Add helper Quaternion methods

Signed-off-by: Slendi <slendi@socopon.com>

include/smath.hpp

@@ -188,9 +188,12 @@ public:
 	// NOTE: This can (probably) be improved with C++26 reflection in the
 	// future.
 #define VEC_ACC(component, req, idx) \
-	constexpr auto component() noexcept -> T &requires(N >= req) { \
+	constexpr auto component() noexcept -> T & \
+	requires(N >= req) \
+	{ \
 		return (*this)[idx]; \
-	} constexpr auto component() const->T const & \
+	} \
+	constexpr auto component() const -> T const & \
 	requires(N >= req) \
 	{ \
 		return (*this)[idx]; \
@@ -281,13 +284,13 @@ public:
 	VEC_OP(/)
 #undef VEC_OP
 #define VEC_OP_ASSIGN(sym) \
-	constexpr Vec &operator sym##=(Vec const &rhs) noexcept \
+	constexpr Vec &operator sym## = (Vec const &rhs) noexcept \
 	{ \
 		for (std::size_t i = 0; i < N; ++i) \
 			(*this)[i] sym## = rhs[i]; \
 		return *this; \
 	} \
-	constexpr Vec &operator sym##=(T const &s) noexcept \
+	constexpr Vec &operator sym## = (T const &s) noexcept \
 	{ \
 		for (std::size_t i = 0; i < N; ++i) \
 			(*this)[i] sym## = s; \
@@ -421,8 +424,9 @@ public:
 	}
 
 	template<class U>
-	requires(std::is_arithmetic_v<U> && N >= 1) constexpr explicit(
-	    !std::is_convertible_v<T, U>) operator Vec<N, U>() const noexcept
+	requires(std::is_arithmetic_v<U> && N >= 1)
+	constexpr explicit(!std::is_convertible_v<T, U>)
+	operator Vec<N, U>() const noexcept
 	{
 		Vec<N, U> r {};
 		for (std::size_t i = 0; i < N; ++i)
@@ -446,9 +450,8 @@ private:
 	}
 #ifdef SMATH_IMPLICIT_CONVERSIONS
 	template<class U>
-	requires std::is_arithmetic_v<U>
-	    && (!std::is_same_v<U, T>)constexpr void fill_one(
-	    std::size_t &i, const U &v) noexcept
+	requires std::is_arithmetic_v<U> && (!std::is_same_v<U, T>)constexpr void
+	fill_one(std::size_t &i, const U &v) noexcept
 	{
 		(*this)[i++] = static_cast<T>(v);
 	}
@@ -577,49 +580,54 @@ using Vec2d = Vec<2, double>;
 using Vec3d = Vec<3, double>;
 using Vec4d = Vec<4, double>;
 
-template<class T> constexpr auto deg(T const value)
+template<class T>
+using angle_ret_t = std::conditional_t<std::is_same_v<T, float>, float, double>;
+
+template<class T> constexpr auto deg(T value)
 {
-	using R = std::common_type_t<T, double>;
+	using R = angle_ret_t<T>;
+
 	if constexpr (detail::SMATH_ANGLE_UNIT_ID == detail::AngularUnit::Degrees) {
 		return static_cast<R>(value);
 	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
 	    == detail::AngularUnit::Radians) {
 		return static_cast<R>(value) * static_cast<R>(std::numbers::pi / 180.0);
-	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
-	    == detail::AngularUnit::Turns) {
+	} else {
 		return static_cast<R>(value) / static_cast<R>(360.0);
 	}
 }
 
-template<class T> constexpr auto rad(T const value)
+template<class T> constexpr auto rad(T value)
 {
-	using R = std::common_type_t<T, double>;
+	using R = angle_ret_t<T>;
+
 	if constexpr (detail::SMATH_ANGLE_UNIT_ID == detail::AngularUnit::Degrees) {
 		return static_cast<R>(value) * static_cast<R>(180.0 / std::numbers::pi);
 	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
 	    == detail::AngularUnit::Radians) {
 		return static_cast<R>(value);
-	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
-	    == detail::AngularUnit::Turns) {
+	} else {
 		return static_cast<R>(value)
 		    / (static_cast<R>(2.0) * static_cast<R>(std::numbers::pi));
 	}
 }
 
