Introduce cubic timing function.

Numeric/CubicCurve.hpp

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+//
+//  CubicCurve.hpp
+//  Clock Signal
+//
+//  Created by Thomas Harte on 04/10/2025.
+//  Copyright © 2025 Thomas Harte. All rights reserved.
+//
+
+#pragma once
+
+#include <cassert>
+
+/*!
+	Provides a cubic Bezier-based timing function.
+*/
+struct CubicCurve {
+	CubicCurve(const float c1x, const float c1y, const float c2x, const float c2y) :
+		c1(c1x, c1y), c2(c2x, c2y)
+	{
+		assert(0.0f <= c1x);	assert(c1x <= 1.0f);
+		assert(0.0f <= c1y);	assert(c1y <= 1.0f);
+		assert(0.0f <= c2x);	assert(c2x <= 1.0f);
+		assert(0.0f <= c2y);	assert(c2y <= 1.0f);
+	}
+
+	/// @returns A standard ease-in-out animation curve.
+	static CubicCurve easeInOut() {
+		return CubicCurve(0.42f, 0.0f, 0.58f, 1.0f);
+	}
+
+	/// @returns The value for y given x, in range [0.0, 1.0].
+	float value(const float x) const {
+		return axis(t(x), 1);
+	}
+
+private:
+	/// @returns The value for @c t that generates the value @c x.
+	float t(const float x) const {
+		static constexpr float Precision = 0.01f;
+		float bounds[2] = {0.0f, 1.0f};
+		const auto midpoint = [&] { return (bounds[0] + bounds[1]) * 0.5f; };
+
+		while(bounds[1] > bounds[0] + Precision) {
+			const float mid = midpoint();
+			const float value = axis(mid, 0);
+			if(value > x) {
+				bounds[1] = mid;
+			} else {
+				bounds[0] = mid;
+			}
+		}
+		return midpoint();
+	}
+
+	/// @returns The value for axis @c index at time @c t.
+	float axis(const float t, int index) const {
+		const float f1 = t * c1[index];
+		const float f2 = t * c2[index] + (1.0f - t) * c1[index];
+		const float f3 = t + (1.0f - t) * c2[index];
+
+		const float c1 = t * f2 + (1.0f - t) * f1;
+		const float c2 = t * f3 + (1.0f - t) * f2;
+
+		return t * c2 + (1.0f - t) * c1;
+	}
+
+	float c1[2];
+	float c2[2];
+};