EHS/include/Quat.h

#pragma once

#include "EHS.h"
#include "Math.h"
#include "Mat4.h"
#include "Vec3.h"

namespace lwe
{
	template<typename T>
	class Quat
	{
	public:
		T w;
		T x;
		T y;
		T z;

		Quat()
			: w(0), x(0), y(0), z(0)
		{
		}

		Quat(const T w, const T x, const T y, const T z)
				: w(w), x(x), y(y), z(z)
		{
		}

		Quat(const T yaw, const T pitch, const T roll)
				: w(0), x(0), y(0), z(0)
		{
			T c1 = cos(yaw / 2);
			T c2 = cos(pitch / 2);
			T c3 = cos(roll / 2);
			T s1 = sin(yaw / 2);
			T s2 = sin(pitch / 2);
			T s3 = sin(roll / 2);

			w = c1 * c2 * c3 - s1 * s2 * s3;
			x = s1 * s2 * c3 + c1 * c2 * s3;
			y = s1 * c2 * c3 + c1 * s2 * s3;
			z = c1 * s2 * c3 - s1 * c2 * s3;
		}

		explicit Quat(const Vec3<T>& euler)
				: w(0), x(0), y(0), z(0)
		{
			T c1 = cos(euler.x / 2);
			T c2 = cos(euler.y / 2);
			T c3 = cos(euler.z / 2);
			T s1 = sin(euler.x / 2);
			T s2 = sin(euler.y / 2);
			T s3 = sin(euler.z / 2);

			w = c1 * c2 * c3 - s1 * s2 * s3;
			x = s1 * s2 * c3 + c1 * c2 * s3;
			y = s1 * c2 * c3 + c1 * s2 * s3;
			z = c1 * s2 * c3 - s1 * c2 * s3;
		}

		Quat(const Vec3<T>& n, const T a)
				: w(cosf(a / 2)), x(n.x * sinf(a / 2)), y(n.y * sinf(a / 2)), z(n.z * sinf(a / 2))
		{
		}

		explicit Quat(const Mat4<T>& rotMatrix)
				: w(0), x(0), y(0), z(0)
		{
			ToQuaternion(rotMatrix);
		}

		Quat(const Quat& quat)
				: w(quat.w), x(quat.x), y(quat.y), z(quat.z)
		{
		}

		explicit Quat(const T scalar)
				: w(scalar), x(scalar), y(scalar), z(scalar)
		{
		}

		Quat& operator=(const Quat& quat)
		{
			if (this == &quat)
				return *this;

			w = quat.w;
			x = quat.x;
			y = quat.y;
			z = quat.z;

			return *this;
		}

		Quat& operator=(const Mat4<T>& rotMatrix)
		{
			ToQuaternion(rotMatrix);

			return *this;
		}

		Quat operator+(const Quat& other) const
		{
			return {w + other.w, x + other.x, y + other.y, z + other.z};
		}

		Quat operator-() const
		{
			return {-w, -x, -y, -z};
		}

		Quat operator-(const Quat& other) const
		{
			return {w - other.w, x - other.x, y - other.y, z - other.z};
		}

		Quat operator*(const T scalar)
		{
			return {w * scalar, x * scalar, x * scalar, x * scalar};
		}

		Quat operator*(const Quat& other)
		{
			return Quat
			(
				w * other.w - x * other.x - y * other.y - z * other.z,
				w * other.x + x * other.w + y * other.z - z * other.y,
				w * other.y - x * other.z + y * other.w + z * other.x,
				w * other.z + x * other.y - y * other.x + z * other.w
			);
		}

		Vec3<T> operator*(const Vec3<T>& vect)
		{
			Quat tmp(0, vect[0], vect[1], vect[2]);
			Vec3<T> tmpVect(x, y, z);

			Vec3<T> vcV = tmpVect.CrossProduct(vect);
			return vect + vcV * (2 * w) + tmpVect.CrossProduct(vcV) * 2;
		}

		Quat operator^(const T t)
		{
			Vec3<T> n;
			T a;

			ToAxisAngle(&n, &a);

			float at = a * t;

			return Quat<T>(n, at);
		}

		bool operator==(const Quat& quat) const
		{
			return w == quat.w && x == quat.x && y == quat.y && z == quat.z;
		}

		bool operator!=(const Quat& quat) const
		{
			return w != quat.w || x != quat.x || y != quat.y || z == quat.z;
		}

		T operator[](const UInt_64 index) const
		{
			switch (index)
			{
				case 0:
					return w;
				case 1:
					return x;
				case 2:
					return y;
				case 3:
					return z;
				default:
					return w;
			}
		}

		T& operator[](const UInt_64 index)
		{
			switch (index)
			{
				case 0:
					return w;
				case 1:
					return x;
				case 2:
					return y;
				case 3:
					return z;
				default:
					return w;
			}
		}

		void ToAxisAngle(Vec3<T>* vectAxis, T* flAngle)
		{
			Vec3<T> tmp(x, y, z);

			if (tmp.GetDis2() < 0.0001f)
				*vectAxis = Vec3<T>(1, 0, 0);
			else
				*vectAxis = tmp.GetNorm();

