贝泽尔曲线公式
/**
* a 值参考 "杨辉三角"
*
* 二阶贝泽尔曲线
* N = 3
* a = 1,2,1
* b = 2,1,0
* c = 0,1,2
* 公式：P0 * (1-t)^2 + 2P1 * (1-t) * t + P2 * t^2
*
* 三阶贝泽尔曲线
* N = 4
* a = 1,3,3,1
* b = 3,2,1,0
* c = 0,1,2,3
* 公式: P0 * (1-t)^3 + 3P1 * (1-t)^2 * t + 3P2 * (1-t) * t^2 + P3 * t^3
*
* 四阶贝泽尔曲线
* N = 5
* a = 1,4,6,4,1
* b = 4,3,2,1,0
* c = 0,1,2,3,4
* 公式： P0 * (1-t)^4 + 4P1 * (1-t)^3 * t + 6P2 * (1-t)^2 * t^2 + 4P3 * (1-t) * t^3 + P4 * t^4
*
* 五阶贝泽尔曲线
* N = 6
* a = 1,5,10,10,5,1
* b = 5,4,3,2,1,0
* c = 0,1,2,3,4,5
* 公式：P0 * (1-t)^5 + 5P1 * (1-t)^4 * t + 10P2 * (1-t)^3 * t^2 + 10P3 * (1-t)^2 * t^3 + 5P4 * (1-t) * t^4 + P5 * t^5
*
*/
/**
* 打印杨辉三角
*/
@Test
public void test1() {
final int NMAX = 10;//行数
// allocate triangular array
int[][] odds = new int[NMAX + 1][];
for (int n = 0; n <= NMAX; n++)
odds[n] = new int[n + 1];
// fill triangular array
for (int n = 0; n < odds.length; n++)
for (int k = 0; k < odds[n].length; k++) {
/*
* compute binomial coefficient n*(n-1)*(n-2)*...*(n-k+1)/(1*2*3*...*k)
*/
int lotteryOdds = 1;
for (int i = 1; i <= k; i++)
lotteryOdds = lotteryOdds * (n - i + 1) / i;
odds[n][k] = lotteryOdds;
}
// print triangular array
for (int[] row : odds) {
for (int odd : row){
System.out.printf("%4d", odd);
}
System.out.println();
}
}