C++实现类，输入三个点坐标，生成一元二次方程（含推理过程）

来源：互联网发布：开挂软件编辑：程序博客网时间：2024/05/24 13:28

今天实现一个类，通过三个点得到一个一元二次方程。

主要实现三阶求逆，然后就可以很方便求得一元二次方程的三个系数。

求得一元二次方程解的原理很简单，推导过程如下图：

主要实现在init()函数里面，类代码如下：

//  Created by cslzy on 16/5/10.//  Copyright © 2016年 CY. All rights reserved.//#include "heads.hpp"//////////////////////////////class parabolaObject ben//////////////////////////////class parabolaObject{private:    float a = 0.0;    float b = 0.0;    float c = 0.0;    bool check(); // check three initial points is ok; check initialization is ok    bool check_is_ok = false;public:    parabolaObject(float , float , float );    parabolaObject(Point2f , Point2f , Point2f );    parabolaObject();    void setParameters(float , float , float );    void init(Point2f, Point2f, Point2f);    float value(float x); // return y, where y = a*x^2 + b*x + c    void test();};void parabolaObject::test(){    Point2f p1(0.0, 0.0);    Point2f p2(127.5, 255.0);    Point2f p3(255.0, 0.0);    cout<<"--!Infor: test() function setdefault points:"<<p1<<p2<<p3<<"--"<<endl;    init(p1, p2, p3);}void parabolaObject::init(Point2f p1, Point2f p2, Point2f p3){//    cout<<"--Infor:input points are:"<<p1<<p2<<p3<<"--"<<endl;    // get 3x3 matrix    float x1 = p1.x;    float x1_2 = x1 * x1;    float y1 = p1.y;        float x2 = p2.x;    float x2_2 = x2 * x2;    float y2 = p2.y;         float x3 = p3.x;    float x3_2 = x3 * x3;    float y3 = p3.y;        // is this matrix reversible?利用行列式来判断一下是否可逆。    float matrix = (x1_2*x2*1 + x2_2*x3*1 + x3_2*x1*1) - (x1_2*x3*1 + x2_2*x1*1 + x3_2*x2*1);    // test//    cout<<"Matrix value:"<<matrix<<endl;    if(matrix==0.0)    {        cout<<"--Error:input point is wrong!--"<<endl;        exit(-1);    }        // get inverse     float a11 =  (x2 - x3)/matrix;    float a12 = -(x2_2 - x3_2)/matrix;    float a13 =  (x2_2*x3 - x3_2*x2)/matrix;    float a21 = -(x1 - x3)/matrix;    float a22 =  (x1_2 - x3_2)/matrix;    float a23 = -(x1_2*x3 - x3_2*x1)/matrix;    float a31 =  (x1 - x2)/matrix;    float a32 = -(x1_2 - x2_2)/matrix;    float a33 =  (x1_2*x2 - x2_2*x1)/matrix;    //下面可以用来验证结果，在线验证网址：http://matrix.reshish.com/inverCalculation.php//    cout<<a11<<" "<<a12<<" "<<a13<<" "<<endl;//    cout<<a21<<" "<<a22<<" "<<a23<<" "<<endl;//    cout<<a31<<" "<<a32<<" "<<a33<<" "<<endl;    // get a, b, c    a = a11*y1 + a21*y2 + a31*y3;    b = a12*y1 + a22*y2 + a32*y3;    c = a13*y1 + a23*y2 + a33*y3;    cout<<"Y = "<<a<<"x^2 + "<<b<<"x + "<<c<<";"<<endl;}parabolaObject::parabolaObject(float x1, float x2, float x3){    a = x1;    b = x2;    c = x3;}parabolaObject::parabolaObject(){};parabolaObject::parabolaObject(Point2f p1, Point2f p2, Point2f p3){    init(p1, p2, p3);}void parabolaObject::setParameters(float x1, float x2, float x3){    a = x1;    b = x2;    c = x3;}float parabolaObject::value(float x){    return a*x*x + b*x + c;}//////////////////////////////class parabolaObject end//////////////////////////////void test_easyMath() // 测试函数{    Point2f p1(0.0, 0.0);    Point2f p2(127.5, 255.0);    Point2f p3(255.0, 0.0);        parabolaObject test_parabola;//    test_parabola.test();    test_parabola.init(p1, p2, p3);    float x = 200.0;    cout<<"x = "<<x<<" y = "<<test_parabola.value(x)<<endl;    cout<<"Input a value:";    cin >> x;    do{        cout<<"x = "<<x<<" y = "<<test_parabola.value(x)<<endl;        cout<<"Input a value:";        cin >> x;    }while (x!=2.0);}

验证逆矩阵：http://matrix.reshish.com/inverCalculation.php

求逆参考：http://mathworld.wolfram.com/MatrixInverse.html

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