From 730b0f5c5c39fabadc78ab1d1f9331d6256d1533 Mon Sep 17 00:00:00 2001
From: hung <ndgnuh@protonmail.com>
Date: Fri, 1 May 2020 15:17:14 +0700
Subject: [PATCH 1/2] gears.math: add the sign function

---
 lib/gears/math.lua | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/lib/gears/math.lua b/lib/gears/math.lua
index 61c19d004..db295f673 100644
--- a/lib/gears/math.lua
+++ b/lib/gears/math.lua
@@ -76,5 +76,19 @@ function gmath.round(x)
     return math.floor(x + 0.5)
 end
 
+--- Return the sign of the number x
+-- return 1 if x is positive, -1 if negative and 0 if x is 0
+-- @tparam number x
+-- @treturn integer
+-- @staticfct gears.math.sign
+function gmath.sign(x)
+    if x > 0 then
+        return 1
+    elseif x < 0 then
+        return -1
+    else
+        return 0
+    end
+end
 
 return gmath

From fdee02cdcf63fb672efe9c168ecfc819f96cf28f Mon Sep 17 00:00:00 2001
From: hung <ndgnuh@protonmail.com>
Date: Fri, 1 May 2020 15:18:10 +0700
Subject: [PATCH 2/2] gears.shape: new shape (partial) squircle

---
 lib/gears/shape.lua                           | 123 ++++++++++++++++++
 .../examples/gears/shape/partial_squircle.lua |  13 ++
 tests/examples/gears/shape/squircle.lua       |  13 ++
 3 files changed, 149 insertions(+)
 create mode 100644 tests/examples/gears/shape/partial_squircle.lua
 create mode 100644 tests/examples/gears/shape/squircle.lua

diff --git a/lib/gears/shape.lua b/lib/gears/shape.lua
index ac12f58b2..0b8db9260 100644
--- a/lib/gears/shape.lua
+++ b/lib/gears/shape.lua
@@ -41,14 +41,137 @@
 -- @themelib gears.shape
 ---------------------------------------------------------------------------
 local g_matrix = require( "gears.matrix" )
+local g_math   = require( "gears.math" )
 local unpack   = unpack or table.unpack -- luacheck: globals unpack (compatibility with Lua 5.1)
 local atan2    = math.atan2 or math.atan -- lua 5.3 compat
 local min      = math.min
+local max      = math.max
 local cos      = math.cos
 local sin      = math.sin
+local abs      = math.abs
+local pow      = math.pow -- luacheck: globals math.pow
+if not pow then
+  -- math.pow can be disabled in Lua 5.3 via LUA_COMPAT_MATHLIB
+  pow = function(x, y)
+        return x^y
+    end
+end
 
