C++3D数学库设计详解 向量篇
C++ 泛型3D向量库编码及设计
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Preface
为了支持光线追踪的学习，决定写一个3D泛型数学库。
我采用的是windows平台以及C++Template技术
我的库文件组织目录如下
–lvgm
—-test
——testVec.cpp
—-type_vec
——lv_vec2.h
——lv_vec3.h
——type_vec.h
——vec_inout.h
—-lv_precision.h
—-lvgm.h
Ready
这一篇，需要您了解C++Template的基本语法
需要您了解向量的运算
该向量库文件解释：
二维向量模板类
三维向量模板类
数据精度设定
本库提供的向量相关的默认输出形式设置文件
该向量库文件暂时没有四元组lv_vec4，我将在之后添加并单独写一篇进行陈述
该向量库能为您提供的功能：
对向量内部数据方便自由地调取和设定
向量的正负
向量的加减乘除
向量的自增自减
向量的索引
向量判等
向量的赋值以及复合运算赋值
向量的范数
向量的范数平方
向量的自身单位化
返回该向量的高精度单位化向量
向量的内积和外积运算（·、×）
向量判空
Design
由于二维和三维的设计相仿，故此处以三维为例进行描述
<1>类型相关
本类中公开定义数据值类型为模板参T，范数精度类型为经外部宏设定的类型——precision， 默认为double
设计问题：一开始我们可能想到在模板类里面利用宏控制数据存储精度，但你可能会遇到问题。例如：
# ifdef HIGHPRECISION //set the high precision using norm_t = long double; # elif(defined LOWPRECISION) //set the low preciion using norm_t = float; # else using norm_t = double; //default precision # endif //set precision
假设我现在有一个int的三维向量，我想要返回一个实数精度（norm_t）的单位化向量，于是我们写了一个成员函数vec3<norm_t> ret_unit()const,我们在主函数中需要创建一个vec3去接收ret_unit的返回值
那么，我们两手一摊，无可奈何你可能这样做：
vec3<？？> normal = intV.ret_unit();
你可能做不到，？？可能是vec3::norm_t 吗，显然不是，vec3是一个模板，只能先将vec3<T>中的T特化。突然觉得，模板类中公开公布了精度类型norm_t，但是却用不上？？
解决方案
综合考量到其他类可能也需要精度设定，所以干脆把这设置部分代码单独出来，然后将norm_t 改名为precision，于是问题就解决了
模板类中只需要提前预处理precision文件即可进行如下简单定义：
using norm_t = precision;
而主函数中也方便多了
vec3<precision> normal = intV.ret_unit();
<2>参数类型
我看过glm数学库的源码有一类函数是这么实现的
template <typename T, precision P> template <typename U> GLM_FUNC_QUALIFIER tvec3<T, P> & tvec3<T, P>::operator+=(tvec3<U, P> const & v) { this->x += static_cast<T>(v.x); this->y += static_cast<T>(v.y); this->z += static_cast<T>(v.z); return *this; }
其实，意思就是它允许+=另外一种类型的向量，然后我都强转到自身类型T之后进行运算
解决方案
个人有一拙见，我是下面这样实现的，如果有什么漏洞请邮件或者评论留言。
我可以通过“重载”static_cast，或者进行一些操作使得vec3模板类能够实现类似内置整型之间的隐式自动类型转换
那么，我就不需要设定多个模板参在内部static_cast了。
好，我们这么做就可以了：
template<typename E> vec3(const vec3<E>& vec); //static_cast
我在定义构造函数的时候支持其他类型的vec3，哪里需要vec3值传递，我就调用它。
<3>对数据进行方便自由的操作
很多数学库貌似可以直接v.x v.y ，很多C-struct设计，但作为C++党，用C++语言写代码，要严格遵守数据隐藏，在不失语言原则的情况下做到最方便。
1）很多库支持 v.x = 3;
于是我定义：
inline T& x() { return _x; }
但我还是重载了常量版本
inline const T& x()const { return _x; }
我希望对内部数据的修改的禁止令可以通过参数来实现，比如：
template<typename T> inline vec3<T> operator/(const vec3<T>& v1, const vec3<T>& v2) { //the operator of / ,example 3 * 5 -> 15 , (1,2,3) * (2,3,4) -> (1/2,2/3,3/4) assert(v2.isnull()); return operator/<T, T> (v1, v2); }
所以，我仅仅去重载v.x()的const版本，而不去禁止x()可修改
2）GLSL中还支持这种骚操作：v.rgb = v.gbr; or v.rg = v1.rg
我看了glm库，它暂时没有实现上述的操作支持
而GLSL库我还没研读
所以，凭着自身粗浅的技术，只能实现获取数据元组，而不能实现修改：
inline vec2<T> xy() { return vec2<T>{_x, _y}; }
<4>运算符设计
按照C++operator普遍的设计原则，依旧是将单目和（复合）赋值运算符重载定义为成员函数，而将双目运算符定义为友元或者外部函数，在本库中采用STL设计原则，定义为命名空间内的类外函数，为了不破坏C++类的封装性
++、–等单目运算符请参见我的另外一篇专门解说运算符重载的文章
此处，我只陈述与vec3类相关的设计细节
关于加减法，从数学角度讲，一个向量加减一个标量是非法的，所以，本库中不支持向量和标量的加减法，对于将每一个元素加同一个值，请用偏移向量进行。
而乘法和除法则支持与标量进行运算，因为一个标量乘以一个向量，只是把向量长度延伸了，在数学上也是合法的。
除此之外，考虑到两个vec3对象进行乘除法，如果this是int其他是另外一个是实数的话，我觉得还是进行精度提升的好，所以有专门的重载，且应用了C++11的自动追踪返回值类型技术
关于%以及%=，从数学角度讲，实数并不支持%运算，只有integer才有，而在图形运算过程中，大多是实数，尽管本库不全应用于图形计算，但是%合法运算在工程项目中占得也并不多，所以，如果需要，请自行将每一个元素进行%，库设计中不会因为极小部分的应用而使库变得臃肿
向量范数以及单位化（标准化）
一个类型设计点：利用用户设定精度类型norm_t定义范数的值类型以及返回的标准化向量模板参。
关于向量单位化，我写了两个，一个是自身单位化，此时遵循本身类型进行，意思就是int进行单位化仍然里面的元素是int。
另一个是返回单位化向量，这个时候是实数向量。
我想陈述的本库相关的设计原则基本完毕。
TEST
测试效果：
△--****************** CONSTRUCTOR TEST ****************** ******* ivec3 test ********* there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows [ 1, -2, 3 ] [ 1, 0, 0 ] there is a ivec2 : _2ivec{1,2}, and a integer 7 to construct a ivec3 as follows the vec2 in front of the integer of 7: [ 1, 2, 7 ] the number of 7 in front of vec2: [ 7, 1, 2 ] ******* fvec3 test ********** there is a fvec3 as fV{ 1.f,2.1f, }, the value of which as follows [ 1, 2.1, 0 ] there is a fvec2 : t{1.2f,}, and a value 3 to construct a ivec3 as follows f2to3 : [ 1.2, 0, 3 ] △--******************* FUNCTIONS TEST ******************** there is a ivec3{1, -2, 3} the operator + or - of ivec3 as follows: + : [ 1, -2, 3 ] - :[ -1, 2, -3 ] ----------------------------------------------------------- there is a ivec3{1, -2, 3} ++ivec3: the val of expression:[ 2, -1, 4 ] the val of ivec3:[ 2, -1, 4 ] ivec3++: the val