#include
#include
using?namespace?std;

struct?Point3f
{
	double?x;
	double?y;
	double?z;
};

struct?Point2f
{
	double?x;
	double?y;
};

bool?ballFit（const?vector?&points?double?¢er_x?double?¢er_y?double?¢er_z?double?&radius）
{
	center_x?=?0.0f;
	center_y?=?0.0f;
	center_z?=?0.0f;
	radius?=?0.0f;
	if?（points.size（）?	{
		return?false;
	}

	double?sum_x?=?0.0f?sum_y?=?0.0f?sum_z?=?0.0f;
	double?sum_x2?=?0.0f?sum_y2?=?0.0f?sum_z2?=?0.0f;
	double?sum_x3?=?0.0f?sum_y3?=?0.0f?sum_z3?=?0.0f;
	double?sum_xy?=?0.0f?sum_x1y2?=?0.0f?sum_x2y1?=?0.0f;
	double?sum_xz?=?0.0f?sum_x1z2?=?0.0f?sum_x2z1?=?0.0f;
	double?sum_yz?=?0.0f?sum_y1z2?=?0.0f?sum_y2z1?=?0.0f;

	int?N?=?points.size（）;
	for?（int?i?=?0;?i?	{
		double?x?=?points[i].x;
		double?y?=?points[i].y;
		double?z?=?points[i].z;
		double?x2?=?x?*?x;
		double?y2?=?y?*?y;
		double?z2?=?z?*?z;
		sum_x?+=?x;
		sum_y?+=?y;
		sum_z?+=?z;

		sum_x2?+=?x2;
		sum_y2?+=?y2;
		sum_z2?+=?z2;

		sum_x3?+=?x2?*?x;
		sum_y3?+=?y2?*?y;
		sum_z3?+=?z2?*?z;

		sum_xy?+=?x?*?y;
		sum_x1y2?+=?x?*?y2;
		sum_x2y1?+=?x2?*?y;

		sum_xz?+=?x?*?z;
		sum_x1z2?+=?x?*?z2;
		sum_x2z1?+=?x2?*?z;

		sum_yz?+=?y?*?z;
		sum_y1z2?+=?y?*?z2;
		sum_y2z1?+=?y2?*?z;

	}

	double?C?D?E?P?G?F?H?J?K;
	double?a?b?c?d;

	C?=?N?*?sum_x2?-?sum_x?*?sum_x;
	D?=?N?*?sum_xy?-?sum_x?*?sum_y;
	P?=?N?*?sum_xz?-?sum_x?*?sum_z;
	E?=?N?*?sum_x3?+?N?*?sum_x1y2?+?N?*?sum_x1z2?-?（sum_x2?+?sum_y2?+?sum_z2）?*?sum_x;

	G?=?N?*?sum_y2?-?sum_y?*?sum_y;
	F?=?N?*?sum_yz?-?sum_y?*?sum_z;
	H?=?N?*?sum_x2y1?+?N?*?sum_y3?+?N?*?sum_y1z2?-?（sum_x2?+?sum_y2?+?sum_z2）?*?sum_y;

	J?=?N?*?sum_z2?-?sum_z?*?sum_z;
	K?=?N?*?sum_x2z1?+?N?*?sum_y2z1?+?N?*?sum_z3?-?（sum_x2?+?sum_y2?+?sum_z2）?*?sum_z;

	double?CC?DD?EE?GG?HH;
	CC?=?C*J?-?P*P;
	DD?=?D*J?-?F*P;
	EE?=?E*J?-?P*K;
	GG?=?G*J?-?F*F;
	HH?=?H*J?-?F*K;

	a?=?（HH?*?DD?-?EE?*?GG）?/?（CC?*?GG?-?DD?*?DD）;
	b?=?（HH?*?CC?-?EE?*?DD）?/?（DD?*?DD?-?GG?*?CC）;
	c?=?0.0f;
	if?（P?!=?0）
	{
		c?=?（-C*a?-?D*b?-?E）?/?P;
	}
	else?if?（F?!=?0）
	{
		c?=?（-D*a?-?G*b?-?H）?/?F;
	}
	else?if?（J?!=?0）
	{
		c?=?（-P*a?-?F*b?-?K）?/?J;
	}
	d?=?-（a?*?sum_x?+?b?*?sum_y?+?c?*?sum_z?+?sum_x2?+?sum_y2?+?sum_z2）?/?N;

	center_x?=?a?/?（-2）;
	center_y?=?b?/?（-2）;
	center_z?=?c?/?（-2）;

	radius?=?sqrt（a?*?a?+?b?*?b?+?c?*?c?-?4?*?d）?/?2;
	return?true;
}

int?main（）
{
	vector?point_3d;
	Point3f?xyz;

	for?（float?i?=?0.5;i?	{
		float?j_nub?=?sqrt（25?-?（i?-?0.5）*（i?-?0.5））;
		for?（float?j?=?1.5;j?		{
			xyz.x?=?i;
			xyz.y?=?j;
			float?z?=?sqrt（25?-?（i?-?0.5）*（i?-?0.5）?-?（j?-?1.5）*（j?-?1.5））?+?2;
			xyz.z?=?z;
			point_3d.push_back（xyz）;
		}
	}

	double?x_3d?y_3d?z_3d?r_3d;
	ballFit（point_3d?x_3d?y_3d?z_3d?r_3d）;
	cout?<	system（“p

?屬性????????????大小?????日期????時(shí)間???名稱
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?????文件???????3022??2017-12-21?11:31??test.cpp

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?????????????????3022????????????????????1