 local module = {}
 
+--- Add a squircle shape with only some of the corner are "circled" to the current path.
+-- The squircle is not exactly as the definition.
+-- It will expand to the shape's width and height, kinda like an ellipse
+--
+-- @DOC_gears_shape_partial_squircle_EXAMPLE@
+--
+-- @param cr A cairo context
+-- @tparam number width The shape width
+-- @tparam number height The shape height
+-- @tparam boolean tl If the top left corner is rounded
+-- @tparam boolean tr If the top right corner is rounded
+-- @tparam boolean br If the bottom right corner is rounded
+-- @tparam boolean bl If the bottom left corner is rounded
+-- @tparam number rate The "squareness" of the squircle, should be greater than 1
+-- @tparam number delta The "smoothness" of the shape, delta must be greater than 0.01 and will be reset to 0.01 if not
+-- @staticfct gears.shape.partial_squircle
+function module.partial_squircle(cr, width, height, tl, tr, br, bl, rate, delta)
+   -- rate ~ 2 can be used by icon
+   -- this shape doesn't really fit clients
+   -- but you can still use with rate ~ 32
+   rate = rate or 2
+   -- smaller the delta the smoother the shape
+   -- but probably more laggy
+   -- so we'll limit delta to the miminum of 0.01
+   -- so people don't burn their computer
+   delta = delta or 1 / max(width, height)
+   delta = delta > 0.01 and delta or 0.01
+
+   -- just ellipse things
+   local a = width / 2
+   local b = height / 2
+   local phi = 0
+
+   -- move to origin
+   -- the shape goes counter clock wise
+   -- start from (w h / 2)
+   cr:save()
+   cr:translate(a, b)
+   cr:move_to(a, 0)
+
+   -- draw the corner if that corner is rounded
+   local curved_corner = function()
+      local end_angle = phi + math.pi / 2
+      while phi < end_angle do
+         local cosphi = cos(phi)
+         local sinphi = sin(phi)
+         local x = a * pow(abs(cosphi), 1 / rate) * g_math.sign(cosphi)
+         local y = b * pow(abs(sinphi), 1 / rate) * g_math.sign(sinphi)
+         -- so weird, y axis is inverted
+         cr:line_to(x, -y)
+         phi = phi + delta
+      end
+   end
+
+   -- draw with polar cord
+   -- draw top right
+   if tr then
+      curved_corner()
+   else
+      cr:move_to(a,  0)
+      cr:line_to(a, -b)
+      cr:line_to(0, -b)
+      phi = math.pi * 0.5
+   end
+
+   -- draw top left
+   if tl then
+      curved_corner()
+   else
+      cr:line_to(-a, -b)
+      cr:line_to(-a,  0)
+      phi = math.pi
+   end
+
+   if bl then
+      curved_corner()
+   else
+      cr:line_to(-a, b)
+      cr:line_to( 0, b)
+      phi = math.pi * 1.5
+   end
+
+   -- bottom right
+   if br then
+      curved_corner()
+   else
+      cr:line_to(a, b)
+      cr:line_to(a, 0)
+      phi = math.pi * 2
+   end
+
+   -- it's time to stop
+   cr:close_path()
+
+   -- restore cairo context
+   cr:restore()
+end
+
+--- Add a squircle shape to the current path.
+-- This will behave the same as `partial_squircle`
+--
+-- @DOC_gears_shape_squircle_EXAMPLE@
+--
+-- @param cr A cairo context
+-- @tparam number width The shape width
+-- @tparam number height The shape height
+-- @tparam number rate The "squareness" of the squircle, should be greater than 1
+-- @tparam number delta The "smoothness" of the shape, delta must be greater than 0.01 and will be reset to 0.01 if not
+-- @staticfct gears.shape.squircle
+function module.squircle(cr, width, height, rate, delta)
+   module.partial_squircle(cr, width, height, true, true, true, true, rate, delta)
+end
+
 --- Add a star shape to the current path.
 -- The star size will be the minimum of the given width and weight
 --
diff --git a/tests/examples/gears/shape/partial_squircle.lua b/tests/examples/gears/shape/partial_squircle.lua
new file mode 100644
index 000000000..bbf336c23
--- /dev/null
+++ b/tests/examples/gears/shape/partial_squircle.lua
@@ -0,0 +1,13 @@
+--DOC_GEN_IMAGE --DOC_HIDE
+local shape,cr,show = ... --DOC_HIDE
+
+shape.partial_squircle(cr, 70, 70, false, true)
+show(cr) --DOC_HIDE
+
+shape.partial_squircle(cr, 70, 70, true, false, true)
+show(cr) --DOC_HIDE
+
+shape.partial_squircle(cr, 70, 70, true, false, true, true)
+show(cr) --DOC_HIDE
+
+--DOC_HIDE vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80
diff --git a/tests/examples/gears/shape/squircle.lua b/tests/examples/gears/shape/squircle.lua
new file mode 100644
index 000000000..7aa0692be
--- /dev/null
+++ b/tests/examples/gears/shape/squircle.lua
@@ -0,0 +1,13 @@
+--DOC_GEN_IMAGE --DOC_HIDE
+local shape,cr,show = ... --DOC_HIDE
+
+shape.squircle(cr, 70, 70, 2)
+show(cr) --DOC_HIDE
+
+shape.squircle(cr, 70, 70, 8)
+show(cr) --DOC_HIDE
+
+shape.squircle(cr, 70, 70, 1.5)
+show(cr) --DOC_HIDE
+
+--DOC_HIDE vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80