From bcbbc578546c390fe763d82036a1b564af24716d Mon Sep 17 00:00:00 2001
From: soumik12345 <19soumik.rakshit96@gmail.com>
Date: Tue, 15 Jul 2025 16:34:22 +0530
Subject: [PATCH 1/6] chore: configure mkdocs to add mathjax support

---
 docs/javascripts/mathjax.js | 19 +++++++++++++++++++
 mkdocs.yml                  |  4 ++++
 2 files changed, 23 insertions(+)
 create mode 100644 docs/javascripts/mathjax.js

diff --git a/docs/javascripts/mathjax.js b/docs/javascripts/mathjax.js
new file mode 100644
index 00000000..160fedef
--- /dev/null
+++ b/docs/javascripts/mathjax.js
@@ -0,0 +1,19 @@
+window.MathJax = {
+    tex: {
+      inlineMath: [["\\(", "\\)"]],
+      displayMath: [["\\[", "\\]"]],
+      processEscapes: true,
+      processEnvironments: true
+    },
+    options: {
+      ignoreHtmlClass: ".*|",
+      processHtmlClass: "arithmatex"
+    }
+  };
+  
+  document$.subscribe(() => { 
+    MathJax.startup.output.clearCache()
+    MathJax.typesetClear()
+    MathJax.texReset()
+    MathJax.typesetPromise()
+  })
diff --git a/mkdocs.yml b/mkdocs.yml
index dae49493..d3120939 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -168,12 +168,16 @@ markdown_extensions:
       anchor_linenums: true
       line_spans: __span
       pygments_lang_class: true
+  - pymdownx.arithmatex:
+      generic: true
 
 extra_javascript:
   - "javascripts/init_kapa_widget.js"
   - "javascripts/cookbooks-card.js"
   - "javascripts/segment.js"
+  - "javascripts/mathjax.js"
   - "https://cdnjs.cloudflare.com/ajax/libs/dompurify/3.0.8/purify.min.js"
+  - "https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js"
 
 # Messages shown during document build
 # Reference: https://www.mkdocs.org/user-guide/configuration/#validation

From 9400270e34d49a851bf67a571c52da7403444ae3 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 15 Jul 2025 11:05:26 +0000
Subject: [PATCH 2/6] =?UTF-8?q?fix(pre=5Fcommit):=20=F0=9F=8E=A8=20auto=20?=
 =?UTF-8?q?format=20pre-commit=20hooks?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 docs/javascripts/mathjax.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/javascripts/mathjax.js b/docs/javascripts/mathjax.js
index 160fedef..0c7803cf 100644
--- a/docs/javascripts/mathjax.js
+++ b/docs/javascripts/mathjax.js
@@ -10,8 +10,8 @@ window.MathJax = {
       processHtmlClass: "arithmatex"
     }
   };
-  
-  document$.subscribe(() => { 
+
+  document$.subscribe(() => {
     MathJax.startup.output.clearCache()
     MathJax.typesetClear()
     MathJax.texReset()

From af31b96199df8b0cdd487a6531a6f95061519566 Mon Sep 17 00:00:00 2001
From: soumik12345 <19soumik.rakshit96@gmail.com>
Date: Tue, 15 Jul 2025 16:41:54 +0530
Subject: [PATCH 3/6] update: docstring for box_iou to add formula

---
 supervision/detection/utils.py | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/supervision/detection/utils.py b/supervision/detection/utils.py
index 13c3f1a6..733775e8 100644
--- a/supervision/detection/utils.py
+++ b/supervision/detection/utils.py
@@ -52,11 +52,14 @@ def box_iou(
     box_true: Union[List[float], np.ndarray],
     box_detection: Union[List[float], np.ndarray],
 ) -> float:
-    """
+    r"""
     Compute the Intersection over Union (IoU) between two bounding boxes.
 
