逐点比较直线插补和圆弧插补

对于只在第一象限的各种插补方式,都比较的简单。

逐点比较直线插补

由于我们将直线的起点平移到了原点,那么我们所比较的就是当前点和目标直线的斜率,当在直线下方,y++;
当在直线上方,x++;
当在直线上,规定x++;

设(xm,ym)为当前点,(xe,ye)为终点
则Fm=ymxe-xmye可表示点在直线的位置。
Fm=0,点在直线上;
Fm>0,点在直线上方;
Fm<0,点在直线下方;
于是当Fm≥0时,x++;
Fm<0时,y++;

如果每次都计算Fm=ymxe-xmye运算时间比较长,我们可以通过xm=xm+1,ym=ym+1来简化运算;
于是Fm≥0时,Fm-=ye;
Fm<0,Fm+=xe;
由此因为起始点为0,所以Fm=0,然后根据上述规则进行步进。c++代码如下

void go()
{
    int xe, ye;
    int xs, ys;
    queue<int>a;//表示往哪里走
    queue<int>Fm;//标记Fm
    cout << "请输入初始点" << endl;
    cin >> xs >> ys;
    cout << "请输入终止点" << endl;
    cin >> xe >> ye;
    cout << "输入结束,下面开始进行计算" << endl;
    int fm = 0;
    Fm.push(fm);
    int NXY = xe - xs + ye - ys;
    for (int i = 0; i < NXY; i++)
    {
        if (fm >= 0)
        {
            fm -= ye;
            a.push(1);
            Fm.push(fm);
        }
        else
        {
            fm += xe;
            a.push(3);
            Fm.push(fm);
        }
    }
    for (int i = 0; i <= NXY; i++)
    {
        cout << Fm.front() << endl;
        Fm.pop();

    }
    int mx = 100;
    int my = 300;
    int length = 30;
    int flag = 0;
    initgraph(640, 480);
    setlinecolor(BLUE);
    line(mx, my, mx + length * xe, my - length * ye);
    setlinecolor(WHITE);
    line(mx - 90, my, mx + 240, my);
    line(mx, my + 90, mx, my - 240);
    setlinecolor(RED);
    for (int i = 0; i < NXY; i++)
    {
        flag = a.front();
        a.pop();
        jiantou(mx, my, flag, length, i);
    }
    //closegraph();
    _getch();
}

逐点比较圆弧插补
同样的,对于直线而言,比较斜率;那么对于圆弧来说比较的是到圆心的距离。
这里我们都是需要将圆心平移到坐标原点。
这里我们讨论逆圆弧。

假设初始点为xm,ym;终止点为xe,ye。
那么半径R^2 = xe^2 + ye^2
定义Fm=xm^2 + ym^2 - R^2

如果Fm≥0,那么xm–;
Fm<0,ym++;

将上述带到Fm表达式可得:
Fm≥0,Fm+=1-2xm;
Fm<0,Fm+=1+2ym;
c++程序如下:

void go2()
{
    int xe, ye;
    int xs, ys;
    int xm, ym;
    queue<int>a;//表示往哪里走
    queue<int>Fm;//标记Fm
    cout << "请输入初始点" << endl;
    cin >> xs >> ys;
    cout << "请输入终止点" << endl;
    cin >> xe >> ye;
    cout << "输入结束,下面开始进行计算" << endl;
    xm = xs;
    ym = ys;
    int fm = 0;
    Fm.push(fm);
    int NXY = abs(xe - xs) + abs(ye - ys);
    for (int i = 0; i < NXY; i++)
    {
        if (fm >= 0)
        {
            fm += 1 - 2 * xm;
            a.push(2);
            Fm.push(fm);
            xm--;
        }
        else
        {
            fm += 1 + 2 * ym;
            a.push(3);
            Fm.push(fm);
            ym++;
        }
    }
    for (int i = 0; i <= NXY; i++)
    {
        cout << Fm.front() << endl;
        Fm.pop();
    }

    int mx = 300;
    int my = 300;
    int length = 30;
    int flag = 0;
    initgraph(640, 480);
    setlinecolor(BLUE);
    circle(mx, my, length * sqrt(xe * xe + ye * ye));
    setlinecolor(WHITE);
    line(mx - length * sqrt(xe * xe + ye * ye), my, mx + length * sqrt(xe * xe + ye * ye), my);
    line(mx , my+length * sqrt(xe * xe + ye * ye), mx , my-length * sqrt(xe * xe + ye * ye));
    setlinecolor(RED);
    mx += xs * length;
    my -= ys * length;
    for (int i = 0; i < NXY; i++)
    {
        flag = a.front();
        a.pop();
        jiantou(mx, my, flag, length, i);
    }
    _getch();
    closegraph();
}

这里给出画图的走步程序

void jiantou(int& x1, int& y1, int flag, int length, int i)
{
    TCHAR A[5];
    swprintf_s(A, _T("%d"), i+1);
    int x2, y2;
    if (flag == 1)//+x
    {
        x2 = x1 + length;
        y2 = y1;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 - 7, x2, y2);
        line(x2 - 7, y2 + 7, x2, y2);
        outtextxy((x1 + x2) / 2, y1 - 6,A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 2)//-x
    {
        x2 = x1 - length;
        y2 = y1;
        line(x1, y1, x2, y2);
        line(x2 + 7, y2 - 7, x2, y2);
        line(x2 + 7, y2 + 7, x2, y2);
        outtextxy((x1 + x2) / 2, y1 - 6, A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 3)//+y
    {
        x2 = x1;
        y2 = y1 - length;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 + 7, x2, y2);
        line(x2 + 7, y2 + 7, x2, y2);
        outtextxy(x2 + 6, (y1 + y2) / 2, A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 4)//-y
    {
        x2 = x1;
        y2 = y1 + length;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 - 7, x2, y2);
        line(x2 + 7, y2 - 7, x2, y2);
        x1 = x2;
        y1 = y2;
    }
}

