Add cubic bezier easing #273

mbouron · 2025-05-12T07:06:10Z

No description provided.

ubitux · 2025-05-13T11:58:27Z

libnopegl/src/node_animkeyframe.c

+ *
+ * See: https://cs.android.com/androidx/platform/frameworks/support/+/androidx-main:compose/ui/ui-util/src/commonMain/kotlin/androidx/compose/ui/util/MathHelpers.kt;l=160
+ */
+static float fast_cbrt(float x)


Can we use the native cbrtf? (you can also drop the android copyright then)

ubitux · 2025-05-13T13:09:32Z

libnopegl/src/node_animkeyframe.c

+    if (double_close_to(d, 0.0, FLT_EPSILON)) {
+        if (double_close_to(a, 0.0, FLT_EPSILON)) {
+            if (double_close_to(b, 0.0, FLT_EPSILON)) {


If you want to prevent a division by zero you can check directly against 0.0, it is enough to cover all NaN cases (assuming the numerator is finite). So I'm assuming this check is to prevent an Inf value (caused by overflows). Unfortunately you can't check for it like that. For example 3e-16 will pass the epsilon check, but 1e+308/3e-16 will make an Inf.

Note
You probably wanted to use DBL_EPSILON here since you're working with double precision. But in general, epsilon is never a good threshold against NaN/Inf (and actually using double epsilon here will make it worse).

ubitux · 2025-05-13T13:10:55Z

libnopegl/src/node_animkeyframe.c

+
+static int double_close_to(double value, double ref, double eps)
+{
+    return fabs(value - ref) < eps;


ref and eps are always the same in your calls, so it could probably be called close_to_zero and take only one parameter.

ubitux · 2025-05-13T13:12:47Z

libnopegl/src/node_animkeyframe.c

+    const double da = 3.0f * (b - a);
+    const double db = 3.0f * (c - b);
+    const double dc = 3.0f * (d - c);


Why use f suffix if you're working with doubles?

ubitux · 2025-05-13T13:19:26Z

libnopegl/src/node_animkeyframe.c

+static float clamp_root(float r)
+{
+    const float s = NGLI_CLAMP(r, 0.f, 1.f);
+    return fabsf(s - r) > FLT_EPSILON ? NAN : s;


FLT_EPSILON is, as far as I can tell, not a very good threshold choice as it's probably going to filter out all sorts of cases where the root is close to 0 or 1: it's a very restrictive value, and at the same time not 100%. A more arbitrary 1e-6 (that can be understood as a "precision" rounding) will likely do a better job.

ubitux · 2025-05-13T13:27:49Z

libnopegl/src/node_animkeyframe.c

+    double a = 3.0 * (p0 - 2.0 * p1 + p2);
+    double b = 3.0 * (p1 - p0);
+    double c = p0;
+    double d = -p0 + 3.0 * (p1 - p2) + p3;


So I'm assuming this is the cubic points being converted to polynomial coefficients, but the value are weirdly shuffled. You made your polynomial $dx^3+ax^2+bx+c$, which I'm assuming you did because you're making it monic later down the line and reusing a/b/c naming. I think it would make sense to keep it as $ax^3+bx^2+cx+d$ for clarity, then pass it down to another function as $f(\frac{b}{a}, \frac{c}{a}, \frac{d}{a})$ where you can name again the parameters a, b and c.

I implemented it so it matches the ref mentioned in the comment, see: https://pomax.github.io/bezierinfo/#yforx

ubitux · 2025-05-13T13:32:29Z

libnopegl/src/node_animkeyframe.c

+            double q = sqrt(b * b - 4.0 * a * c);
+            double a2 = 2.0 * a;
+
+            float root = clamp_root(((float) ((q - b) / a2)));
+            if (!isnan(root))
+                return root;
+
+            return clamp_root(((float) ((-b - q) / a2)));


Non-blocking: there is a simpler quadratic formula which we're using in distmap where you find a middle point $m=-\frac{b}{2a}$ that you offset by $±\sqrt{\Delta}$ where $\Delta=m^2-\frac{c}{a}$ to get each root.

