first commit

.gitignore

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+# ---> C++
+# Prerequisites
+*.d
+
+# Compiled Object files
+*.slo
+*.lo
+*.o
+*.obj
+
+# Precompiled Headers
+*.gch
+*.pch
+
+# Compiled Dynamic libraries
+*.so
+*.dylib
+*.dll
+
+# Fortran module files
+*.mod
+*.smod
+
+# Compiled Static libraries
+*.lai
+*.la
+*.a
+*.lib
+
+# Executables
+*.exe
+*.out
+*.app
+
+
+#vs2015
+Debug
+Release
+x64
+.git
+ipch
+*.VC.db
+*.VC.VC.opendb

3dMath.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio 15
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+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "3dMath", "3dMath.vcxproj", "{BAB2F10C-2B89-463F-B785-9A18937F6238}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|x64 = Debug|x64
+		Debug|x86 = Debug|x86
+		Release|x64 = Release|x64
+		Release|x86 = Release|x86
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Debug|x64.ActiveCfg = Debug|x64
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Debug|x64.Build.0 = Debug|x64
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Debug|x86.ActiveCfg = Debug|Win32
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Debug|x86.Build.0 = Debug|Win32
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Release|x64.ActiveCfg = Release|x64
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Release|x64.Build.0 = Release|x64
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Release|x86.ActiveCfg = Release|Win32
+		{BAB2F10C-2B89-463F-B785-9A18937F6238}.Release|x86.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {B523576E-FA21-49B7-90A5-0F9CF9D239BD}
+	EndGlobalSection
+EndGlobal

3dMath.vcxproj

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+<?xml version="1.0" encoding="utf-8"?>
+<Project DefaultTargets="Build" ToolsVersion="15.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup Label="ProjectConfigurations">
+    <ProjectConfiguration Include="Debug|Win32">
+      <Configuration>Debug</Configuration>
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+    <ProjectConfiguration Include="Release|Win32">
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+      <Platform>x64</Platform>
+    </ProjectConfiguration>
+    <ProjectConfiguration Include="Release|x64">
+      <Configuration>Release</Configuration>
+      <Platform>x64</Platform>
+    </ProjectConfiguration>
+  </ItemGroup>
+  <PropertyGroup Label="Globals">
+    <VCProjectVersion>15.0</VCProjectVersion>
+    <ProjectGuid>{BAB2F10C-2B89-463F-B785-9A18937F6238}</ProjectGuid>
+    <RootNamespace>My3dMath</RootNamespace>
+    <WindowsTargetPlatformVersion>10.0.17763.0</WindowsTargetPlatformVersion>
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+    <Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
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+    <Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
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+    <Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
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+  <PropertyGroup Label="UserMacros" />
+  <PropertyGroup />
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+      <Optimization>Disabled</Optimization>
+      <SDLCheck>true</SDLCheck>
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+    <Link>
+      <SubSystem>Console</SubSystem>
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+      <SDLCheck>true</SDLCheck>
+      <ConformanceMode>true</ConformanceMode>
+    </ClCompile>
+    <Link>
+      <SubSystem>Console</SubSystem>
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+      <OptimizeReferences>true</OptimizeReferences>
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+  </ItemDefinitionGroup>
+  <ItemDefinitionGroup Condition="'$(Configuration)|$(Platform)'=='Release|x64'">
+    <ClCompile>
+      <WarningLevel>Level3</WarningLevel>
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+      <FunctionLevelLinking>true</FunctionLevelLinking>
+      <IntrinsicFunctions>true</IntrinsicFunctions>
+      <SDLCheck>true</SDLCheck>
+      <ConformanceMode>true</ConformanceMode>
+    </ClCompile>
+    <Link>
+      <SubSystem>Console</SubSystem>
+      <EnableCOMDATFolding>true</EnableCOMDATFolding>
+      <OptimizeReferences>true</OptimizeReferences>
+    </Link>
+  </ItemDefinitionGroup>
+  <ItemGroup>
+    <ClInclude Include="GMath.h" />
+  </ItemGroup>
+  <ItemGroup>
+    <ClCompile Include="GMath.cpp" />
+    <ClCompile Include="main.cpp" />
+  </ItemGroup>
+  <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
+  <ImportGroup Label="ExtensionTargets">
+  </ImportGroup>
+</Project>

