[Decoding    (Basis ideas)]

(1) "Integration" of 5-tile code sequences

By decoding the 5-tile code sequence of a polygonal chain, we would obtain a n-simplex sequence representation of the chain, which accurately reproduces the local structure. In the following, we permit translation during the approximation process to keep the length of the line segments of a polygonal chain equal. (See PROGRAMS / TetraGenSeq for the program.)

Shown on the left in figure A is a polygonal chain with 5-tile code sequence 9HHIA81.
As you see, simple approximation of the chain by a triangle sequence results in a folded tetrahedron sequence whose 5-tile code sequence, 9GHIB81, is different from that of the original chain. And some of the local features of the original chain are missed in the representation.

jpg image
Fig. A: Simple approximation of a shape

On the other hand, if we consider decoding of its 5-tile code sequence, we obtain another representation of the polygonal chain as shown in figure B. Since the obtained representation has the same 5-tile code sequence as the original chain, no local structures are damaged during the approximation process.

jpg image
Fig. B: Decoding of a 5-tile code sequence

(2) Polygonal chains with the same 5-tile code sequence

Figure C shows variation of backbone of folded triangle sequences which share the same 5-tile code sequence.
For example, the pink and red polygonal chains have the same 5-tile code sequence of 8GHI (left).

jpg image
Fig. C: Polygonal chains with the same 5-tile code sequence

Figure D shows the structural difference between backbones of folded triangle fragments of different 5-tile code sequences. For example, in the left figure, the red polygonal chain of 8GHI is compared with the black polygonal chain of 9GHI, where the circle denotes the location of the 5-tile code disagreement.

jpg image
Fig. D: Polygonal chains with different 5-tile code sequences