Bezier画线算法

编译器：VS2013

描述：Bezier画线是利用导数相同拼接曲线，使曲线十分光滑，而不是随意拼接观赏性很差

主函数段

 #include "stdafx.h"
 #include<stdio.h>
 #include"graphics.h"
 #include<stdlib.h>
 #include<math.h>

 //函数声明
 void Bezier4(int a[]);//四个控制点画出曲线
 void Beziern(int a[], int N);//N个点画出曲线
 int factorial(int n);//利用递归求出阶乘

 int main()
 {
     int *p, N,gdriver = DETECT, gmove, i;

     printf("please input the number of point\n");
     scanf_s("%d", &N);

     p = (int *)malloc( * N*sizeof(int));

     printf("please input the coordinate:\n");
     for (i = ; i <  * N; i += )
         scanf_s("%d%d", &p[i], &p[i + ]);

     initgraph(&gdriver, &gmove, "");

     //画出多边形
     for (i = ; i < *N-; i += )
         line(p[i], p[i + ], p[i + ], p[i + ]);

     Beziern(p, N);

     system("pause");

     closegraph();

     return ;
 }

Bezier画线函数

 //N个点画出曲线
 void Beziern(int a[], int N)
 {
     double t, X1 = a[], Y1 = a[];
     int k,i;

     for (t = ; t <= ; t += 0.02)
     {
         putpixel(X1, Y1, YELLOW);

         X1 = , Y1 = ;

         for (i=,k = ; k<N; i+=,k ++)
         {
             X1 += 1.0*a[i] * factorial(N-) / factorial(k) / factorial(N- - k)*pow(t, k)*pow( - t, N- - k);//pow函数为求指数的函数
             Y1 += 1.0*a[i+] * factorial(N-) / factorial(k) / factorial(N- - k)*pow(t, k)*pow( - t, N -- k);
         }

     }
 }

 //利用递归求出阶乘
 inline int factorial(int n)
 {
     if (n > )
         return n*factorial(n - );
     else
         return ;
 }

结果：