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

 1 #include "stdafx.h"
 2 #include<stdio.h>
 3 #include"graphics.h"
 4 #include<stdlib.h>
 5 #include<math.h>
 6 
 7 //函数声明
 8 void Bezier4(int a[]);//四个控制点画出曲线
 9 void Beziern(int a[], int N);//N个点画出曲线
10 int factorial(int n);//利用递归求出阶乘
11 
12 int main()
13 {
14     int *p, N,gdriver = DETECT, gmove, i;
15 
16     printf("please input the number of point
");
17     scanf_s("%d", &N);
18 
19     p = (int *)malloc(2 * N*sizeof(int));
20 
21     printf("please input the coordinate:
");
22     for (i = 0; i < 2 * N; i += 2)
23         scanf_s("%d%d", &p[i], &p[i + 1]);
24 
25     initgraph(&gdriver, &gmove, "");
26 
27     //画出多边形
28     for (i = 0; i < 2*N-2; i += 2)
29         line(p[i], p[i + 1], p[i + 2], p[i + 3]);
30 
31     Beziern(p, N);
32 
33     system("pause");
34 
35     closegraph();
36 
37     return 0;
38 }

Bezier画线函数

 1 //N个点画出曲线
 2 void Beziern(int a[], int N)
 3 {
 4     double t, X1 = a[0], Y1 = a[1];
 5     int k,i;
 6 
 7     for (t = 0; t <= 1; t += 0.02)
 8     {
 9         putpixel(X1, Y1, YELLOW);
10 
11         X1 = 0, Y1 = 0;
12 
13         for (i=0,k = 0; k<N; i+=2,k ++)
14         {
15             X1 += 1.0*a[i] * factorial(N-1) / factorial(k) / factorial(N-1 - k)*pow(t, k)*pow(1 - t, N-1 - k);//pow函数为求指数的函数
16             Y1 += 1.0*a[i+1] * factorial(N-1) / factorial(k) / factorial(N-1 - k)*pow(t, k)*pow(1 - t, N -1- k);
17         }
18 
19     }
20 }
21 
22 //利用递归求出阶乘
23 inline int factorial(int n)
24 {
25     if (n > 1)
26         return n*factorial(n - 1);
27     else
28         return 1;
29 }

结果：