Add math::quadratic_spline_acceleration helper

libs/math/include/psemek/math/math.hpp

@@ -235,4 +235,17 @@ namespace psemek::math
 		return T{1} / T{2} - std::sin(std::asin(T{1} - T{2} * x) / T{3});
 	}
 
+	// Stateless piecewise-quadratic spline acceleration
+	// based on current velocity, current distance to target,
+	// and max acceleration
+	template <typename T>
+	T quadratic_spline_acceleration(T velocity, T distance, T max_acceleration)
+	{
+		T max_velocity = std::sqrt(2.f * std::abs(distance) * max_acceleration);
+		return max_acceleration
+			* (distance < 0.f ? -1.f : 1.f)
+			* ((std::abs(velocity) < max_velocity || (distance > 0.f) != (velocity > 0.f))? 1.f : -1.f)
+			;
+	}
+
 }