C++ ON_NurbsCurve::PointAt方法代码示例

bool ON_Arc::GetNurbFormParameterFromRadian(double RadianParameter, double* NurbParameter ) const
{
	if(!IsValid() || NurbParameter==NULL) 
		return false;

  ON_Interval ADomain = DomainRadians();

  double endtol = 10.0*ON_EPSILON*(fabs(ADomain[0]) + fabs(ADomain[1]));

  double del = RadianParameter - ADomain[0];
	if(del <= endtol && del >= -ON_SQRT_EPSILON)
  {
		*NurbParameter=ADomain[0];
		return true;
	} 
  else {
    del = ADomain[1] - RadianParameter;
    if(del <= endtol && del >= -ON_SQRT_EPSILON){
		  *NurbParameter=ADomain[1];
		  return true;
    }
	}

	if( !ADomain.Includes(RadianParameter ) )
		return false;


	ON_NurbsCurve crv;

	if( !GetNurbForm(crv))
		return false;

	//Isolate a bezier that contains the solution
	int cnt = crv.SpanCount();	
	int si =0;	//get span index
	int ki=0;		//knot index
	double ang = ADomain[0];
	ON_3dPoint cp;
	cp = crv.PointAt( crv.Knot(0) ) - Center();
	double x = ON_DotProduct(Plane().Xaxis(),cp);
	double y = ON_DotProduct(Plane().Yaxis(),cp);
	double at = atan2( y, x);	//todo make sure we dont go to far

	for( si=0, ki=0; si<cnt; si++, ki+=crv.KnotMultiplicity(ki) ){
		cp = crv.PointAt( crv.Knot(ki+2)) - Center();
		x = ON_DotProduct(Plane().Xaxis(),cp);
		y = ON_DotProduct(Plane().Yaxis(),cp);
		double at2 = atan2(y,x);
		if(at2>at)
			ang+=(at2-at);
		else
			ang += (2*ON_PI + at2 - at);
		at = at2;
		if( ang>RadianParameter)
			break;
	} 

	// Crash Protection trr#55679
	if( ki+2>= crv.KnotCount())
	{
		 *NurbParameter=ADomain[1];
		 return true;		
	}
	ON_Interval BezDomain(crv.Knot(ki), crv.Knot(ki+2));

	ON_BezierCurve bez;
	if(!crv.ConvertSpanToBezier(ki,bez))
		return false;

 	ON_Xform COC;
	COC.ChangeBasis( ON_Plane(),Plane());   

	
	bez.Transform(COC);	// change coordinates to circles local frame
	double a[3];							// Bez coefficients of a quadratic to solve
	for(int i=0; i<3; i++)
		a[i] = tan(RadianParameter)* bez.CV(i)[0] - bez.CV(i)[1];

	//Solve the Quadratic
	double descrim = (a[1]*a[1]) - a[0]*a[2];
	double squared = a[0]-2*a[1]+a[2];
	double tbez;
	if(fabs(squared)> ON_ZERO_TOLERANCE){
		ON_ASSERT(descrim>=0);
		descrim = sqrt(descrim);
		tbez = (a[0]-a[1] + descrim)/(a[0]-2*a[1]+a[2]);
		if( tbez<0 || tbez>1){
			double tbez2 = (a[0]-a[1]-descrim)/(a[0] - 2*a[1] + a[2]);
			if( fabs(tbez2 - .5)<fabs(tbez-.5) )
				tbez = tbez2;
		}

		ON_ASSERT(tbez>=-ON_ZERO_TOLERANCE && tbez<=1+ON_ZERO_TOLERANCE);
	}
	else{
		// Quadratic degenerates to linear
		tbez = 1.0;
		if(a[0]-a[2])
			tbez = a[0]/(a[0]-a[2]);
	}	
//.........这里部分代码省略.........

bool ON_Arc::GetRadianFromNurbFormParameter(double NurbParameter, double* RadianParameter  ) const
{
	//  TRR#53994.
	// 16-Sept-09  Replaced this code so we dont use LocalClosestPoint.
	// In addition to being slower than neccessary the old method suffered from getting the
	// wrong answer at the seam of a full circle,  This probably only happened with large 
	// coordinates where many digits of precision get lost.

	ON_NurbsCurve crv;
	
	if( !IsValid()|| RadianParameter==NULL) 
		return false;

	ON_Interval dom= Domain();

	if( fabs(NurbParameter- dom[0])<=2.0*ON_EPSILON*fabs(dom[0]))
	{
		*RadianParameter=dom[0];
		return true;
	} 
	else if(  fabs(NurbParameter- dom[1])<=2.0*ON_EPSILON*fabs(dom[1]))
	{
		*RadianParameter=dom[1];
		return true;
	}

	if( !dom.Includes(NurbParameter) )
		return false;

	if( !GetNurbForm(crv) )
		return false;
		
	ON_3dPoint cp;
	cp = crv.PointAt(NurbParameter);
	cp -= Center();

	double x = ON_DotProduct(Plane().Xaxis(), cp);
	double y = ON_DotProduct(Plane().Yaxis(), cp);
	double theta = atan2(y,x);

	theta -= floor( (theta-dom[0])/(2*ON_PI)) * 2* ON_PI;
	if( theta<dom[0] || theta>dom[1])
	{
		// 24-May-2010 GBA 
		// We got outside of the domain because of a numerical error somewhere.
		// The only case that matters is because we are right near an endpoint.
		// So we need to decide which endpoint to return.  (Other possibilities 
		// are that the radius is way to small relative to the coordinates of the center.
		// In this case the circle is just numerical noise around the center anyway.)
		if( NurbParameter< (dom[0]+dom[1])/2.0)
			theta = dom[0];
		else 
			theta = dom[1];
	}


	// Carefully handle the potential discontinuity of this function
	//  when the domain is a full circle
	if(dom.Length()>.99999*2.0*ON_PI)
	{
		double np_theta = dom.NormalizedParameterAt(theta);
		double np_nurb = dom.NormalizedParameterAt(NurbParameter);
		if( np_nurb<.01 && np_theta>.99)
			theta = dom[0];
		else if( np_nurb>.99 && np_theta<.01)
			theta = dom[1];
	}

	*RadianParameter = theta;

//#if defined(ON_DEBUG)
//	double np2;
//	ON_3dPoint AP = PointAt(*RadianParameter);
//
//	GetNurbFormParameterFromRadian( *RadianParameter, &np2);
//	ON_ASSERT(fabs(np2-NurbParameter)<=100* ON_EPSILON*( fabs(NurbParameter) + AP.MaximumCoordinate()+1.0) ); 
//#endif

	return true;
  
}