Easing changes

- Use Ostrowski Method in easing
- More precise inverse easing for RYB Biased

coloraide/algebra.py

@@ -243,6 +243,8 @@ def solve_newton(
     yn = xn - f(xn) / f'(xn)
     ostrowski = yn - f(xn) / (f(xn) - 2 * f(yn)) * (f(yn) / f'(xn))
     ```
+
+    Return result along with True if converged, False if did not converge, None if could not converge.
     """
 
     for _ in range(maxiter):
@@ -281,9 +283,9 @@ def solve_newton(
                 return x0, True
             fy_x2 = 2 * fy
             if fy_x2 == fx:
-                return x0, False
+                return x0, None
             x1 = x0 - fx / (fx - fy_x2) * (fy / d1)
-            if abs(x1 - x0) < epsilon:
+            if abs(x1 - prev) < epsilon:
                 return x1, True
             x0 = x1
 

coloraide/easing.py

@@ -43,7 +43,7 @@
 from . import algebra as alg
 from typing import Callable
 
-EPSILON = 1e-6
+EPSILON = 1e-12
 MAX_ITER = 8
 
 
@@ -87,7 +87,9 @@ def _solve_bezier(
         t,
         f0,
         _bezier_derivative(a, b, c),
-        maxiter=maxiter
+        maxiter=maxiter,
+        epsilon=eps,
+        ostrowski=True
     )
 
     # We converged or we are close enough

coloraide/spaces/ryb.py

@@ -11,7 +11,7 @@
 from ..channels import Channel
 from ..cat import WHITES
 from ..types import Vector, Matrix
-from ..easing import _bezier, _solve_bezier
+from ..easing import _bezier
 
 # In terms of RGB
 GOSSET_CHEN_CUBE = [
@@ -32,7 +32,7 @@ def srgb_to_ryb(rgb: Vector, cube_t: Matrix, cube: Matrix, biased: bool) -> Vect
     # Calculate the RYB value
     ryb = alg.ilerp3d(cube_t, rgb, vertices_t=cube)
     # Remove smoothstep easing if "biased" is enabled.
-    return [_solve_bezier(t, -2.0, 3.0, 0.0) if 0 <= t <= 1 else t for t in ryb] if biased else ryb
+    return [_bezier(2, -3, 2)(t) if 0 <= t <= 1 else t for t in ryb] if biased else ryb
 
 
 def ryb_to_srgb(ryb: Vector, cube_t: Matrix, biased: bool) -> Vector:

docs/src/markdown/about/changelog.md

@@ -2,6 +2,7 @@
 
 ## 4.2.2
 
+-   **FIX**: More precise inverse of RYB Biased.
 -   **FIX**: Speed up solving of cubic bezier for easing functions.
 -   **FIX**: Protect against possible divide by zero in HCT reverse transform.
 

tests/test_easing.py

@@ -32,7 +32,7 @@ def test_bisect(self):
         """
 
         ease_in_out_expo = cubic_bezier(1.000, 0.000, 0.000, 1.000)
-        self.assertEqual(ease_in_out_expo(0.43), 0.14556343840627634)
+        self.assertEqual(ease_in_out_expo(0.43), 0.14556294236066833)
 
 
 class TestEasingMethods(unittest.TestCase):
@@ -90,7 +90,7 @@ def test_ease(self):
                 -0.08000000000000002,
                 -0.040000000000000015,
                 -1.1102230246251566e-17,
-                0.09479630571604325,
+                0.09479630571604322,
                 0.2952443342678225,
                 0.5133151609733584,
                 0.6825405059781395,
@@ -120,15 +120,15 @@ def test_ease_in(self):
                 0.0,
                 0.0,
                 0.0,
-                0.01702660965156293,
+                0.017026609651562934,
                 0.06228200013673226,
                 0.12957676084535252,
                 0.21486093875289342,
                 0.3153568125725393,
-                0.4291197692963171,
+                0.42911976929631723,
                 0.5548140325286628,
                 0.6916339333193129,
-                0.8394278457624664,
+                0.8394278457624662,
                 0.9999999999999998,
                 1.172413793103448,
                 1.3448275862068964,
@@ -152,14 +152,14 @@ def test_ease_out(self):
                 -4.785444071660158e-17,
                 0.16057215423753346,
                 0.3083660666806869,
-                0.445185967471337,
+                0.44518596747133715,
                 0.5708802307036829,
                 0.6846431874274606,
                 0.7851390612471065,
                 0.8704232391546475,
                 0.9377179998632681,
-                0.982973390348437,
-                0.9999999999999998,
+                0.9829733903484374,
+                1.0,
                 1.0,
                 1.0,
                 1.0,
@@ -183,13 +183,13 @@ def test_ease_in_out(self):
                 0.01972245354831119,
                 0.08165985626589745,
                 0.18739590670531256,
-                0.33188387009764614,
+                0.3318838700976461,
                 0.5,
                 0.668116129902354,
-                0.8126040932946875,
+                0.8126040932946876,
                 0.9183401437341026,
-                0.9802775464516886,
-                1.0,
+                0.9802775464516889,
+                0.9999999999999998,
                 1.0,
                 1.0,
                 1.0,