Triangle smoothing

Fig. 12.20 4-Acetamido benzoic acid. Triangle smoothing predicts that the lower bound distance between the amide nitrogen and the carbonyl oxygen is equal to the sum of the van der Waals radii. The actual distance is about 6.4A.

Fig. E6.16 Output versus gear frequency of rotation for a 5.6-in-diameter 4.5 in wide, double (30°) helical, 14-teeth 0.67-in-deep gear pump, and with LDPE (circles) and PS (triangles). Smooth curves are the theoretical ones at the respective densities. [Reprinted with permission from C. Y. Cheng, Farrel Corp., Ansonia, CT, private communication, 1972.]...

To produce a reasonable U matrix a process known as triangle smoothing is applied to every triplet of points in turn. So, for three points, i, j, k, the... 

Figure 13 Triangle smoothing of lower and upper distance bounds for use in distance geometry. The top diagram illustrates that the upper bound on the A-C interatomic distance cannot be greater than the sum of the upper bounds on the A-B and B-C distances. The lower diagram shows that the lower bound on the A-C distance cannot be smaller than the difference between the lower bound on the A-B distance and the upper bound on the B-C distance.

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