Vd3A	bezier	(const Vd3& q0,const Vd3& q1,const Vd3& q2,const Vd3& q3,const long div_c)
{
	Vd3A	vd3a ;
	for (long index=0 ; index<=div_c ; index++) {
		double	t	= 1./div_c*index ;
		double	b0	= (1.-t)*(1.-t)*(1.-t) ;
		double	b1	= 3.* t *(1.-t)*(1.-t) ;
		double	b2	= 3.*(1.-t)*t*t ;
		double	b3	= t*t*t ;
		double	px = (b0*q0.x) + (b1*q1.x) + (b2*q2.x) + (b3*q3.x) ;
		double	py = (b0*q0.y) + (b1*q1.y) + (b2*q2.y) + (b3*q3.y) ;
		vd3a.push_back(Vd3(px,py,0)) ;
		}
	return	vd3a ;
	}

Vd3A	b_spline	(const Vd3& q0,const Vd3& q1,const Vd3& q2,const Vd3& q3,const long div_c)
{
	Vd3A	vd3a ;
	for (long index=0 ; index<=div_c ; index++) {
		double	t	= 1./div_c*index ;
		double	n0	= 1./6 * (1.-t)*(1.-t)*(1.-t) ;
		double	n1	= 1./2 * t*t*t - t*t + 2./3 ;
		double	n2	=-1./2 * t*t*t + 1./2 * t*t + 1./2 *t + 1./6 ;
		double	n3	= 1./6 * t*t*t ;
		double	px = (n0*q0.x) + (n1*q1.x) + (n2*q2.x) + (n3*q3.x) ;
		double	py = (n0*q0.y) + (n1*q1.y) + (n2*q2.y) + (n3*q3.y) ;
		vd3a.push_back(Vd3(px,py,0)) ;
		}
	return	vd3a ;
	}


q0 から q3 までを与えての座標の生成部分
{
	#define	div_n	5
	{
		vd3_b = ::bezier(q0,q1,q2,q3,div_n+11) ;
		}
	{
		Vd3A	vd_01  = ::b_spline(q0,q0,q1,q2,div_n) ;
		Vd3A	vd_12  = ::b_spline(q0,q1,q2,q3,div_n) ;
		Vd3A	vd_23  = ::b_spline(q1,q2,q3,q3,div_n) ;
		vd3_n.insert(vd3_n.end(),vd_01.begin(),vd_01.end()) ;
		vd3_n.insert(vd3_n.end(),vd_12.begin(),vd_12.end()) ;
		vd3_n.insert(vd3_n.end(),vd_23.begin(),vd_23.end()) ;
		}
	}

カーディナルスプライン

Vd3A	cardinal	(const Vd3& q0,const Vd3& q1,const Vd3& q2,const Vd3& q3,const long div_c,double av=0.5)
{
	Vd3A	vd3a ;
	for (long index=0 ; index<=div_c ; index++) {
		double	t	= 1./div_c*index ;
		double	c0	= 2. * t*t*t - 3.*t*t + 1. ;
		double	c1	=-2. * t*t*t + 3.*t*t ;
		double	c2	= t*t*t - 2. * t*t + t ;
		double	c3	= t*t*t - t*t ;
		Vd3		d1	= (q2-q0)*av ;
		Vd3		d2	= (q3-q1)*av ;
		double	px = (c0*q1.x) + (c1*q2.x) + (c2*d1.x) + (c3*d2.x) ;
		double	py = (c0*q1.y) + (c1*q2.y) + (c2*d1.y) + (c3*d2.y) ;
		vd3a.push_back(Vd3(px,py,0)) ;
		}
	return	vd3a ;
	}

	{
		Vd3A	vd_01  = ::cardinal(q0,q0,q1,q2,div_n*5) ;
		Vd3A	vd_12  = ::cardinal(q0,q1,q2,q3,div_n*5) ;
		Vd3A	vd_23  = ::cardinal(q1,q2,q3,q3,div_n*5) ;
		vd3_c.insert(vd3_c.end(),vd_01.begin(),vd_01.end()) ;
		vd3_c.insert(vd3_c.end(),vd_12.begin(),vd_12.end()) ;
		vd3_c.insert(vd3_c.end(),vd_23.begin(),vd_23.end()) ;
		}

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