Trips color code

Imagine, Geometry form choices

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block EIE This is a story of three primary colors: red, yellow, and blue. The plot involves eight light triangles and several forms. The adventure is evolution. The cube on the left is the beginning of the story. The multifaceted form on the right, the EIE, is the ending of the story. There are some problems with seeing them. I want to see the forms from within. My goal is to do QTVR movies of the forms and how they evolve. I need to flay and warp the images.


The image of the outside of a solid form is hard to see. We just see it from one side. The solution is to flay the object and lay it out flat. For example, take a map of the world. A globe is the natural analog of the round earth. But to see the whole thing at once, we flay the earth. Look at an atlas, you see many ways of flaying, each kind of map with its own distortion.

flat cubeflat EIEThe mapping that is useful for QTVR is the equatorial projection. That mapping is correct, or true to the object, only at the equator. See it as the equator of the object. It gets more and more distorted toward the top and the bottom of the rectanglar map. The map on the left is the cube. The map on the right is the EIE (with the orange frame of the related icosahedron).

The maps help to see all the sides at once and compare the color areas. The map is the source of the QTVR movie. Imagine the map wrapped around you and you are turning around inside to look at all sides.


icosa in QTVRicosa warped mapThe second problem is warping. A flat rectangle map is distorted in the QTVR. The QTVR on the left is an icosahedron. See how the straight lines now look curved? The warped map on the right is the solution. The edges look straight in the QTVR below, following. (Click on either of the QTVR images to see the actual QTVR).

icosa unwarped in QTVR

Flaying and warping help explain the many arrays of marbles in the missing link movies. The marbles are actually the outer layer of spheres closely packed to perform the jitterbug transition between the vector equilibrium and the icosahedron. (A description is on the first movie page. I have flayed the shells to see them all at once and warped the maps for the QTVR (not yet finished).

Notice the red, blue, and yellow areas across the changes in form. How are they similar? Notice the 8 white triangles in all forms except the cube. Are they related to the cube corners? Notice subdivision of one of the color areas, for example, red. There are 2 in the cube, 4 in the icosahedron, and 8 in the EIE.

The studies and sketches published here are up-to-date but the investigation and demonstration is still incomplete. It should be simplified, streamlined, improved, and easier to see with additional work in the days and weeks to come.

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© Caroling 1999 All rights reserved. Last Modified: Jan 11 1999