Magic_Game/core/math/Matrix.hpp

// Copyright (c) 2016-2018 Easy2D - Nomango
// 
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
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// furnished to do so, subject to the following conditions:
// 
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// THE SOFTWARE.

#pragma once
#include "vector.hpp"
#include <d2d1.h>

namespace easy2d
{
	namespace math
	{
		class Matrix;

		template <typename L, typename R>
		struct MatrixMultiply;

		inline MatrixMultiply<Matrix, Matrix>
		operator *(Matrix const& lhs, Matrix const& rhs);

		template <typename L, typename R>
		inline MatrixMultiply<MatrixMultiply<L, R>, Matrix>
		operator *(MatrixMultiply<L, R> const& lhs, Matrix const& rhs);


		class Matrix
		{
			union
			{
				struct
				{
					float m[6];  // m[3][2]
				};
				
				struct
				{
					float
						_11, _12,
						_21, _22,
						_31, _32;
				};
			};

		public:
			Matrix()
				: _11(1.f), _12(0.f)
				, _21(0.f), _22(1.f)
				, _31(0.f), _32(0.f)
			{
			}

			Matrix(float _11, float _12, float _21, float _22, float _31, float _32)
				: _11(_11), _12(_12), _21(_21), _22(_22), _31(_31), _32(_32)
			{
			}

			Matrix(const float* p)
			{
				for (int i = 0; i < 6; i++)
					m[i] = p[i];
			}

			Matrix(Matrix const& other)
				: _11(other._11), _12(other._12)
				, _21(other._21), _22(other._22)
				, _31(other._31), _32(other._32)
			{
			}

			template <typename T>
			Matrix(T const& other)
			{
				for (int i = 0; i < 6; i++)
					m[i] = other[i];
			}

			inline float operator [](unsigned int index) const
			{
				return m[index];
			}

			template <typename T>
			inline Matrix& operator =(T const& other)
			{
				for (int i = 0; i < 6; i++)
					m[i] = other[i];
				return *this;
			}

			inline Matrix& Identity()
			{
				_11 = 1.f; _12 = 0.f;
				_21 = 0.f; _12 = 1.f;
				_31 = 0.f; _32 = 0.f;
				return *this;
			}

			inline float Determinant() const
			{
				return (_11 * _22) - (_12 * _21);
			}

			inline bool IsIdentity() const
			{
				return	_11 == 1.f && _12 == 0.f &&
						_21 == 0.f && _22 == 1.f &&
						_31 == 0.f && _32 == 0.f;
			}

			inline bool IsInvertible() const
			{
				return 0 != Determinant();
			}

			Vector2 Transform(const Vector2& v) const
			{
				return Vector2(
					v.x * _11 + v.y * _21 + _31,
					v.x * _12 + v.y * _22 + _32
				);
			}

			void Translate(const Vector2& v)
			{
				_31 += _11 * v.x + _21 * v.y;
				_32 += _12 * v.x + _22 * v.y;
			}

			inline operator D2D1_MATRIX_3X2_F const& () const
			{
				return reinterpret_cast<D2D1_MATRIX_3X2_F const&>(*this);
			}

			inline operator D2D1_MATRIX_3X2_F& ()
			{
				return reinterpret_cast<D2D1_MATRIX_3X2_F&>(*this);
			}

			static Matrix Translation(const Vector2& v)
			{
				return Matrix(
					1.f, 0.f,
					0.f, 1.f,
					v.x, v.y
				);
			}

			static Matrix Translation(
				float x,
				float y)
			{
				return Translation(Vector2(x, y));
			}

			static Matrix Scaling(
				const Vector2& v,
				const Vector2& center = Vector2())
			{
				return Matrix(
					v.x, 0.f,
					0.f, v.y,
					center.x - v.x * center.x,
					center.y - v.y * center.y
				);
			}

			static Matrix Scaling(
				float x,
				float y,
				const Vector2& center = Vector2())
			{
				return Scaling(Vector2(x, y), center);
			}

			static Matrix Rotation(
				float angle,
				const Vector2& center = Vector2())
			{
				float s = math::Sin(angle);
				float c = math::Cos(angle);
				return Matrix(
					c, s,
					-s, c,
					center.x * (1 - c) + center.y * s,
					center.y * (1 - c) - center.x * s
				);
			}

			static Matrix Skewing(
				float angle_x,
				float angle_y,
				const Vector2& center = Vector2())
			{
				float tx = math::Tan(angle_x);
				float ty = math::Tan(angle_y);
				return Matrix(
					1.f, -ty,
					-tx, 1.f,
					center.y * tx, center.x * ty
				);
			}

			static Matrix Invert(Matrix const& matrix)
			{
				float det = 1.f / matrix.Determinant();

				return Matrix(
					det * matrix._22,
					-det * matrix._12,
					-det * matrix._21,
					det * matrix._11,
					det * (matrix._21 * matrix._32 - matrix._22 * matrix._31),
					det * (matrix._12 * matrix._31 - matrix._11 * matrix._32)
				);
			}
		};


		template <typename L, typename R>
		struct MatrixMultiply
		{
			L const& lhs;
			R const& rhs;

			MatrixMultiply(L const& lhs, R const& rhs)
				: lhs(lhs)
				, rhs(rhs)
			{}

			inline float operator [](unsigned int index) const
			{
				switch (index)
				{
				case 0:
					return lhs[0] * rhs[0] + lhs[1] * rhs[2];
				case 1:
					return lhs[0] * rhs[1] + lhs[1] * rhs[3];
				case 2:
					return lhs[2] * rhs[0] + lhs[3] * rhs[2];
				case 3:
					return lhs[2] * rhs[1] + lhs[3] * rhs[3];
				case 4:
					return lhs[4] * rhs[0] + lhs[5] * rhs[2] + rhs[4];
				case 5:
					return lhs[4] * rhs[1] + lhs[5] * rhs[3] + rhs[5];
				default:
					return 0.f;
				}
			}
		};

		inline MatrixMultiply<Matrix, Matrix> operator *(Matrix const& lhs, Matrix const& rhs)
		{
			return MatrixMultiply<Matrix, Matrix>(lhs, rhs);
		}

		template <typename L, typename R>
		inline MatrixMultiply<MatrixMultiply<L, R>, Matrix> operator *(MatrixMultiply<L, R> const& lhs, Matrix const& rhs)
		{
			return MatrixMultiply<MatrixMultiply<L, R>, Matrix>(lhs, rhs);
		}
	}
}