任意次bezier曲线的生成 C++ 代码

//介乘
int factrial(int factrialCount)
{
	int factrialResult = 1;	//声明一个long型的变量
	if (factrialCount == 0)			//0的阶乘为1
	{
		return 1;
	}

	for (int i = 2; i <= factrialCount; i++){	//求大于等于2的数的阶乘
		factrialResult = factrialResult*i;
	}

	return factrialResult;	//返回结果

}


//bezierPoints 贝塞尔曲线点的集合
//bezierControlPoints  贝塞尔曲线控制点的集合
//sectionNum 贝塞尔阶乘的冥次数
//bezierStep 贝塞尔曲线的点的个数
void makeUpBezierLine(float* bezierPoints, float* bezierControlPoints, int sectionNum, int bezierStep)
{


	int sectionNumber = sectionNum - 1;
	float factResArr[1000];//介乘结果的集合
	for (int i = 0; i <= sectionNumber; i++){	//求0到n的阶乘
		factResArr[i] = factrial(i);
	}
	//循环每个点
	for (int i = 0; i <= bezierStep; i++)
	{
		//在bezier曲线上的节点的百分数
		float bezierPercentFractor = float(i) / float(bezierStep);
		if (bezierPercentFractor > 1)
		{
			bezierPercentFractor = 1;
		}

		float tka[1000];
		float otka[1000];
		for (int j = 0; j <= sectionNumber; j++)
		{
			//计算t的j次幂
			tka[j] = (float)pow(bezierPercentFractor, j); 
			//计算1-t的j次幂
			otka[j] = (float)pow(1.0 - bezierPercentFractor, j);
		}

		float xf = 0.0;
		float yf = 0.0;
		float zf = 0.0;
		for (int k = 0; k <= sectionNumber; k++)
		{
			float xs = (factResArr[sectionNumber] / (factResArr[k] * factResArr[sectionNumber - k])) * tka[k] * otka[sectionNumber - k];
			xf = xf + bezierControlPoints[k * 3] * xs;
			yf = yf + bezierControlPoints[k * 3 + 1] * xs;
			zf = zf + bezierControlPoints[k * 3 + 2] * xs;
		}

		bezierPoints[i * 3] = xf;
		bezierPoints[i * 3 + 1] = yf;
		bezierPoints[i * 3 + 2] = zf;

	}


}