of expression:[ 1, -2, 3 ] the val of ivec3:[ 2, -1, 4 ] the operator of -- is the same as above ----------------------------------------------------------- the operator[] of ivec3 as follows: the intV[2] is 4 ----------------------------------------------------------- there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows intV is not equ to intV2 the operator = such that: intV2 = intV; the result as follows: intV2 is [ 2, -1, 4 ] intV is equ to intV2 there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows the operator += such that: intV += intV2, the result of which as follows: intV is: [ 3, -1, 4 ] the operator -= such that: intV -= intV2, the result of which as follows: intV is: [ 2, -1, 4 ] the value of intV is to become the original value there are two ivec3s as intV{ 1,-2,3 } and intV2{ 2,1,3 }, the value of which as follows the operator *= such that: intV *= intV2, the result of which as follows: intV is: [ 4, -1, 12 ] the operator /= such that: intV /= intV2, the result of which as follows: intV is: [ 2, -1, 4 ] the value of intV is to become the original value ----------------------------------------------------------- the operator *= (number)such that: intV *= 5, the result of which as follows: intV is: [ 10, -5, 20 ] the operator /= (number) such that: intV /= 5, the result of which as follows: intV is: [ 2, -1, 4 ] the value of intV is to become the original value the operator + 、 -、 * 、/ (ivec3 or number) is the same as above ----------------------------------------------------------- the operator* between ivec3 and fvec3 as follows: there is a ivec3: intV{1,-2,3}, there is a fvec3: fV{1.1f,2.3f,3.8f}, and the result of ivec3*fvec3 as follows: res is: [ 1.1, -4.6, 11.4 ] the result of * is up to the higher precision of both the operator* between ivec3 and float as follows: there is a ivec3: intV{1,-2,3}, there is a float: 3.14, and the result of ivec3*3.14 as follows: res2 is: [ 3, -6, 9 ] the type of ivec3 * float is not fvec3 but ivec3, and the factor is just a factor that shouldn\'t change the vec\'s precision if you need the result\'s type to become fvec3,you should use static_cast<fvec3>(intV) * float res3 is: [ 3.14, -6.28, 9.42 ] the operator/ between different type is the same as above ----------------------------------------------------------- the normal() test as follows: there is a ivec3: intV{1,-2,3} the Norm of intV is: 3.74166 there is a fvec3: fV{ 1.1, 2.3, 3.5} the Norm of fV is: 4.57602 ----------------------------------------------------------- there is a ivec3: intV{0, 4, 3} the unitization of intV is: [ 0, 0.8, 0.6 ] ----------------------------------------------------------- there is a ivec3: intV{1,-2,3}, there is a fvec3: fV{1.1f,2.3f,3.8f}, and the result of ivec3·fvec3 as follows: the dotval is: 7.9 crossVec is: [ -14.5, -0.5, 4.5 ]
test result
#define LOWPRECISION //开启低精度 #define VEC3_OUT //开启vec3输出 #include <lvgm\lvgm.h> #define stds std:: #define enter stds endl << stds endl using lvgm::ivec2; using lvgm::ivec3; using lvgm::fvec3; using lvgm::fvec2; int main() { ivec3 intV{ 1,-2,3 }, intV2{ 1, }, null; //null.self_unitization(); ivec3 b; ivec2 _2ivec{ 1,2 }; fvec3 fV{ 1.f,2.1f, }; stds cout << "△--****************** CONSTRUCTOR TEST ******************" << enter; stds cout << " ******* ivec3 test *********" << stds endl; stds cout << "there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows" << enter; stds cout << intV << enter; stds cout << intV2 << enter; stds cout << "there is a ivec2 : _2ivec{1,2}, and a integer 7 to construct a ivec3 as follows" << enter; ivec3 _2to3{ _2ivec, 7 }; stds cout << "the vec2 in front of the integer of 7: " << _2to3 << enter; _2to3 = ivec3{ 7, _2ivec }; stds cout << "the number of 7 in front of vec2: " << _2to3 << enter << enter; stds cout << " ******* fvec3 test **********" << enter; stds cout << "there is a fvec3 as fV{ 1.f,2.1f, }, the value of which as follows" << enter; stds cout << fV << enter; stds cout << "there is a fvec2 : t{1.2f,}, and a value 3 to construct a ivec3 as follows" << enter; fvec2 t{ 1.2f }; fvec3 f2to3{ t,3 }; stds cout << "f2to3 : " << f2to3 << enter; stds cout << "△--******************* FUNCTIONS