Add btrtile

Patch refactor, updated readme.

Added link for with gapps patch to readme.

patches/btrtile/README.md

@@ -0,0 +1,106 @@
+### Description
+
+# btrtile — A Focus-Driven Tiling Layout
+
+It provides a focus-driven, mouse- and keyboard-friendly tiling layout that grants you granular control over how clients are placed and resized.
+
+![btrtile in action](./demos/btrtiledemo.gif)
+
+---
+
+# Why btrtile
+
+While dwl’s patches folder is full of different layouts, I couldn't find suitable layout that would work well with my workflow and single ultrawide monitor setup. btrtile aims to solve that by introducing a layout strategy that splits clients according to user focus and pointer position.
+
+---
+
+# Features
+
+- **Combined Tiling and Management**  
+  Combines tiling layout and management of clients under one patchset.
+
+- **Focus-Driven Splits**  
+  When you add a new client, btrtile checks where your pointer is relative to the focused client’s geometry.  
+  - If the pointer is on the left half (for a horizontally large client), the new client spawns on the left side, and vice versa.  
+  - By default, new splits are 50/50.
+
+- **Adaptive Splitting**  
+  - If the area to be split is wider than its height, btrtile does a horizontal split.  
+  - Otherwise, it does a vertical split.
+
+- **Keyboard and Mouse Driven**  
+  - Supports keyboard-based commands for quick ratio adjustments and client swapping.  
+  - Mouse-based resizing and moving are integrated for more intuitive manipulation.
+
+---
+
+# How It Works
+
+btrtile organizes clients using a binary tree data structure that represents splits either vertically or horizontally.
+
+When a new client appears:
+1. **Focused Client Detection**  
+   btrtile checks your pointer location to find which client (if any) you’re interacting with.
+2. **Split Creation**  
+   - If there’s a focused client, btrtile creates a split node around it, placing the new client on the side where your pointer is.  
+
+3. **Ratio Management**  
+   Each split node has a `split_ratio` (defaulting to 0.5). This ratio defines how much space is allocated to each child node. You can adjust this ratio using keyboard or mouse actions.
+
+---
+
+# What It Doesn’t Handle
+
+- **Multi-Tag client Management**  
+  btrtile intentionally reverts clients to a single tag if they span multiple tags. This prevents potential inconsistencies or duplicate entries in its per-tag client tree.  
+  - If you attempt to place a single client on multiple tags while using the btrtile layout, btrtile will enforce a single-tag assignment to maintain stability.
+
+- **Suckless philosophy**
+  - Yea, it's a bloat. I tried to hide the suck inside a single file as much I could. While this approach is not ideal, it's how it's at least for now.
+
+---
+
+# Configuring btrtile
+
+btrtile adds couple variables to config.h to fine tune the mouse resizing of tiled clients.
+
+1. **resize_factor**
+	- A multiplier to transfer pointer movement to client weight ratio. Depends heavily on mouse sensivity.
+      Defaults to 0.0002f.
+
+2. **resize_interval_ms**
+	- A time based resize call limiter. Depends on framerate and screen refresh rate. 
+      Defaults to 16ms. (~60 resize updates per second)
+
+Fine tune these values to find the best values for your setup, smoother resizing can significally increase cpu overhead.
+If mouse resizing feels sluggish, you can try compiling dwl with more aggressive optimization flags like -O2/-O3. 
+
+---
+
+# Patch recommendations
+
+1. **Patches that I use with my btrtile**
+     
+   - [focusdir](https://codeberg.org/dwl/dwl-patches/src/branch/main/patches/focusdir)
+     Great patch to move focus between clients.
+
+   - [rotatetags](https://codeberg.org/dwl/dwl-patches/src/branch/main/patches/rotatetags)
+     Good patch to rotate the view or shift clients between tags.
+
+   - [warpcursor](https://codeberg.org/dwl/dwl-patches/src/branch/main/patches/warpcursor)
+     Moves cursor location to focused client.
+
+   - [pertag](https://codeberg.org/dwl/dwl-patches/src/branch/main/patches/pertag)
+     Allows each tag to have individual layout setups.
+
+   - [gaps](https://codeberg.org/dwl/dwl-patches/src/branch/main/patches/gaps)
+     Add gaps between clients.
+
+---
+
+### Download
+- [0.7](https://codeberg.org/dwl/dwl-patches/raw/branch/main/patches/btrtile/btrtile-v0.7.patch)
+- [0.7 WITH gapps](https://codeberg.org/dwl/dwl-patches/raw/branch/main/patches/btrtile/btrtile-v0.7-gapps.patch)
+
+### Authors
+- [julmajustus](https://codeberg.org/julmajustus)