1 files changed, 89 insertions, 0 deletions
diff --git a/.config/awesome/quarrel/animation/bezier.lua b/.config/awesome/quarrel/animation/bezier.lua
new file mode 100644
index 0000000..a505e48
--- /dev/null
+++ b/.config/awesome/quarrel/animation/bezier.lua
@@ -0,0 +1,89 @@
+local gtable = require "gears.table"
+
+-- port of https://github.com/WebKit/WebKit/blob/da934454c84ac2dcbf9fca9e5f4ac2644ef25d72/Source/WebCore/platform/graphics/UnitBezier.h
+
+local bezier = {}
+
+function bezier:sample_x(t)
+    -- `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
+    return ((self.ax * t + self.bx) * t + self.cx) * t
+end
+
+function bezier:sample_y(t)
+    return ((self.ay * t + self.by) * t + self.cy) * t
+end
+
+function bezier:sample_derivative_x(t)
+    return (3.0 * self.ax * t + 2.0 * self.bx) * t + self.cx
+end
+
+function bezier:solve_x(x, epsilon)
+    local x2, d2
+    local t2 = x
+
+    -- First try a few iterations of Newton's method -- normally very fast.
+    for _ = 1, 8 do
+        x2 = self:sample_x(t2) - x
+        if math.abs(x2) < epsilon then
+            return t2
+        end
+        d2 = self:sample_derivative_x(t2)
+        if math.abs(d2) < 1e-6 then
+            break
+        end
+        t2 = t2 - x2 / d2
+    end
+
+    -- Fall back to the bisection method for reliability.
+    local t0 = 0
+    local t1 = 1
+    t2 = x
+
+    if t2 < t0 then
+        return t0
+    end
+    if t2 > t1 then
+        return t1
+    end
+
+    while t0 < t1 do
+        x2 = self:sample_x(t2)
+        if math.abs(x2 - x) < epsilon then
+            return t2
+        end
+        if x > x2 then
+            t0 = t2
+        else
+            t1 = t2
+        end
+        t2 = (t1 - t0) * 0.5 + t0
+    end
+
+    -- Failure.
+    return t2
+end
+
+function bezier:solve(x, epsilon)
+    return self:sample_y(self:solve_x(x, epsilon))
+end
+
+local function new(x1, y1, x2, y2)
+    local obj = gtable.crush({}, bezier)
+
+    -- Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
+    obj.cx = 3.0 * x1
+    obj.bx = 3.0 * (x2 - x1) - obj.cx
+    obj.ax = 1.0 - obj.cx - obj.bx
+
+    obj.cy = 3.0 * y1
+    obj.by = 3.0 * (y2 - y1) - obj.cy
+    obj.ay = 1.0 - obj.cy - obj.by
+
+    return obj
+end
+
+return setmetatable(bezier, {
+    __call = function(_, ...)
+        return new(...)
+    end,
+})