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docs(docs): add interval overlap condition and formula SVG illustrations

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Prad Nukala committed 2026-09-30 11:25:39 -04:00
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apps/docs/public/intervals_overlap-condition.svg
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<svg viewBox="0 0 820 380" xmlns="http://www.w3.org/2000/svg">
<!-- Background (REQUIRED) - MUST BE FIRST ELEMENT -->
<rect width="820" height="380" fill="#f8f9fa" rx="10"/>
<!-- Title (left-anchored, manually centered) -->
<text x="239" y="44" font-family="Arial, sans-serif" font-size="22" font-weight="bold" fill="#2c3e50">When do intervals overlap?</text>
<!-- Panel 1: no overlap. Labels sit OUTSIDE the bars. -->
<text x="60" y="94" font-family="Arial, sans-serif" font-size="16" fill="#2c3e50">No overlap: a ends before b starts</text>
<text x="90" y="132" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#3498db">a</text>
<rect x="110" y="110" width="180" height="32" fill="#3498db" rx="4"/>
<text x="330" y="132" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f39c12">b</text>
<rect x="350" y="110" width="180" height="32" fill="#f39c12" rx="4"/>
<text x="560" y="132" font-family="monospace" font-size="18" fill="#2c3e50">a.end &lt; b.start</text>
<!-- Panel 2: overlap. Bars on separate rows so they never visually collide. -->
<text x="60" y="210" font-family="Arial, sans-serif" font-size="16" fill="#2c3e50">Overlap: their times cross</text>
<text x="90" y="250" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#3498db">a</text>
<rect x="110" y="228" width="240" height="32" fill="#3498db" rx="4"/>
<text x="480" y="300" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f39c12">b</text>
<rect x="230" y="278" width="240" height="32" fill="#f39c12" rx="4"/>
<!-- guide lines marking the shared x-range (paths, no arrowheads) -->
<path d="M 230,224 L 230,314" stroke="#7f8c8d" stroke-width="1.5" stroke-dasharray="4 3" fill="none"/>
<path d="M 350,224 L 350,314" stroke="#7f8c8d" stroke-width="1.5" stroke-dasharray="4 3" fill="none"/>
<rect x="230" y="324" width="120" height="12" fill="#d1fae5" stroke="#10b981" stroke-width="1.5" rx="3"/>
<text x="244" y="362" font-family="Arial, sans-serif" font-size="15" fill="#27ae60">shared = [max start, min end]</text>
</svg>
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apps/docs/public/intervals_overlap-formula.svg
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<svg viewBox="0 0 820 340" xmlns="http://www.w3.org/2000/svg">
<!-- Background (REQUIRED) - MUST BE FIRST ELEMENT -->
<rect width="820" height="340" fill="#f8f9fa" rx="10"/>
<!-- Title (left-anchored, manually centered) -->
<text x="206" y="42" font-family="Arial, sans-serif" font-size="20" font-weight="bold" fill="#2c3e50">Overlap = [max(starts), min(ends)]</text>
<!-- interval x = [2, 8]; endpoints labeled ABOVE the bar -->
<text x="184" y="82" font-family="monospace" font-size="15" fill="#2c3e50">2</text>
<text x="512" y="82" font-family="monospace" font-size="15" fill="#2c3e50">8</text>
<text x="158" y="112" font-family="monospace" font-size="16" font-weight="bold" fill="#3498db">x</text>
<rect x="190" y="90" width="330" height="30" fill="#3498db" rx="4"/>
<!-- interval y = [5, 11]; endpoints labeled BELOW the bar -->
<text x="158" y="157" font-family="monospace" font-size="16" font-weight="bold" fill="#f39c12">y</text>
<rect x="355" y="135" width="330" height="30" fill="#f39c12" rx="4"/>
<text x="349" y="185" font-family="monospace" font-size="15" fill="#2c3e50">5</text>
<text x="672" y="185" font-family="monospace" font-size="15" fill="#2c3e50">11</text>
<!-- shared range [5, 8] -->
<path d="M 355,86 L 355,205" stroke="#7f8c8d" stroke-width="1.5" stroke-dasharray="4 3" fill="none"/>
<path d="M 520,86 L 520,205" stroke="#7f8c8d" stroke-width="1.5" stroke-dasharray="4 3" fill="none"/>
<rect x="355" y="210" width="165" height="14" fill="#d1fae5" stroke="#10b981" stroke-width="2" rx="3"/>
<text x="405" y="252" font-family="monospace" font-size="16" font-weight="bold" fill="#27ae60">overlap = [5, 8]</text>
<!-- computation -->
<text x="206" y="300" font-family="monospace" font-size="16" fill="#2c3e50">max(2, 5) = 5 and min(8, 11) = 8</text>
</svg>
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