Since there are less subtractions, I also believe it leads to a lower risk of catastrophic cancellation (to be verified though).

ubitux · 2025-05-13T13:33:15Z

libnopegl/src/node_animkeyframe.c

+            }
+            return clamp_root((float) (-c / b));
+        } else {
+            double q = sqrt(b * b - 4.0 * a * c);


This is missing a check if the $b^2-4ac < 0$

ubitux · 2025-05-13T13:35:54Z

libnopegl/src/node_animkeyframe.c

+    double u1 = fast_cbrt((float)(-q2 + sd));
+    double v1 = fast_cbrt((float)(q2 + sd));
+
+    return clamp_root((float)(u1 - v1 - a3));


Note that in my experience the analytic cubic is filled with numerical instability and I wouldn't recommend it... I ended up dropping it from the distmap for a more stable iterative algorithm.

ubitux · 2025-05-13T13:36:36Z

libnopegl/src/node_animkeyframe.c

+    double a = 1.0 / 3.0 + (p1 - p2);
+    double b = (p2 - 2.0 * p1);
+    double c = p1;
+    return 3.0 * ((a * t + b) * t + c) * t;


I would recommend computing and caching the polynomial for faster evaluation.

ubitux · 2025-05-15T10:25:54Z

libnopegl/src/node_animkeyframe.c

+    const easing_type a = PARAM(0, 0.0);
+    const easing_type b = PARAM(1, 0.0);
+    const easing_type c = PARAM(2, 1.0);
+    const easing_type d = PARAM(3, 1.0);


So here is something: with easing, the starting and ending points are always respectively (0,0) and (1,1). If you need some sort of offsetting, you can use easing_start_offset and easing_end_offset.

Next, you can't have the curve going backward, which means $b_x ≤ c_x$ must be verified (maybe this is already the case due to the points being in a single dimension).

All these constraints may also make the solver and friends way more convenient and may avoid a bunch of tests. You also won't need to extend the number of parameter from 2 to 4.

ubitux · 2025-05-15T10:26:24Z

libnopegl/src/node_animkeyframe.c

+    const easing_type c = PARAM(2, 1.0);
+    const easing_type d = PARAM(3, 1.0);
+
+    const easing_type v = NGLI_MAX(t, FLT_EPSILON);


why is $t=0$ not allowed? It should just be the starting point

ubitux · 2025-05-15T19:50:59Z

libnopegl/src/node_animkeyframe.c

+        return 1.0;
+    }
+
+    return evaluate_cubic(db, 0.f, r);


evaluate_cubic() takes double arguments so 0.f should be 0.0.

This is needed to support easings based on cubic Bézier curves.

mbouron force-pushed the to-upstream-v6 branch from 0ba21f0 to 0c4a9cb Compare May 12, 2025 07:09

mbouron force-pushed the to-upstream-v7 branch from 7421b6c to 448db40 Compare May 12, 2025 07:09

mbouron force-pushed the to-upstream-v6 branch 2 times, most recently from 92affc3 to cd8b6fb Compare May 12, 2025 07:17

mbouron force-pushed the to-upstream-v7 branch from 448db40 to f57f2cb Compare May 12, 2025 07:17

mbouron force-pushed the to-upstream-v6 branch from cd8b6fb to 43abfc6 Compare May 12, 2025 16:52

Base automatically changed from to-upstream-v6 to main May 12, 2025 22:39

ubitux reviewed May 13, 2025

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ubitux reviewed May 15, 2025

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pynopegl: raise the limit of easing params to 4

e931d75

This is needed to support easings based on cubic Bézier curves.

mbouron force-pushed the to-upstream-v7 branch 3 times, most recently from 2ea27d9 to 6f59a2f Compare November 11, 2025 10:10

mbouron added 2 commits November 11, 2025 11:14

animkeyframe: add cubic bezier support

df08d37

tests: add bezier_cubic test

8749f01

mbouron force-pushed the to-upstream-v7 branch from 6f59a2f to 8749f01 Compare November 11, 2025 10:14

Add cubic bezier easing #273

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Add cubic bezier easing #273

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