-template<class T> constexpr auto turns(T const value)
+template<class T> constexpr auto turns(T value)
 {
-	using R = std::common_type_t<T, double>;
+	using R = angle_ret_t<T>;
+
 	if constexpr (detail::SMATH_ANGLE_UNIT_ID == detail::AngularUnit::Degrees) {
 		return static_cast<R>(value) * static_cast<R>(360.0);
 	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
 	    == detail::AngularUnit::Radians) {
 		return static_cast<R>(value)
 		    * (static_cast<R>(2.0) * static_cast<R>(std::numbers::pi));
-	} else if constexpr (detail::SMATH_ANGLE_UNIT_ID
-	    == detail::AngularUnit::Turns) {
+	} else {
 		return static_cast<R>(value);
 	}
 }
+template<std::size_t R, std::size_t C, typename T>
+requires std::is_arithmetic_v<T> struct Mat;
 
 template<class T> struct Quaternion : Vec<4, T> {
 	using Base = Vec<4, T>;
@@ -654,6 +662,42 @@ template<class T> struct Quaternion : Vec<4, T> {
 
 		return r;
 	}
+
+	[[nodiscard]] constexpr auto as_matrix() const noexcept -> Mat<4, 4, T>
+	{
+		auto const xx = x() * x();
+		auto const yy = y() * y();
+		auto const zz = z() * z();
+		auto const xy = x() * y();
+		auto const xz = x() * z();
+		auto const yz = y() * z();
+		auto const wx = w() * x();
+		auto const wy = w() * y();
+		auto const wz = w() * z();
+
+		return Mat<4, 4, T> {
+			Vec<4, T> { 1 - 2 * (yy + zz), 2 * (xy + wz), 2 * (xz - wy), 0 },
+			Vec<4, T> { 2 * (xy - wz), 1 - 2 * (xx + zz), 2 * (yz + wx), 0 },
+			Vec<4, T> { 2 * (xz + wy), 2 * (yz - wx), 1 - 2 * (xx + yy), 0 },
+			Vec<4, T> { 0, 0, 0, 1 },
+		};
+	}
+
+	[[nodiscard]] static constexpr auto from_axis_angle(
+	    Vec<3, T> const &axis, T const angle) noexcept -> Quaternion
+	{
+		auto const normalized_axis { axis.normalized_safe() };
+		auto const half_angle { angle / static_cast<T>(2) };
+		auto const sine { std::sin(half_angle) };
+		auto const cosine { std::cos(half_angle) };
+
+		return Quaternion {
+			normalized_axis.x() * sine,
+			normalized_axis.y() * sine,
+			normalized_axis.z() * sine,
+			cosine,
+		};
+	}
 };
 
 template<class T>
@@ -1105,28 +1149,18 @@ inline auto matrix_perspective(
 
 template<typename T>
 [[nodiscard]] inline auto matrix_look_at(Vec<3, T> const eye,
-    Vec<3, T> const center, Vec<3, T> const up, bool flip_z_axis = false)
-    -> Mat<4, 4, T>
+    Vec<3, T> const center, Vec<3, T> const up) -> Mat<4, 4, T>
 {
-	auto f = (center - eye).normalized();
-	auto s = f.cross(up).normalized();
+	auto f = (center - eye).normalized_safe();
+	auto s = f.cross(up).normalized_safe();
 	auto u = s.cross(f);
 
-	if (!flip_z_axis) {
 	return Mat<4, 4, T> {
-			Vec<4, T> { s.x(), s.y(), s.z(), 0 },
-			Vec<4, T> { u.x(), u.y(), u.z(), 0 },
-			Vec<4, T> { -f.x(), -f.y(), -f.z(), 0 },
+		Vec<4, T> { s.x(), u.x(), -f.x(), 0 },
+		Vec<4, T> { s.y(), u.y(), -f.y(), 0 },
+		Vec<4, T> { s.z(), u.z(), -f.z(), 0 },
 		Vec<4, T> { -s.dot(eye), -u.dot(eye), f.dot(eye), 1 },
 	};
-	} else {
-		return Mat<4, 4, T> {
-			Vec<4, T> { s.x(), s.y(), s.z(), 0 },
-			Vec<4, T> { u.x(), u.y(), u.z(), 0 },
-			Vec<4, T> { f.x(), f.y(), f.z(), 0 },
-			Vec<4, T> { -s.dot(eye), -u.dot(eye), -f.dot(eye), 1 },
-		};
-	}
 }
 
 template<typename T>