add material motion

kivymd/motion.py

@@ -0,0 +1,117 @@
+"""
+
+"""
+
+import math
+
+float_epsilon = 8.3446500e-7
+
+class CubicBezier:
+    p0 = 0
+    p1 = 0
+    p2 = 0
+    p3 = 0
+
+    def __init__(self, *args):
+        self.p0, self.p1, self.p2, self.p3 = args
+
+    def evaluate_cubic(self, p1, p2, t):
+        a = 1.0 / 3.0 + (p1 - p2)
+        b = p2 - 2.0 * p1
+        c = p1
+        return 3.0 * ((a * t + b) * t + c) * t
+
+    def clamp_range(self, r):
+        if r < 0.0:
+            if -float_epsilon <= r < 0.0:
+                return 0.0
+            else:
+                return math.nan
+        elif r > 1.0:
+            if 1.0 <= r <= 1.0 + float_epsilon:
+                return 1.0
+            else:
+                return math.nan
+        else:
+            return r
+
+    def close_to(self, x, y):
+        return abs(x - y) < float_epsilon
+
+    def find_first_cubic_root(self, p0, p1, p2, p3):
+        a = 3.0 * (p0 - 2.0 * p1 + p2)
+        b = 3.0 * (p1 - p0)
+        c = p0
+        d = -p0 + 3.0 * (p1 - p2) + p3
+
+        if self.close_to(d, 0.0):
+            if self.close_to(a, 0.0):
+                if self.close_to(b, 0.0):
+                    return math.nan
+                return self.clamp_range(-c / b)
+            else:
+                q = math.sqrt(b * b - 4.0 * a * c)
+                a2 = 2.0 * a
+
+                root = self.clamp_range((q - b) / a2)
+                if not math.isnan(root):
+                    return root
+
+                return self.clamp_range((-b - q) / a2)
+
+        a /= d
+        b /= d
+        c /= d
+        o3 = (3.0 * b - a * a) / 9.0
+        q2 = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0
+        discriminant = q2 * q2 + o3 * o3 * o3
+        a3 = a / 3.0
+
+        if discriminant < 0.0:
+            mp33 = -(o3 * o3 * o3)
+            r = math.sqrt(mp33)
+            t = -q2 / r
+            cos_phi = max(-1.0, min(t, 1.0))
+            phi = math.acos(cos_phi)
+            t1 = 2.0 * math.cbrt(r)
+            root = self.clamp_range(t1 * math.cos(phi / 3.0) - a3)
+            if not math.isnan(root):
+                return root
+            root = self.clamp_range(t1 * math.cos((phi + 2.0 * math.pi) / 3.0) - a3)
+            if not math.isnan(root):
+                return root
+            return self.clamp_range(t1 * math.cos((phi + 4.0 * math.pi) / 3.0) - a3)
+
+        elif self.close_to(discriminant, 0.0): 
+            u1 = -math.cbrt(q2)
+            root = self.clamp_range(2.0 * u1 - a3)
+            if not math.isnan(root):
+                return root
+            return self.clamp_range(-u1 - a3)
+
+        sd = math.sqrt(discriminant)
+        u1 = math.cbrt(-q2 + sd)
+        v1 = math.cbrt(q2 + sd)
+        return self.clamp_range(u1 - v1 - a3)
+
+    def transform(self, value: float):    
+        return self.evaluate_cubic(
+            self.p1, self.p3, self.find_first_cubic_root(
+                -value,
+                self.p0 - value,
+                self.p2 - value,
+                1.0 - value,
+            )
+        )
+
+
+class MaterialMotion:
+
+    easing_standard = CubicBezier(0.4, 0.0, 0.2, 1.0)
+    easing_decelerated = CubicBezier(0.0, 0.0, 0.2, 1.0)
+    easing_accelerated = CubicBezier(0.4, 0.0, 1.0, 1.0)
+    easing_linear = CubicBezier(0.0, 0.0, 1.0, 1.0)
+
+    # TODO: add `easing_emphasized` here
+    # it's defination is 
+    # path(M 0,0 C 0.05, 0, 0.133333, 0.06, 0.166666, 0.4 C 0.208333, 0.82, 0.25, 1, 1, 1)