3dMath.vcxproj.filters

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+<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <ItemGroup>
+    <Filter Include="源文件">
+      <UniqueIdentifier>{4FC737F1-C7A5-4376-A066-2A32D752A2FF}</UniqueIdentifier>
+      <Extensions>cpp;c;cc;cxx;def;odl;idl;hpj;bat;asm;asmx</Extensions>
+    </Filter>
+    <Filter Include="头文件">
+      <UniqueIdentifier>{93995380-89BD-4b04-88EB-625FBE52EBFB}</UniqueIdentifier>
+      <Extensions>h;hh;hpp;hxx;hm;inl;inc;ipp;xsd</Extensions>
+    </Filter>
+    <Filter Include="资源文件">
+      <UniqueIdentifier>{67DA6AB6-F800-4c08-8B7A-83BB121AAD01}</UniqueIdentifier>
+      <Extensions>rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms</Extensions>
+    </Filter>
+  </ItemGroup>
+  <ItemGroup>
+    <ClInclude Include="GMath.h">
+      <Filter>头文件</Filter>
+    </ClInclude>
+  </ItemGroup>
+  <ItemGroup>
+    <ClCompile Include="GMath.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
+    <ClCompile Include="main.cpp">
+      <Filter>源文件</Filter>
+    </ClCompile>
+  </ItemGroup>
+</Project>

3dMath.vcxproj.user

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+<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="15.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup />
+</Project>

