One year ago, we were reading this by Kevin Kelly on GeekDad:
Dick Termes paints complicated scenes on spheres. These pictures are complete worlds that provide an eire optical illusion. As you twirl the sphere it can seem as if you are inside the sphere looking out at the scene. This illusion is accomplished with a mathematical trick call 6-point perspective.
You’ve heard of a vanishing point perspective that artist use? Well, great landscape painters of old would employ a 2- vanishing point perspective in order to correctly capture the lines in a city. Or a 3-point perspective in drawing a dramatic comic book view of a city from a great height. As you increase the complexity of the view, you can add a 4th and 5th vanishing point if you are trying to take in a panorama, as a fish-eyed lens will. To paint say rooms and buildings on a sphere you need a 6-point perspective.
Here is how Dick Termes explains it on his website:
Imagine that you are standing inside a transparent ball suspended fifty feet above the Grand Canyon floor. You are higher than some canyon walls and lower than others. You have paints and a brush, and you begin to paint what you see on the inside surface of the ball. You paint the north face, then the east, south, and west. Finally, you paint everything visible above and below you. You move your globe to safe ground and step out to observe your paintings. Walking around the sphere, you see that you have captured the entire three dimensional landscape. In fact, you’ve discovered the structure of your visual experience.
I can’t say I have mastered the complications of this view, but Termes offers a digital (and analog) manual on drawing higher order perspectives. Our project will be to help the kids draw their room on a ball. It’s not elementary, but it is cool geometry. It’s an ideal math class project too.
For inspiration check out Termes’ gallery of Termespheres.