From 19dedc52ce10648051d187e8c5e7e4700b61140e Mon Sep 17 00:00:00 2001
From: Prad Nukala <prad@sonr.io>
Date: Wed, 30 Sep 2026 11:25:39 -0400
Subject: [PATCH] docs(docs): add interval overlap condition and formula SVG
 illustrations

---
 .../public/intervals_overlap-condition.svg    | 28 +++++++++++++++++++
 .../docs/public/intervals_overlap-formula.svg | 28 +++++++++++++++++++
 2 files changed, 56 insertions(+)
 create mode 100644 apps/docs/public/intervals_overlap-condition.svg
 create mode 100644 apps/docs/public/intervals_overlap-formula.svg

diff --git a/apps/docs/public/intervals_overlap-condition.svg b/apps/docs/public/intervals_overlap-condition.svg
new file mode 100644
index 0000000..6299e9f
--- /dev/null
+++ b/apps/docs/public/intervals_overlap-condition.svg
@@ -0,0 +1,28 @@
+<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>
diff --git a/apps/docs/public/intervals_overlap-formula.svg b/apps/docs/public/intervals_overlap-formula.svg
new file mode 100644
index 0000000..3ba4fa6
--- /dev/null
+++ b/apps/docs/public/intervals_overlap-formula.svg
@@ -0,0 +1,28 @@
+<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>