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October 11, 2004
Nodal Point Pan and Tile: Part 1
A level camera creates vertical lines that are vertical. An upwardly tilted camera creates vertical lines that converge to a vanishing point high above.
It's hard to imagine how to stitch those together. For a good intuitive grasp of what goes on in nodal point pan and tile work, try this simple experiment in Maya.
Place a perspective camera inside a sphere of any radius you like. (try changing the radius of the sphere. Notice the change has no effect on the sphere as seen from the perspective camera.)
Make the sphere "live," and draw a little street scene on it. A road. Some trees. Whatever you like. Notice how the longitude lines of the sphere are all perfectly straight lines. That's because they are actually "great circles" around the sphere aimed directly edge-on at you in the center of the sphere.
The lines you drew look straight to you, but to an outside observer they too are great circles curving around the sphere.
Tilt the camera up. Notice that from the point of view of the camera, the longitude lines remain straight, although they now converge to a vanishing point above. Draw in some clouds if you like.
Tilt up some more. Add some more clouds, if you like. The idea is to fill in the rest of the environment - or at least to understand the perspective change the environment undergoes during a nodal point pan or tilt.
Now tilt down. Notice the straight lines of the road continue to look straight, even though they are actually wrapped around the sphere.
Fill in some more of the road, if you like.
Pan sideways and add a building. Why not? As long as you remain in the exact center of the sphere, the illusion of straight lines will continue to hold true.
If you leave the center of the sphere, the illusion of straight lines will be lost, and the true curvature will emerge. That would be bad.
The whole point of this technique is to preserve the illusion of straight lines remaining straight. You are modelling a nodal point pan and tile camera move, as if you are shooting live action footage from a tripod. Don't leave the center of the sphere.
UPDATE 12/27/2004:
Here's a guy named
Dick Termes who goes out of his way to make sure the viewer is not at the center of the sphere:
http://www.boingboing.net/2004/12/27/spherical_paintings.html
The idea that points in space can be represented as if viewed from the center of a sphere has formed the basis of Astronomical observation since at least the time of Aristotle.
Posted by digital artform at October 11, 2004 11:41 PM