结果如下:
直线插补起点(0,0),终点(5,3)
逐点比较直线插补和圆弧插补_第1张图片逆圆弧插补起点(5,0),终点(0,5)
逐点比较直线插补和圆弧插补_第2张图片
全部程序如下

#include
#include                    //头文件为graphics.h
#include 
#include 
#include 
using namespace std;
void go();
void go2();
int main()
{
    //go();
    go2();
}
void jiantou(int& x1, int& y1, int flag, int length, int i)
{
    TCHAR A[5];
    swprintf_s(A, _T("%d"), i+1);
    int x2, y2;
    if (flag == 1)//+x
    {
        x2 = x1 + length;
        y2 = y1;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 - 7, x2, y2);
        line(x2 - 7, y2 + 7, x2, y2);
        outtextxy((x1 + x2) / 2, y1 - 6,A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 2)//-x
    {
        x2 = x1 - length;
        y2 = y1;
        line(x1, y1, x2, y2);
        line(x2 + 7, y2 - 7, x2, y2);
        line(x2 + 7, y2 + 7, x2, y2);
        outtextxy((x1 + x2) / 2, y1 - 6, A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 3)//+y
    {
        x2 = x1;
        y2 = y1 - length;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 + 7, x2, y2);
        line(x2 + 7, y2 + 7, x2, y2);
        outtextxy(x2 + 6, (y1 + y2) / 2, A);
        x1 = x2;
        y1 = y2;
    }
    else if (flag == 4)//-y
    {
        x2 = x1;
        y2 = y1 + length;
        line(x1, y1, x2, y2);
        line(x2 - 7, y2 - 7, x2, y2);
        line(x2 + 7, y2 - 7, x2, y2);
        x1 = x2;
        y1 = y2;
    }
}
void go()
{
    int xe, ye;
    int xs, ys;
    queue<int>a;//表示往哪里走
    queue<int>Fm;//标记Fm
    cout << "请输入初始点" << endl;
    cin >> xs >> ys;
    cout << "请输入终止点" << endl;
    cin >> xe >> ye;
    cout << "输入结束,下面开始进行计算" << endl;
    int fm = 0;
    Fm.push(fm);
    int NXY = xe - xs + ye - ys;
    for (int i = 0; i < NXY; i++)
    {
        if (fm >= 0)
        {
            fm -= ye;
            a.push(1);
            Fm.push(fm);
        }
        else
        {
            fm += xe;
            a.push(3);
            Fm.push(fm);
        }
    }
    for (int i = 0; i <= NXY; i++)
    {
        cout << Fm.front() << endl;
        Fm.pop();

    }
    int mx = 100;
    int my = 300;
    int length = 30;
    int flag = 0;
    initgraph(640, 480);
    setlinecolor(BLUE);
    line(mx, my, mx + length * xe, my - length * ye);
    setlinecolor(WHITE);
    line(mx - 90, my, mx + 240, my);
    line(mx, my + 90, mx, my - 240);
    setlinecolor(RED);
    for (int i = 0; i < NXY; i++)
    {
        flag = a.front();
        a.pop();
        jiantou(mx, my, flag, length, i);
    }
    //closegraph();
    _getch();
}

void go2()
{
    int xe, ye;
    int xs, ys;
    int xm, ym;
    queue<int>a;//表示往哪里走
    queue<int>Fm;//标记Fm
    cout << "请输入初始点" << endl;
    cin >> xs >> ys;
    cout << "请输入终止点" << endl;
    cin >> xe >> ye;
    cout << "输入结束,下面开始进行计算" << endl;
    xm = xs;
    ym = ys;
    int fm = 0;
    Fm.push(fm);
    int NXY = abs(xe - xs) + abs(ye - ys);
    for (int i = 0; i < NXY; i++)
    {
        if (fm >= 0)
        {
            fm += 1 - 2 * xm;
            a.push(2);
            Fm.push(fm);
            xm--;
        }
        else
        {
            fm += 1 + 2 * ym;
            a.push(3);
            Fm.push(fm);
            ym++;
        }
    }
    for (int i = 0; i <= NXY; i++)
    {
        cout << Fm.front() << endl;
        Fm.pop();
    }

    int mx = 300;
    int my = 300;
    int length = 30;
    int flag = 0;
    initgraph(640, 480);
    setlinecolor(BLUE);
    circle(mx, my, length * sqrt(xe * xe + ye * ye));
    setlinecolor(WHITE);
    line(mx - length * sqrt(xe * xe + ye * ye), my, mx + length * sqrt(xe * xe + ye * ye), my);
    line(mx , my+length * sqrt(xe * xe + ye * ye), mx , my-length * sqrt(xe * xe + ye * ye));
    setlinecolor(RED);
    mx += xs * length;
    my -= ys * length;
    for (int i = 0; i < NXY; i++)
    {
        flag = a.front();
        a.pop();
        jiantou(mx, my, flag, length, i);
    }
    _getch();
    closegraph();
}

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