TEST ********************" << enter; stds cout << "there is a ivec3{1, -2, 3}" << stds endl; stds cout << "the operator + or - of ivec3 as follows:" << enter; intV = +intV; stds cout << "+ : " << intV << stds endl; intV = -intV; stds cout << "- :" << intV << enter; intV = -intV; stds cout << "-----------------------------------------------------------" << enter; stds cout << "there is a ivec3{1, -2, 3}" << enter; auto re = ++intV; stds cout << "++ivec3: the val of expression:" << re << "\tthe val of ivec3:" << intV << enter; --intV; re = intV++; stds cout << "ivec3++: the val of expression:" << re << "\tthe val of ivec3:" << intV << enter; stds cout << "the operator of -- is the same as above" << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "the operator[] of ivec3 as follows:" << enter; stds cout << "the intV[2] is " << intV[2] << stds endl; //stds cout << "the intV[4] is " << intV[4] << stds endl; stds cout << "-----------------------------------------------------------" << enter; stds cout << "there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows" << enter; if (intV != intV2)stds cout << "intV is not equ to intV2" << enter; stds cout << "the operator = such that: intV2 = intV; the result as follows:" << stds endl; intV2 = intV; stds cout << "intV2 is " << intV2 << stds endl; if (intV2 == intV)stds cout << "intV is equ to intV2" << enter; stds cout << stds endl << "there are two ivec3s as intV{ 1,-2,3 } and intV2{ 1, }, the value of which as follows" << enter; stds cout << "the operator += such that: intV += intV2, the result of which as follows:" << enter; intV2 = { 1, }; intV += intV2; stds cout << "intV is: " << intV << enter; stds cout << "the operator -= such that: intV -= intV2, the result of which as follows:" << enter; intV -= intV2; stds cout << "intV is: " << intV << enter; stds cout << "the value of intV is to become the original value" << enter; stds cout << stds endl << "there are two ivec3s as intV{ 1,-2,3 } and intV2{ 2,1,3 }, the value of which as follows" << enter; stds cout << "the operator *= such that: intV *= intV2, the result of which as follows:" << enter; intV2 = { 2,1,3 }; intV *= intV2; stds cout << "intV is: " << intV << enter; intV /= intV2; stds cout << "the operator /= such that: intV /= intV2, the result of which as follows:" << enter; stds cout << "intV is: " << intV << enter; stds cout << "the value of intV is to become the original value" << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "the operator *= (number)such that: intV *= 5, the result of which as follows:" << enter; intV *= 5; stds cout << "intV is: " << intV << enter; stds cout << "the operator /= (number) such that: intV /= 5, the result of which as follows:" << enter; intV /= 5; stds cout << "intV is: " << intV << enter; stds cout << "the value of intV is to become the original value" << enter; stds cout << "the operator + 、 -、 * 、/ (ivec3 or number) is the same as above" << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "the operator* between ivec3 and fvec3 as follows:" << enter; stds cout << "there is a ivec3: intV{1,-2,3}, there is a fvec3: fV{1.1f,2.3f,3.8f}, and the result of ivec3*fvec3 as follows:" << enter; intV = { 1,-2,3 }; fV = { 1.1f,2.3f,3.8f }; auto res = intV*fV; stds cout << "res is: " << res << enter; stds cout << "the result of * is up to the higher precision of both" << enter; stds cout << "the operator* between ivec3 and float as follows:" << enter; stds cout << "there is a ivec3: intV{1,-2,3}, there is a float: 3.14, and the result of ivec3*3.14 as follows:" << enter; intV = { 1,-2,3 }; auto res2 = intV*3.14; stds cout << "res2 is: " << res2 << enter; stds cout << "the type of ivec3 * float is not fvec3 but ivec3, and the factor is just a factor that shouldn\'t change the vec\'s precision" << stds endl << "if you need the result\'s type to become fvec3,you should use static_cast<fvec3>(intV) * float" << enter; intV = { 1,-2,3 }; auto res3 = (static_cast<fvec3>(intV))*3.14; stds cout << "res3 is: " << res3 << enter; stds cout << "the operator/ between different type is the same as above" << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "the normal() test as follows: " << enter; stds cout << "there is a ivec3: intV{1,-2,3}" << enter; stds cout << "the Norm of intV is: " << intV.normal() << enter; stds cout << "there is a fvec3: fV{ 1.1, 2.3, 3.5}" << enter; stds cout << "the Norm of fV is: " << fV.normal() << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "there is a ivec3: intV{0, 4, 3}" << enter; intV = { 0,4,3 }; lvgm::vec3<lvgm::precision> normal = intV.ret_unitization(); stds cout << "the unitization of intV is: " << normal << enter; stds cout << "-----------------------------------------------------------" << enter; stds cout << "there is a ivec3: intV{1,-2,3}, there is a fvec3: fV{1.1f,2.3f,3.8f}, and the result of ivec3·fvec3 as follows:" << enter; intV = { 1,-2,3 }; fV = { 1.1f,2.3f,3.8f }; lvgm::precision dotval = lvgm::dot(intV, fV); stds cout << "the dotval is: " << dotval << enter; auto crossVec = cross(intV, fV); stds cout << "crossVec is: " << crossVec << enter; }
test code
库文件代码
/// lvgm.h // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] include all of the mymath\'s head files // ----------------------------------------------------- #ifndef LVGM_H #define LVGM_H #include <lvgm\type_vec\type_vec.h> #endif //LVGM_H
lvgm.h
/// precision.h // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] control the precision of data // ----------------------------------------------------- #ifndef LV_PRECISION_H #define LV_PRECISION_H namespace lvgm { # ifdef HIGHPRECISION //set the high precision using precision = long double; # elif(defined LOWPRECISION) //set the low preciion using precision = float; # else using precision = double; //default precision # endif //set precision } //namespace lvgm #endif //LV_PRECISION_H
precision.h
/// myVec2.h // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] the definition of two-dimensional vector // ----------------------------------------------------- #ifndef LV_VEC2_H #define LV_VEC2_H namespace lvgm { template<typename T> class vec2 { public: using value_type = T; using norm_t = precision; public: template<typename E> vec2(const vec2<E>& vec); //static_cast vec2(const T x = T(), const T y = T())noexcept; vec2(const vec2&); ~vec2() { } public: //inline get function inline T& x() { return _x; } inline T& y() { return _y; } inline T& u() { return _x; } inline T& v() { return _y; } inline T& r() { return _x; } inline T& g() { return _y; } inline T& s() { return _x; } inline T& t() { return _y; } inline vec2 xy() { return vec2<T>{_x, _y}; } inline vec2 yx() { return vec2<T>{_y, _x}; } inline vec2 rg() { return vec2<T>{_x, _y}; } inline vec2 gr() { return vec2<T>{_y, _x}; } inline vec2 uv() { return vec2<T>{_x, _y}; } inline vec2 vu() { return vec2<T>{_y, _x}; } inline vec2 st() { return vec2<T>{_x, _y}; } inline vec2 ts() { return vec2<T>{_y, _x}; } inline const T& x()const { return _x; } inline const T& y()const { return _y; } inline const T& u()const { return _x; } inline const T& v()const { return _y; } inline const T& r()const { return _x; } inline const T& g()const { return _y; } inline const T& s()const { return _x; } inline const T& t()const { return _y; } //inline operator function inline const vec2& operator+()const; inline vec2 operator-()const; inline vec2& operator++(); inline vec2& operator--(); inline const vec2 operator++(int); inline const vec2 operator--(int); inline const T& operator[](const int index)const; inline T& operator[](const int index); inline vec2& operator=(const vec2& rhs); inline vec2& operator+=(const vec2& rhs); inline vec2& operator-=(const vec2& rhs); inline vec2& operator*=(const vec2& rhs); inline vec2& operator/=(const vec2& rhs); inline vec2& operator*=(const T factor); inline vec2& operator/=(const T factor); public: //return the Norm of vec2 inline norm_t normal()const; inline norm_t squar()const; //let self become to the unit vector of vec_type inline void self_unitization(); //return a non-integer three-dimensional unit vector [the type is norm_t] inline vec2<precision> ret_unitization()const; inline bool isnull()const; private: T _x, _y; }; //constructor functions template<typename T> vec2<T>::vec2(const T x, const T y)noexcept :_x(x) , _y(y) { } template<typename T> template<typename E> vec2<T>::vec2(const vec2<E>& rhs) :_x(static_cast<T>(rhs.x())) , _y(static_cast<T>(rhs.y())) { } template<typename T> vec2<T>::vec2(const vec2<T>& rhs) : _x(rhs._x) , _y(rhs._y) { } // Binary operator functions [non-mem] template<typename T> inline vec2<T> operator+(const vec2<T>& v1, const vec2<T>& v2) { return vec2<T>(v1[0] + v2[0], v1[1] + v2[1]); } template<typename T> inline vec2<T> operator-(const vec2<T>& v1, const vec2<T>& v2) { //the operator of - ,example (5,4) - (2,2) -> (3,2) return v1 + (-v2); } template<typename A, typename B> inline auto operator*(const vec2<A>& v1, const vec2<B>& v2) { //the operator of * ,example (1.1, 2.1) * (2, 3) -> (2.2, 6.3) using type = decltype(v1[0] * v2[0]); return vec2<type>((type)v1[0] * v2[0], (type)v1[1] * v2[1]); } template<typename T> inline vec2<T> operator*(const vec2<T>& v1, const vec2<T>& v2) { //the operator of * ,example (1,2) * (2,3) -> (2,6) return vec2<T>(v1[0] * v2[0], v1[1] * v2[1]); } template<typename T, typename E> inline vec2<T> operator*(const vec2<T>& v, const E factor) { return vec2<T>(v.x() * factor, v.y() * factor); } template<typename T, typename E> inline vec2<T> operator*(const E factor, const vec2<T>& v) { return vec2<T>(v.x() * factor, v.y() * factor); } template<typename A, typename B> inline auto operator/(const vec2<A>& v1, const vec2<B>& v2) { //the operator of / ,example (1.1, 2.1) * (2, 3) -> (0.55, 0.7) assert(v2.isnull()); using type = decltype(v1[0] / v2[0]); return vec2<type>((type)v1[0] / v2[0], (type)v1[1] / v2[1]); } template<typename T> inline vec2<T> operator/(const vec2<T>& v1, const vec2<T>& v2) { //the operator of / ,example 3 * 5 -> 15 , (1,2) * (2,3) -> (1/2,2/3) assert(v2.isnull()); return operator/<T, T> (v1, v2); } template<typename T, typename E> inline vec2<T> operator/(const vec2<T>& v, const E factor) { assert(factor != 0 && factor != 0.); return vec2<T>(v.x() / factor, v.y() / factor); } template<typename T> inline bool operator==(const vec2<T>& v1, const vec2<T>& v2) { return v1.x() == v2.x() && v1.y() == v2.y(); } template<typename T> inline bool operator!=(const vec2<T>& v1, const vec2<T>& v2) { return !(v1 == v2); } // Unary operator functions [mem] template<typename T> inline const vec2<T>& vec2<T>::operator+() const { //the operator of + ,example 5 -> +5, +(1,-2) -> (1,-2) return *this; } template<typename T> inline vec2<T> vec2<T>::operator-() const { //the operator of - ,example 5 -> -5, -(1,-2) -> (-1,2) return vec2<T>(-_x, -_y); } template<typename T> inline vec2<T>& vec2<T>::operator++() { ++this->_x; ++this->_y; return *this; } template<typename T> inline const vec2<T> vec2<T>::operator++(int) { vec2<T>ori(*this); ++*this; return ori; } template<typename T> inline vec2<T>& vec2<T>::operator--() { --this->_x; --this->_y; return *this; } template<typename T> inline const vec2<T> vec2<T>::operator--(int) { vec2<T>ori(*this); --*this; return ori; } template<typename T> inline const T& vec2<T>::operator[](const int index)const { if (index == 0)return _x; else if (index == 1)return _y; else throw "the index is error"; } template<typename T> inline T& vec2<T>::operator[](const int index) { if (index == 0)return _x; else if (index == 1)return _y; else throw "the index is error"; } // member functions template<typename T> inline vec2<T>& vec2<T>::operator=(const vec2<T>& rhs) { if (this != &rhs) { _x = rhs._x; _y = rhs._y; } return *this; } template<typename T> inline vec2<T>& vec2<T>::operator+=(const vec2& rhs) { this->_x += rhs._x; this->_y += rhs._y; return *this; } template<typename T> inline vec2<T>& vec2<T>::operator-=(const vec2& rhs) { return *this += (-rhs); } template<typename T> inline vec2<T>& vec2<T>::operator/=(const vec2<T>& rhs) { assert(!rhs.isnull()); this->_x /= rhs._x; this->_y /= rhs._y; return *this; } template<typename T> inline vec2<T>& vec2<T>::operator*=(const vec2<T>& rhs) { this->_x *= rhs._x; this->_y *= rhs._y; return *this; } template<typename T> inline vec2<T>& vec2<T>::operator*=(const T factor) { this->_x *= factor; this->_y *= factor; return *this; } template<typename T> inline vec2<T>& vec2<T>::operator/=(const