GMath.h

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+#pragma once
+#include <cmath>
+#include <stdio.h>
+#include <cassert>
+#include <iostream>
+#include <iomanip>
+#include <stdarg.h>
+
+#define PRECISION 0.000001
+#define SQRT(X)	sqrt((X)) //求平方根
+#define SQR(X) ((X)*(X)) //求平方
+#define ABS(X) abs((X))
+#define EQ(X,Y,EPS) (ABS((X)-(Y))<EPS)//通过误差去判断，两个数是否相等
+#define EQ_ZERO(X,EPS) (ABS((X))<EPS)
+#define ARR_ZERO(A, N) memset((A), 0, sizeof(A[0])*(N))
+#define MIN(x,y) (x)<(y)?(x):(y);
+#define SWAP(type, x, y) {type tmp=(x); (x)=(y); (y) = tmp;}
+
+using namespace std;
+
+class GVector3 {
+private:
+	float v[3];
+public:
+	GVector3(float x = 0.0f, float y = 0.0f, float z = 0.0f);
+	GVector3(const GVector3& copy);
+	GVector3& operator =(const GVector3& rhs);
+
+	//向量加减
+	GVector3 operator +(const GVector3& rhs) const; // u + v
+	GVector3 operator -(const GVector3& rhs) const; // u - v
+
+	//向量和常量乘除
+	friend GVector3 operator *(const GVector3& lhs, const float& k); // u * k
+	friend GVector3 operator *(const float& k, const GVector3& rhs); // k * u
+	friend GVector3 operator /(const GVector3& lhs, const float& k); // u / k
+
+	//求向量的模和方向
+	friend float norm(const GVector3& v); //求向量大小或模或范数
+	GVector3& normalize(); //求向量方向 单位向量
+
+	//求向量的内积
+	float operator *(const GVector3& rhs) const;
+
+	//向量投影
+	friend GVector3 proj(const GVector3& p, const GVector3& q);
+	friend GVector3 perp(const GVector3& p, const GVector3& q);
+
+	//求向量内积 叉乘
+	GVector3 operator^(const GVector3& rhs) const;
+
+	//完善向量类1
+	GVector3& Set(const float& x, const float& y, const float& z);
+	friend float distance(const GVector3& v, const GVector3 u);
+
+	//完善向量类2
+	GVector3& operator +=(const GVector3& rhs);
+	GVector3& operator -=(const GVector3& rhs);
+	friend ostream& operator<<(ostream& os, const GVector3& v);
+
+	//完善向量类3
+	GVector3& operator *=(const float& k);
+	GVector3& operator /=(const float& k);
+	GVector3& operator ^=(const GVector3& rhs);
+
+	//完善向量类4
+	bool operator ==(const GVector3 rhs) const;
+	bool operator !=(const GVector3 rhs) const;
+
+	//完善向量类5
+	GVector3 operator+() const;
+	GVector3 operator-() const;
+	float& operator [](const int& idx); //下标赋值
+	const float operator [](const int& idx) const;//下标获取分量
+};
+
+class GMatrix;
+class GVector {
+public:
+	//GVector 1~2
+	GVector(int dim = 3);
+	GVector(int dim, double x, ...);
+	GVector(const GVector3& copy);
+	GVector(const GVector& copy);
+	~GVector();
+	
+	//GVector 3
+	GVector& Set(double x, ...);
+	GVector& Set(float *p);
+
+	//GVector 4
+	GVector& operator =(const GVector& rhs);
+	GVector& operator +=(const GVector& rhs);
+	GVector& operator -=(const GVector& rhs);
+	GVector& operator +=(const float& k);
+	GVector& operator -=(const float& k);
+
+	GVector &operator *=(const float &k);
+	GVector	&operator /=(const float &k);
+
+	bool operator ==(const GVector& rhs) const;
+	bool operator !=(const GVector& rhs) const;
+
+	GVector operator +() const;
+	GVector operator -() const;
+
+	GVector operator +(const GVector& rhs) const;
+	GVector operator -(const GVector& rhs) const;
+	float   operator *(const GVector& rhs) const;
+	GVector operator /(const float& k) const;
+
+	float& operator [](const int& idx);
+	const float& operator [](const int& idx) const;
+
+	GVector& Nornalize();
+
+	int GetDim() const;
+
+	friend GVector operator *(const float& k, const GVector& rhs);
+	friend GVector operator *(const GVector& lhs, const float& k);
+	friend GVector operator *(const GMatrix& m, const GVector& v);
+	friend GMatrix operator *(const GVector& v, const GMatrix& m);
+	friend float norm(const GVector& v);
+	friend float distance(const GVector& v, const GVector& u);
+	friend ostream& operator <<(ostream& os, const GVector& v);
+
+	friend class GMatrix;
+private:
+	int n;
+	float* v;
+};
+
+class GMatrix {
+public:
+	GMatrix(int row = 4, int col = 4, float *elem = NULL);
+	GMatrix(const GMatrix& copy);
+	~GMatrix();
+
+	GMatrix& operator =(const GMatrix& rhs);
+
+	GMatrix& operator +=(const GMatrix& rhs);
+	GMatrix& operator -=(const GMatrix& rhs);
+	GMatrix& operator *=(const float& k);
+	GMatrix& operator *=(const GMatrix& rhs);
+	GMatrix& operator /=(const float& k);
+
+	bool operator ==(const GMatrix& rhs) const;
+	bool operator !=(const GMatrix& rhs) const;
+
+	float* operator [](const int idx);
+	const float* operator [](const int idx) const;
+
+	GMatrix operator +() const;
+	GMatrix operator -() const;
+
+	GMatrix operator +(const GMatrix& rhs) const;
+	GMatrix operator -(const GMatrix& rhs) const;
+	GMatrix operator *(const GMatrix& rhs) const;
+	GMatrix operator /(const float& k) const;
+
+	GMatrix& SetTranspose();
+	GMatrix& SetIdentity();
+	GMatrix& SetZeros();
+
+	GMatrix& SetRowVec(const int idx, const GVector& v);
+	GMatrix& SetColVec(const int idx, const GVector& v);
+
+	GVector GetRowVec(const int idx) const;
+	GVector GetColVec(const int idx) const;
+
+	GMatrix& ExchangeRows(const int idx0, const int idx1);
+	GMatrix& ExchangeCols(const int idx0, const int idx1);
+
+	int GetRowNum() const;
+	int GetColNum() const;
+
+	bool IsSquare() const;
+
+	friend GMatrix operator *(const GMatrix& lhs, const float& k);
+	friend GMatrix operator *(const float& k , const GMatrix& rhs);
+
+	friend GVector operator *(const GMatrix& m, const GVector& v);
+	friend GMatrix operator *(const GVector& v, const GMatrix& m);
+	
+	friend ostream& operator <<(ostream& os, const GMatrix& m);
+
+	friend GMatrix RowEchelonForm(const GMatrix& m);
+	friend GMatrix ReduceRowEchelonForm(const GMatrix& m);
+
+	friend float* from_arr(const GMatrix& m);
+
+	friend int Rank(const GMatrix& m);//获取矩阵的秩
+	friend int Nullity(const GMatrix& m);//获取矩阵的零化度
+
+	friend GMatrix Mij(const GMatrix& m, int r, int c); //计算余子式
+	friend float Det(const GMatrix& m);
+
+private:
+	int r;
+	int c;
+	float *m;
+};

main.cpp

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+#include "GMath.h"
+
+int main() {
+
+	float f1[] = { 
+		1.0f, 4.0f, -8.0,
+		0.0f, 2.0f, 9.0,
+		0.0f, 6.0f, 1.0f
+	};
+
+	GMatrix M1(3,3, f1);
+	cout << M1 << endl;
+
+	cout << Det(M1) << endl;
+	
+	return 0;
+}