add curves: constant, linear, bezier

res/modules/animation.lua

@@ -0,0 +1,53 @@
+local this = {}
+
+local function bezier(a, b, c, d, u)
+    local s = 1 - u
+    return s * s * s * a +
+        3 * s * s * u * b +
+        3 * s * u * u * c +
+        u * u * u * d
+end
+
+local function bezier_derivative(a, b, c, d, u)
+    local s = 1 - u
+    return
+        3 * s * s * (b - a) +
+        6 * s * u * (c - b) +
+        3 * u * u * (d - c)
+end
+
+function this.bezier_interpolation(k0, k1, t)
+    local frame = k0.frame + t * (k1.frame - k0.frame)
+
+    local u = t
+
+    for i=1,8 do
+        local x = bezier(
+            k0.frame,
+            k0.rx,
+            k1.lx,
+            k1.frame,
+            u
+        )
+
+        local dx = bezier_derivative(
+            k0.frame,
+            k0.rx,
+            k1.lx,
+            k1.frame,
+            u
+        )
+        if math.abs(dx) < 1e-8 then
+            break
+        end
+
+        u = u - (x - frame) / dx
+
+        if u < 0 then u = 0 end
+        if u > 1 then u = 1 end
+    end
+
+    return bezier(k0.value, k0.ry, k1.ly, k1.value, u)
+end
+
+return this