T factor) { assert(factor != 0); this->_x /= factor; this->_y /= factor; return *this; } template<typename T> inline typename vec2<T>::norm_t vec2<T>::normal()const { return sqrt(squar()); } template<typename T> inline typename vec2<T>::norm_t vec2<T>::squar()const { return _x*_x + _y*_y; } template<typename T> inline void vec2<T>::self_unitization() { *this /= normal(); } template<typename T> inline vec2<precision> vec2<T>::ret_unitization()const { norm_t div = normal(); return vec2<norm_t>{ (norm_t)this->_x / div, (norm_t)this->_y / div, (norm_t)this->_z / div }; } template<typename T, typename E> inline auto dot(const vec2<T>& v1, const vec2<E>& v2) //-> decltype(v1.x() * v2.x() + v1.y() * v2.y() {// x1 * x2 + y1 * y2 return v1.x() * v2.x() + v1.y() * v2.y(); } template<typename T, typename E> inline auto cross(const vec2<T> v1, const vec2<E>& v2) {// v1 × v2 return v1[0] * v2[1] - v1[1] * v2[0]; } template<typename T> inline bool vec2<T>::isnull()const { return *this == vec2<T>(); } } //namespace lvgm #endif //LV_VEC2_H
lv_vec2.h
/// myVec3.h // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] the definition of Three-dimensional vector // ----------------------------------------------------- #ifndef LV_VEC3_H #define LV_VEC3_H namespace lvgm { template<typename T> class vec3 { public: using value_type = T; using norm_t = precision; public: template<typename E> vec3(const vec3<E>& vec); //static_cast vec3(const T e1 = T(), const T e2 = T(), const T e3 = T())noexcept; explicit vec3(const vec2<T>& v2, const T e3 = T())noexcept; explicit vec3(const T e1, const vec2<T>& v)noexcept; explicit vec3(const vec3&); ~vec3() { } public: inline T& x() { return _x; } inline T& y() { return _y; } inline T& z() { return _z; } inline T& r() { return _x; } inline T& g() { return _y; } inline T& b() { return _z; } inline vec2<T> xy() { return vec2<T>{_x, _y}; } inline vec2<T> yx() { return vec2<T>{_y, _x}; } inline vec2<T> xz() { return vec2<T>{_x, _z}; } inline vec2<T> zx() { return vec2<T>{_z, _x}; } inline vec2<T> yz() { return vec2<T>{_y, _z}; } inline vec2<T> zy() { return vec2<T>{_z, _y}; } inline vec2<T> rg() { return vec2<T>{_x, _y}; } inline vec2<T> gr() { return vec2<T>{_y, _x}; } inline vec2<T> rb() { return vec2<T>{_x, _z}; } inline vec2<T> br() { return vec2<T>{_z, _x}; } inline vec2<T> gb() { return vec2<T>{_y, _z}; } inline vec2<T> bg() { return vec2<T>{_z, _y}; } inline vec3 rgb() { return vec3{_x, _y, _z}; } inline vec3 rbg() { return vec3{_x, _z, _y}; } inline vec3 gbr() { return vec3{_y, _z, _x}; } inline vec3 grb() { return vec3{_y, _x, _z}; } inline vec3 bgr() { return vec3{_z, _y, _x}; } inline vec3 brg() { return vec3{_z, _x, _y}; } inline const T& x()const { return _x; } inline const T& y()const { return _y; } inline const T& z()const { return _z; } inline const T& r()const { return _x; } inline const T& g()const { return _y; } inline const T& b()const { return _z; } //inline oprator function inline const vec3& operator+() const; inline vec3 operator-()const; inline vec3& operator++(); inline vec3& operator--(); inline const vec3 operator++(int); inline const vec3 operator--(int); inline const T& operator[](const int index)const; inline T& operator[](const int index); inline vec3& operator=(const vec3& rhs); inline vec3& operator+=(const vec3& rhs); inline vec3& operator-=(const vec3& rhs); inline vec3& operator*=(const vec3& rhs); inline vec3& operator/=(const vec3& rhs); inline vec3& operator*=(const T factor); inline vec3& operator/=(const T factor); public: //return the Norm of vec3 inline norm_t normal()const; inline norm_t squar()const; //let self become to the unit vector of vec_type inline void self_unitization(); //return a non-integer three-dimensional unit vector [the type is norm_t] inline vec3<precision> ret_unitization()const; inline bool isnull()const; private: T _x, _y, _z; }; //constructor functions template<typename T> template<typename E> vec3<T>::vec3(const vec3<E>& vec) :_x(static_cast<T>(vec.x())) ,_y(static_cast<T>(vec.y())) ,_z(static_cast<T>(vec.z())) { } template<typename T> vec3<T>::vec3(const T e1, const T e2, const T e3)noexcept :_x{e1} ,_y{e2} ,_z{e3} { } template<typename T> vec3<T>::vec3(const vec2<T>& v, const T e3)noexcept :_x(v.x()) ,_y(v.y()) ,_z(e3) { } template<typename T> vec3<T>::vec3(const T e, const vec2<T>& v)noexcept :_x(e) ,_y(v.x()) ,_z(v.y()) { } template<typename T> vec3<T>::vec3(const vec3<T>& rhs) :_x{rhs._x} ,_y{rhs._y} ,_z{rhs._z} { } // Binary operator functions [non-mem] template<typename T> vec3<T> operator+(const vec3<T>& v1, const vec3<T>& v2) { //the operator of + ,example (5,4,3) + (2,-2,1) -> (7,2,4) return vec3<T>(v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]); } template<typename T> inline vec3<T> operator-(const vec3<T>& v1, const vec3<T>& v2) { //the operator of - ,example (5,4,3) - (2,2,1) -> (3,2,2) return v1 + (-v2); } template<typename A, typename B> inline auto operator*(const vec3<A>& v1, const vec3<B>& v2) { //the operator of * ,example (1.1, 2.1, 3.1) * (2, 3, 4) -> (2.2, 6.3, 12.4) using type = decltype(v1[0] * v2[0]); return vec3<type>((type)v1[0] * v2[0], (type)v1[1] * v2[1], (type)v1[2] * v2[2]); } template<typename T> inline vec3<T> operator*(const vec3<T>& v1, const vec3<T>& v2) { //the operator of * ,example 3 * 5 -> 15 , (1,2,3) * (2,3,4) -> (2,6,12) return vec3<T>(v1[0] * v2[0], v1[1] * v2[1], v1[2] * v2[2]); } template<typename T, typename E> inline vec3<T> operator*(const vec3<T>& v, const E factor) { return vec3<T>(v.x() * factor, v.y() * factor, v.z() * factor); } template<typename T, typename E> inline vec3<T> operator*(const E factor, const vec3<T>& v) { return vec3<T>(v.x() * factor, v.y() * factor, v.z() * factor); } template<typename A, typename B> inline auto operator/(const vec3<A>& v1, const vec3<B>& v2) { //the operator of / ,example (1.1, 2.1, 3.2) * (2, 3, 4) -> (0.55, 0.7, 0.8) assert(v2.isnull()); using type = decltype(v1[0] / v2[0]); return vec3<type>((type)v1[0] / v2[0], (type)v1[1] / v2[1], (type)v1[2] / v2[2]); } template<typename T> inline vec3<T> operator/(const vec3<T>& v1, const vec3<T>& v2) { //the operator of / ,example 3 * 5 -> 15 , (1,2,3) * (2,3,4) -> (1/2,2/3,3/4) assert(v2.isnull()); return operator/<T, T> (v1, v2); } template<typename T, typename E> inline vec3<T> operator/(const vec3<T>& v, const E factor) { assert(factor != 0 && factor != 0.); return vec3<T>(v.x() / factor, v.y() / factor, v.z() / factor); } template<typename T> inline bool operator==(const vec3<T>& v1, const vec3<T>& v2) { return v1.x() == v2.x() && v1.y() == v2.y() && v1.z() == v2.z(); } template<typename T> inline bool operator!=(const vec3<T>& v1, vec3<T>& v2) { return !(v1 == v2); } // Unary operator functions [mem] template<typename T> inline const vec3<T>& vec3<T>::operator+() const { //the operator of + ,example 5 -> +5, +(1,-2,3) -> (1,-2,3) return *this; } template<typename T> inline vec3<T> vec3<T>::operator-() const { //the operator of - ,example 5 -> -5, -(1,-2,3) -> (-1,2,-3) return vec3<T>(-_x, -_y, -_z); } template<typename T> inline vec3<T>& vec3<T>::operator++() { ++this->_x; ++this->_y; ++this->_z; return *this; } template<typename T> inline const vec3<T> vec3<T>::operator++(int) { vec3<T>ori(*this); ++*this; return ori; } template<typename T> inline vec3<T>& vec3<T>::operator--() { --this->_x; --this->_y; --this->_z; return *this; } template<typename T> inline const vec3<T> vec3<T>::operator--(int) { vec3<T>ori(*this); --*this; return ori; } template<typename T> inline const T& vec3<T>::operator[](const int index)const { if (index == 0)return _x; else if (index == 1)return _y; else if (index == 2)return _z; else throw "the index is error"; } template<typename T> inline T& vec3<T>::operator[](const int index) { if (index == 0)return _x; else if (index == 1)return _y; else if (index == 2)return _z; else throw "the index is error"; } // member functions template<typename T> inline vec3<T>& vec3<T>::operator=(const vec3<T>& rhs) { if (this != &rhs) { _x = rhs._x; _y = rhs._y; _z = rhs._z; } return *this; } template<typename T> inline vec3<T>& vec3<T>::operator+=(const vec3& rhs) { this->_x += rhs._x; this->_y += rhs._y; this->_z += rhs._z; return *this; } template<typename T> inline vec3<T>& vec3<T>::operator-=(const vec3& rhs) { this->_x -= rhs._x; this->_y -= rhs._y; this->_z -= rhs._z; return *this; } template<typename T> inline vec3<T>& vec3<T>::operator/=(const vec3<T>& rhs) { assert(!rhs.isnull()); this->_x /= rhs._x; this->_y /= rhs._y; this->_z /= rhs._z; return *this; } template<typename T> inline vec3<T>& vec3<T>::operator*=(const vec3<T>& rhs) { this->_x *= rhs._x; this->_y *= rhs._y; this->_z *= rhs._z; return *this; } template<typename T> inline vec3<T>& vec3<T>::operator*=(const T factor) { this->_x *= factor; this->_y *= factor; this->_z *= factor; return *this; } template<typename T> inline vec3<T>& vec3<T>::operator/=(const T factor) { assert(factor != 0); this->_x /= factor; this->_y /= factor; this->_z /= factor; return *this; } template<typename T> inline typename vec3<T>::norm_t vec3<T>::normal()const { return sqrt(squar()); } template<typename T> inline typename vec3<T>::norm_t vec3<T>::squar()const { return _x*_x + _y*_y + _z*_z; } template<typename T> inline void vec3<T>::self_unitization() { *this /= normal(); } template<typename T> inline vec3<precision> vec3<T>::ret_unitization()const { norm_t div = normal(); return vec3<norm_t>{ (norm_t)this->_x / div,(norm_t)this->_y / div,(norm_t)this->_z / div }; } template<typename T, typename E> inline auto dot(const vec3<T>& v1, const vec3<E>& v2) //-> decltype(v1.x() * v2.x() + v1.y() * v2.y() + v1.z() * v2.z()) {// x1 * x2 + y1 * y2 + z1 * z2 return v1.x() * v2.x() + v1.y() * v2.y() + v1.z() * v2.z(); } template<typename T, typename E> inline auto cross(const vec3<T> v1, const vec3<E>& v2) {// v1 × v2 return vec3<decltype(v1[1] * v2[2] - v1[2] * v2[1])> ( v1[1] * v2[2] - v1[2] * v2[1], v1[2] * v2[0] - v1[0] * v2[2], v1[0] * v2[1] - v1[1] * v2[0] ); } template<typename T> inline bool vec3<T>::isnull()const { return *this == vec3<T>(); } } //namespace lvgm #endif //LV_VEC3_H
lv_vec3.h
/// all vectors are in here // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] all vectors are in here // ----------------------------------------------------- #pragma once #include <iostream> #include <cmath> #include <cassert> #include <lvgm\lv_precision.h> #include "lv_vec2.h" #include "lv_vec3.h" #include "vec_inout.h" namespace lvgm { template<typename T> class vec2; template<typename T> class vec3; template<typename T> class vec4; typedef vec2<bool> bvec2; typedef vec2<char> cvec2; typedef vec2<short> svec2; typedef vec2<int> ivec2; typedef vec2<float> fvec2; typedef vec2<double> dvec2; typedef vec2<long double> ldvec2; typedef vec3<bool> bvec3; typedef vec3<char> cvec3; typedef vec3<short> svec3; typedef vec3<int> ivec3; typedef vec3<float> fvec3; typedef vec3<double> dvec3; typedef vec3<long double> ldvec3; typedef vec4<bool> bvec4; typedef vec4<char> cvec4; typedef vec4<short> svec4; typedef vec4<int> ivec4; typedef vec4<float> fvec4; typedef vec4<double> dvec4; typedef vec4<long double> ldvec4; }
type_vec.h
///vec_inout.h // ----------------------------------------------------- // [author] lv // [ time ] 2018.12 ~ 2018.12 // [brief ] control the iostream of vec // ----------------------------------------------------- #pragma once # ifdef VEC_OUT template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec2<T>& v) { cout << "[ " << v.x() << ", " << v.y() << " ]"; return cout; } template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec3<T>& v) { cout << "[ " << v.x() << ", " << v.y() << ", " << v.z() << " ]"; return cout; } template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec4<T>& v) { cout << "[ " << v.x() << ", " << v.y() << ", " << v.z() << v.w() << " ]"; return cout; } #endif # ifdef VEC2_OUT template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec2<T>& v) { cout << "[ " << v.x() << ", " << v.y() << " ]"; return cout; } #endif # ifdef VEC3_OUT template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec3<T>& v) { cout << "[ " << v.x() << ", " << v.y() << ", " << v.z() << " ]"; return cout; } #endif # ifdef VEC4_OUT template<typename T> std::ostream& operator<<(std::ostream& cout, const lvgm::vec4<T>& v) { cout << "[ " << v.x() << ", " << v.y() << ", " << v.z() << v.w() << " ]"; return cout; } #endif
vec_inout.h
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