新增功能：缓动函数

src/tui/component/easing.cppm

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+/**
+ * @file        tui/component/easing.cppm
+ * @brief       缓动函数
+ * @attention   魔数有点多，不过也算使用比较广泛了
+ * @author      KeqingMoe
+ * @date        2024-12-9
+ * @copyright   Copyright (c) 2024 KeqingMoe
+ * @license     MIT License
+ */
+
+export module kqm.tui.component:easing;
+
+import std;
+
+constexpr auto k_pi(std::floating_point auto x) noexcept
+{
+    return std::numbers::pi_v<decltype(x)> * x;
+}
+
+constexpr auto bounce_out(std::floating_point auto x) noexcept
+{
+    using float_t = decltype(x);
+    if (x < float_t{4} / float_t{11}) return (121 * x * x) / 16;
+    if (x < float_t{8} / float_t{11}) return 9.075 * x * x + 9.9 * x + 3.4;
+    if (x < 0.9) return (4356 * x * x / 361) - (35442 * x / 1805) + float_t{16061} / float_t{1805};
+    return 10.8 * x * x - 20.52 * x + 10.72;
+}
+
+export namespace kqm::tui
+{
+
+inline namespace component
+{
+
+/**
+ * @brief 缓动函数
+ */
+inline namespace easing
+{
+
+/**
+ * @brief 概念 `EasingFunctionsWithFloat`
+ * @details 用于实现 `EasingFunctions` 概念
+ * @tparam EF 缓动函数
+ * @tparam Float 浮点数类型，EF 要能够与它一同工作
+ */
+template <typename EF, typename Float>
+concept EasingFunctionsWithFloat = requires(EF&& ease, Float x) {
+    requires std::floating_point<Float>;
+    { ease.in(x) } -> std::convertible_to<Float>;
+    { ease.out(x) } -> std::convertible_to<Float>;
+    { ease.in_out(x) } -> std::convertible_to<Float>;
+};
+
+/**
+ * @brief 概念 `EasingFunctions`
+ * @details 约束“缓动函数”概念
+ * @tparam EF 缓动函数
+ */
+template <typename EF, typename Base>
+concept EasingFunctions = requires {
+    requires EasingFunctionsWithFloat<EF, float>;
+    requires EasingFunctionsWithFloat<EF, double>;
+    requires EasingFunctionsWithFloat<EF, long double>;
+};
+
+/**
+ * @brief 缓动函数
+ * @details 基于静态多态，派生类需满足 `EasingFunctions` 概念
+ */
+struct ease_base
+{
+    constexpr auto out(this EasingFunctions<ease_base> auto&& self, std::floating_point auto x)
+        noexcept(noexcept(self.in(x))) -> decltype(x)
+    {
+        return 1 - self.in(1 - x);
+    }
+    constexpr auto in_out(this EasingFunctions<ease_base> auto&& self, std::floating_point auto x)
+        noexcept(noexcept(self.in(x)) && noexcept(self.out(x))) -> decltype(x)
+    {
+        if (x < 0.5) return 0.5 * self.in(2 * x);
+        return 0.5 * (self.out(2 * (x - 1)) + 1);
+    }
+};
+
+/**
+ * @brief N 次缓动函数
+ * @tparam N 指数
+ */
+template <std::unsigned_integral auto N>
+    requires(N > 0)
+struct pow : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        auto result = x;
+        for (auto i = 1uz; i < N; ++i) {
+            result *= x;
+        }
+        return result;
+    }
+};
+
+
+/**
+ * @brief 线性缓动函数
+ */
+using linear = pow<1uz>;
+
+/**
+ * @brief 二次缓动函数
+ */
+using quadratic = pow<2uz>;
+
+/**
+ * @brief 三次缓动函数
+ */
+using cubic = pow<3uz>;
+
+/**
+ * @brief 四次缓动函数
+ */
+using quartic = pow<4uz>;
+
+/**
+ * @brief 五次缓动函数
+ */
+using quintic = pow<4uz>;
+
+
+/**
+ * @brief 正弦缓动函数
+ */
+struct sin : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        return std::sin(0.5 * k_pi(x - 1)) + 1;
+    }
+    constexpr auto in_out(std::floating_point auto x) noexcept
+    {
+        return 0.5 * (1 - std::cos(k_pi(x)));
+    }
+};
+
+
+/**
+ * @brief 圆形缓动函数
+ */
+struct circular : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        return 1 - std::sqrt(1 - x * x);
+    }
+};
+
+
+/**
+ * @brief 弹性 (Elastic) 缓动函数
+ */
+struct elastic : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        return std::sin(6.5 * k_pi(x)) * std::pow(2, 10 * (x - 1));
+    }
+};
+
+/**
+ * @brief 向后 (Back) 缓动函数
+ */
+struct back : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        return x * x * x - x * std::pow(k_pi(x));
+    }
+};
+
+/**
+ * @brief 弹跳 (Bounce) 缓动函数
+ */
+struct bounce : ease_base
+{
+    constexpr auto in(std::floating_point auto x) noexcept
+    {
+        return 1 - bounce_out(1 - x);
+    }
+    constexpr auto out(std::floating_point auto x) noexcept
+    {
+        return bounce_out(x);
+    }
+};
+
+
+}
+
+}
+
+}