-    Both `box_true` and `box_detection` should be in (x_min, y_min, x_max, y_max)
-    format.
+    Mathematically, it is defined as:
+
+    \[
+    \text{IoU} = \frac{|\text{box}_{\text{true}} \cap \text{box}_{\text{detection}}|}{|\text{box}_{\text{true}} \cup \text{box}_{\text{detection}}|}
+    \]
 
     Note:
         Use `box_iou` when computing IoU between two individual boxes.
@@ -1473,8 +1476,7 @@ def _jaccard(box_a: List[float], box_b: List[float], is_crowd: bool) -> float:
     """
     Calculate the Jaccard index (intersection over union) between two bounding boxes.
     If a gt object is marked as "iscrowd", a dt is allowed to match any subregion
-    of the gt. Choosing gt' in the crowd gt that best matches the dt can be done using
-    gt'=intersect(dt,gt). Since by definition union(gt',dt)=dt, computing
+    of the gt. Choosing gt'=intersect(dt,gt). Since by definition union(gt',dt)=dt, computing
     iou(gt,dt,iscrowd) = iou(gt',dt) = area(intersect(gt,dt)) / area(dt)
 
     Args:

From 7c1168fbc6d04b3cde4feb7b495905c4f92214ec Mon Sep 17 00:00:00 2001
From: soumik12345 <19soumik.rakshit96@gmail.com>
Date: Tue, 15 Jul 2025 16:46:10 +0530
Subject: [PATCH 4/6] chore: make pre-commit happy

---
 supervision/detection/utils.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/supervision/detection/utils.py b/supervision/detection/utils.py
index 733775e8..0c017919 100644
--- a/supervision/detection/utils.py
+++ b/supervision/detection/utils.py
@@ -87,7 +87,7 @@ def box_iou(
         sv.box_iou(box_true=box_true, box_detection=box_detection)
         # 0.14285814285714285
         ```
-    """
+    """  # noqa: E501
     box_true = np.array(box_true)
     box_detection = np.array(box_detection)
 
@@ -1486,7 +1486,7 @@ def _jaccard(box_a: List[float], box_b: List[float], is_crowd: bool) -> float:
 
     Returns:
         float: Jaccard index between the two bounding boxes.
-    """
+    """  # noqa: E501
     # Smallest number to avoid division by zero
     EPS = np.spacing(1)
 

From 9f3ffdd26dafedbc3dcb8447d13dfc28fea6df2d Mon Sep 17 00:00:00 2001
From: Soumik Rakshit <19soumik.rakshit96@gmail.com>
Date: Tue, 15 Jul 2025 17:17:39 +0530
Subject: [PATCH 5/6] fix: typo in utils.py

---
 supervision/detection/utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/supervision/detection/utils.py b/supervision/detection/utils.py
index 0c017919..e0844b75 100644
--- a/supervision/detection/utils.py
+++ b/supervision/detection/utils.py
@@ -52,7 +52,7 @@ def box_iou(
     box_true: Union[List[float], np.ndarray],
     box_detection: Union[List[float], np.ndarray],
 ) -> float:
-    r"""
+    """
     Compute the Intersection over Union (IoU) between two bounding boxes.
 
     Mathematically, it is defined as:

From cf179b9dfe202ebab0be85e951131505f8f4dc71 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 15 Jul 2025 11:47:55 +0000
Subject: [PATCH 6/6] =?UTF-8?q?fix(pre=5Fcommit):=20=F0=9F=8E=A8=20auto=20?=
 =?UTF-8?q?format=20pre-commit=20hooks?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 supervision/detection/utils.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/supervision/detection/utils.py b/supervision/detection/utils.py
index e0844b75..c485e891 100644
--- a/supervision/detection/utils.py
+++ b/supervision/detection/utils.py
@@ -57,9 +57,9 @@ def box_iou(
 
     Mathematically, it is defined as:
 
-    \[
-    \text{IoU} = \frac{|\text{box}_{\text{true}} \cap \text{box}_{\text{detection}}|}{|\text{box}_{\text{true}} \cup \text{box}_{\text{detection}}|}
-    \]
+    \\[
+    \text{IoU} = \frac{|\text{box}_{\text{true}} \\cap \text{box}_{\text{detection}}|}{|\text{box}_{\text{true}} \\cup \text{box}_{\text{detection}}|}
+    \\]
 
     Note:
         Use `box_iou` when computing IoU between two individual boxes.