didericis
b4ddc7da8b
New experiments/medial_tire_cut_labelling.py: takes a full medial tire graph and an entry up tooth and runs the walk-depth labelling-and-cut procedure, reusing the full medial tire generator's model and emitting TikZ. Add a generator-produced 8-tooth example to the paper (Figure 1, Example 2.3) showing the labelling and the two cuts, plus a remark fixing the cut's closing tooth for descended faces. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
21 lines
1.6 KiB
TeX
21 lines
1.6 KiB
TeX
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\citation{bauerfeld-medial-tire}
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\citation{bauerfeld-medial-tire}
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\citation{bauerfeld-medial-tire}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Cutting a full medial tire graph}}{1}{}\protected@file@percent }
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\newlabel{def:walk-depth-cut}{{2.1}{1}}
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\citation{bauerfeld-medial-tire}
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\bibcite{bauerfeld-medial-tire}{1}
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\newlabel{tocindent3}{0pt}
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\newlabel{rem:closing-tooth}{{2.2}{2}}
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\newlabel{ex:worked-cut}{{2.3}{2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A full medial tire graph (left) and its walk-depth labelling and cut (right), from Example\nonbreakingspace 2.3\hbox {}. Black vertices are the annular medial vertices of the cycle $A(T)$; blue vertices are up-tooth apexes, red vertices are down-tooth apexes, and the larger red vertex is the shared apex of the bite on annular edges $0$ and $4$. On the right, each tooth carries its walk depth, and the two red slits mark the cuts: \emph {cut\nonbreakingspace 1} duplicates $a_5$ as the root-face traversal closes, and \emph {cut\nonbreakingspace 2} duplicates $a_1$ as the bite's inner-gap face closes. After the cuts the only bounded faces are the eight teeth.}}{3}{}\protected@file@percent }
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\newlabel{fig:worked-cut}{{1}{3}}
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\gdef \@abspage@last{3}
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