			*flAngle = acosf(w) * 2;
			*flAngle = Math::Degr<T>(*flAngle);
		}

		void ToQuaternion(const Mat4<T>& rotMatrix)
		{
			T trace = rotMatrix[0][0] + rotMatrix[1][1] + rotMatrix[2][2];

			if (trace > 0)
			{
				T s = 0.5f / Math::Sqrt<T>(trace + 1.0f);
				w = 0.25f / s;

				x = (rotMatrix[2][1] - rotMatrix[1][2]) * s;
				y = (rotMatrix[0][2] - rotMatrix[2][0]) * s;
				z = (rotMatrix[1][0] - rotMatrix[0][1]) * s;
			} else
			{
				if ((rotMatrix[0][0] > rotMatrix[1][1]) && (rotMatrix[0][0] > rotMatrix[2][2]))
				{
					T s = 2.0f * Math::Sqrt(1.0f + rotMatrix[0][0] - rotMatrix[1][1] - rotMatrix[2][2]);
					w = (rotMatrix[2][1] - rotMatrix[1][2]) / s;
					x = 0.25f * s;
					y = (rotMatrix[0][1] + rotMatrix[1][0]) / s;
					z = (rotMatrix[0][2] + rotMatrix[2][0]) / s;
				} else if (rotMatrix[1][1] > rotMatrix[2][2])
				{
					T s = 2.0f * sqrtf(1.0f + rotMatrix[1][1] - rotMatrix[0][0] - rotMatrix[2][2]);
					w = (rotMatrix[0][2] - rotMatrix[2][0]) / s;
					x = (rotMatrix[0][1] + rotMatrix[1][0]) / s;
					y = 0.25f * s;
					z = (rotMatrix[1][2] + rotMatrix[2][1]) / s;
				} else
				{
					T s = 2.0f * sqrtf(1.0f + rotMatrix[2][2] - rotMatrix[0][0] - rotMatrix[1][1]);
					w = (rotMatrix[1][0] - rotMatrix[0][1]) / s;
					x = (rotMatrix[0][2] + rotMatrix[2][0]) / s;
					y = (rotMatrix[1][2] + rotMatrix[2][1]) / s;
					z = 0.25f * s;
				}
			}
		}

		/*
		Vec3<T> ToEulerAngle() const
		{
			Vec3<T> euler;

			float ysqr = y * y;

			float t0 = 2 * (w * x + y * z);
			float t1 = 1 - 2 * (x * x + ysqr);
			euler.z = std::atan2(t0, t1);

			float t2 = 2 * (w * y - z * x);
			t2 = t2 > 1 ? 1 : t2;
			t2 = t2 < -1 ? -1 : t2;
			euler.y = std::asin(t2);

			float t3 = 2 * (w * z + x * y);
			float t4 = 1 - 2 * (ysqr + z * z);
			euler.x = std::atan2(t3, t4);

			return euler;
		}
		*/

		Mat4<T> ToMatrix() const
		{
			Mat4<T> result;

			T x2 = x + x;
			T y2 = y + y;
			T z2 = z + z;
			T x2w = x2 * w;
			T y2w = y2 * w;
			T z2w = z2 * w;
			T x2x = x2 * x;
			T y2x = y2 * x;
			T z2x = z2 * x;
			T y2y = y2 * y;
			T z2y = z2 * y;
			T z2z = z2 * y;

			result[0] = T(1) - (y2y + z2z);
			result[1] = y2x - z2w;
			result[2] = z2x + y2w;
			result[3] = T(0);

			result[4] = y2x + z2w;
			result[5] = T(1) - (x2x + z2z);
			result[6] = z2y - x2w;
			result[7] = T(0);

			result[8] = z2x - y2w;
			result[9] = z2y + x2w;
			result[10] = T(1) - (x2x + y2y);
			result[11] = T(0);

			result[12] = T(0);
			result[13] = T(0);
			result[14] = T(0);
			result[15] = T(1);

			return result;
		}

		float GetMagnitude()
		{
			return Math::Sqrt<T>(Math::Pow<T>(w, 2) + Math::Pow<T>(x, 2) + Math::Pow<T>(y, 2) + Math::Pow<T>(z, 2));
		}

		Quat<T> GetNormalized()
		{
			T mag = GetMagnitude();

			return Quat<T>(w / mag, x / mag, y / mag, z / mag);
		}

		void Normalize()
		{
			T mag = GetMagnitude();

			w = w / mag;
			x = x / mag;
			y = y / mag;
			z = z / mag;
		}

		T Dot(const Quat& other) const
		{
			return w * other.w + x * other.x + y * other.y + z * other.z;
		}

		Quat<T> GetConjugate()
		{
			return Quat<T>(w, -x, -y, -z);
		}

		void Conjugate()
		{
			x = -x;
			y = -y;
			z = -z;
		}

		Quat<T> GetInverse()
		{
			return Quat<T>(w, -x, -y, -z);
		}

		void Inverse()
		{
			x = -x;
			y = -y;
			z = -z;
		}

		static Quat<T> Slerp(Quat<T> start, Quat<T> finish, const T t)
		{
			T cosHalfTheta = start.Dot(finish);
			if (Math::Abs(cosHalfTheta) >= 1.0f)
				return start;

			float halfTheta = Math::ACos(cosHalfTheta);
			float sinHalfTheta = Math::Sqrt(1.0f - cosHalfTheta * cosHalfTheta);
			if (Math::Abs(sinHalfTheta) < 0.001f)
			{
				return {
					start.w * 0.5f + finish.w * 0.5f,
					start.x * 0.5f + finish.x * 0.5f,
					start.y * 0.5f + finish.y * 0.5f,
					start.z * 0.5f + finish.z * 0.5f
				};
			}

			float ratioA = Math::Sin((1 - t) * halfTheta) / sinHalfTheta;
			float ratioB = Math::Sin(t * halfTheta) / sinHalfTheta;

			return {
				start.w * ratioA + finish.w * ratioB,
				start.x * ratioA + finish.x * ratioB,
				start.y * ratioA + finish.y * ratioB,
				start.z * ratioA + finish.z * ratioB
			};
		}
	};

	typedef Quat<float> Quat_f;
}