evolved and, how they influenced each other from the distant past until now. The lecture begins at 4:30 on Sunday November 8, 2015 at the Silvermine Art Center. See Silvermineart.org or daviddunlop.com for more information.

Gail Ingis
We are fortunate to have seen how art and architecture has imploded and exploded with the advantages of new materials and new technology. You tirelessly point out how to see, contemplate and enjoy the advancements. Thank you for your dedication.
Janine Robertson
This is so interesting, I just can’t stop looking at it. The intricate reflections through glass are lumnious and the perspective creates a wonderful composition!
Patricia Scanlan
Your Glass on Madison square painting is like a jewel. It is most intriguing and for some reason captivating. I guess for one reason it’s because it is unexpected.