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Figure 5
(a) An illustration of the process of transforming a single point x0 of the closed interval [a,b ] into the interval itself. The transformation is a homotopy map [H({x,t} ) = {x_0}({1 - t} ) + x]. (b) An illustration of how a homotopy can deform in two steps a six-segment edge graph into a single point. In the first step we contract the four outer segments into their end points using the homotopy from Fig. 4[link](a). Next, we contract with a similar homotopy the remaining two segments to the central point. (c) An example of a homotopy process H(x,t), in which a curve with two fixed end points is continuously transformed into another curve. The intermediate steps of the evolution in time are denoted with H(x,ti) for time points [0 \,\lt\, {t}_1 \,\lt\, {t}_2 \,\lt\, {t}_3 \,\lt\, {t}_4 \,\lt\, {t}_5 \,\lt\, 1.]

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 55| Part 1| February 2022| Pages 154-167
https://doi.org/10.1107/S160057672101205X
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