From 7cf2baebf3d6918f468421d8a22d3198ef4af236 Mon Sep 17 00:00:00 2001
From: moi15moi <moi15moismokerlolilol@gmail.com>
Date: Tue, 7 Nov 2023 15:03:33 -0500
Subject: [PATCH] Create Proof algorithm - ms_to_frames.md

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 docs/Proof algorithm - ms_to_frames.md | 53 ++++++++++++++++++++++++++
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 create mode 100644 docs/Proof algorithm - ms_to_frames.md

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+# ms_to_frames
+To convert an frame to an ms, here is the formula: $$ms = frame * {1 \over fps} * 1000$$
+But depending on what the user want, he may need to floor the result or round it (see docs of timestamps.py for more information)
+Important to note, $frame \in \mathbb{N}$. This means we need to take the **integer** between the 2 bounds of the inequations that are detailed below.
+
+## Explanation for rounding method
+
+Important to note, here the rounding method round up, so, if it encounter $round(x.5)$, it will become $x + 1$
+
+From the previous equation, we can deduce this:
+$$ms - 0.5 \le frame * {1 \over fps} * 1000 < ms + 0.5$$
+
+And from the previous inequation, we can isolate $frame$ like this:
+$$(ms - 0.5) * fps * {1 \over 1000} \le frame < (ms + 0.5) * fps * {1 \over 1000}$$
+
+Algorithm:
+```py
+# We use the upper bound
+upper_bound = (ms + 0.5) * fps * 1/1000
+# Then, we trunc the result
+trunc_frame = int(upper_bound)
+
+# If the upper_bound equals to the trunc_frame, this means that we don't respect the inequation because it is "greater than", not "greater than or equals".
+# So if it happens, this means we need to return the previous frame
+if upper_bound == trunc_frame:
+    return trunc_frame - 1
+else:
+    return trunc_frame
+```
+
+
+## Explanation for floor method
+
+From the previous equation, we can deduce this:
+$$ms \le frame * {1 \over fps} * 1000 < ms + 1$$
+
+And from the previous inequation, we can isolate $frame$ like this:
+$$ms * fps * {1 \over 1000} \le frame < (ms + 1) * fps * {1 \over 1000}$$
+
+Algorithm:
+```py
+# We use the upper bound
+upper_bound = (ms + 1) * fps * 1/1000
+# Then, we trunc the result
+trunc_frame = int(upper_bound)
+
+# If the upper_bound equals to the trunc_frame, this means that we don't respect the inequation because it is "greater than", not "greater than or equals".
+# So if it happens, this means we need to return the previous frame
+if upper_bound == trunc_frame:
+    return trunc_frame - 1
+else:
+    return trunc_frame
+```