GETTING OUT OF THE BOX AND INTO THE SPHERE
When you look at Termesphere paintings you get a sense of geometric order. Why would a painting of Notre Dame in Paris on a sphere give you the feeling of order? What are these orders?
WHAT IS A TERMESPHERE
What you are seeing when you look at a Termesphere painting is an inside-out view of a total physical world around you on the outside surface of the hanging and rotating sphere. If you were on the inside of the sphere this painted image around you would seem normal but I make you read it from the outside. >From any point you look at the spherical painting, the image reads correctly. Termespheres capture the up, down and all around visual world from one revolving point in space. Most of the time these spheres are painted on the outside so it takes a six point perspective system to keep all of this environment around you organized.
I have been painting spherical paintings since 1968-9 when I received my Masters Degree in Art at the University of Wyoming. I continued to do my thesis on the Termesphere at Otis Art Institutes in Los Angeles for the next two years. I received my MFA in design there.
HOW THIS CONCEPT WAS FOUND FROM INSIDE A BOX
The idea of capturing total visual space around you on the sphere or six point perspective came to me in a very odd way. I had been studying and teaching perspective for a number of years. It advanced up to four point perspective but I wasn't satisfied. The main development happened when I focused my attention on perspective while working on my Masters Degree in art at the University of Wyoming. After having come up with some drawings and designs on paper which showed different ways to think of six point perspective, I attempted to put it to use. I decided I would build a small cubical object I could crawl into. This cube would have an exaggerated perspective built into it like my drawings showed. My thought was if you could pull the corners of the cube in toward the center of the cube it would give you the illusion it was a much larger box. I started to imagine what this cube would look like. A fellow student told me it would look like a cube painted on a sphere. The cube would become the sphere if you pulled its corner in far enough. I went back to my studio and tried to construct a cube on a kid's ball. I realized in order to draw the cube accurately on the sphere all the lines of the cube must aim to the center of the adjacent faces of the cube. All the lines became greater circles. If each of the lines of this cube were drawn all the way to the point you would construct a rhombic dodecahedron (twelve diamonds). The points in the center of the cube would create the vertices of the octahedron.
When I looked at this cubical structure on the sphere as a drawing, I had the feeling I could be inside this cube. What if I thought of this cube as a room and I were inside of it? If this cube were thought of as a drawing of a room, the points in the center of each face would be thought of as vanishing points in perspective. The rule in Renaissance one and two point perspective says that all parallel lines converge at the same vanishing point. These parallel line on my cube were projecting in two directions to the center of the adjacent faces. Counting the points of projection it came to six, the same number as the faces of the cube. The lines which came from the four corner of the center square projected out by me. This thinking was inside out but the bottom face of the cube was the floor, the top face of the cube was the ceiling and the four other faces were the four walls. If you put tables and chairs on the floor, hang light fixtures from the ceiling tile and cut windows and doors into the walls, you have a room rather than just a cube and it is the inside of a room on the outside of the spherecube.
What are some of the unique geometries going on in this room on a sphere? If the furniture and other objects in the room are parallel to the room, every line which creates this room or furniture for the room would bisects the sphere if it were continued. Every cubical object created for this room projects to all six equal distant vanishing points. All parallel lines go to two vanishing points. If a railroad track vanishes to a point in front of you, it will also vanish to one behind you. All you have to do is turn around and look.
INSIDE OR OUTSIDE THE SPHERECUBE
The thing that helps to make this all more sensible is to think of yourself inside the sphere looking out. If your eye is in the direct center of the sphere and you are looking at this cube room painted on the sphere it would look very normal. If you were inside and in the center of a real room and your head were inside a transparent sphere and you copied what you saw outside the sphere onto the inside surface of the sphere, it would look exactly the same as the cube painted on the outside of the sphere.
IN THE SPHERE
Another experiment is to imagine having a transparent sphere on you head and place six equal distant large dots on it like the vertices of the octahedron. With the sphere on your head, arrange the dots so that one dot is above your head and another dot is below your head. The other four dots are parallel to the horizon around you. Now, walk into a cubical building. With one eye in the center of the sphere rotate the sphere until one of the points on the sphere overlaps with one of the vanishing points of the building. Keep the four dots on the sphere parallel to the ground. With your eye in the center of the transparent sphere, notice where the other five vanishing points of the building are located. All of the building's vanishing points will line up with the dots you put on the sphere. This is the way it would work. This will work this way no matter where you locate yourself within the building. Can you see why people see mathematics when looking at the Termesphere?
The following Termespheres illustrate my point. Some are real places, some are imaginary environments and some are geometric worlds. Think of yourself inside the sphere.
HAGIA SOPHIA is a 24" diameter sphere. This painting allows you to float about 40 feet off the floor to view the inside of this wonderful Christian and Moslem structure. This building is based upon the cube, a cube with a dome on the top.
INSPIRATIONS FOR ESCHER is a 16" diameter sphere which hangs and rotates from a ceiling motor. This shows M.C. Eschers in his favorite small town of Ravillo, Italy. Around him are found ideas which later become his great works of art.
CHAPEL OF THE ANGELS is a 16" diameter spherical painting. This chapel is found in Ravillo, Italy. It is an example of six point perspective on the sphere.
ST PETERS is a 16" diameter spherical painting. This sphere shows the combination of curves and cubical straight lines which compose this great building all wrap onto the surface of the sphere. Any direction you look at this painting, it reads correctly.
FISSION OF THE CHECK is a 24" diameter spherical painting. Cubes grow from a checker board pattern. Another set of cubes also grow from the diagonal of that first check system. This sphere could be said to hold ten points of perspective.
CONCAVE BUBBLES is a 24" diameter sphere. There a 100 reflective ball that float through this room each reflecting the room from the location they are within the room. If they are floating high in the room they reflect mostly the floor. If they are floating low in the room they reflect mostly the ceiling. Each bubble is slightly different.
SAINTE CHAPELL IN PARIS is a 24" diameter sphere. You are above the floor some thirty feet so you can look straight across at the stain glass windows. This shows how detailed a basic cubical room can get.