C++ ON_Xform::ChangeBasis方法代码示例

int ON_Intersect(
      const ON_Line& line, 
      const ON_Circle& circle,
      double* line_t0,
      ON_3dPoint& circle_point0,
      double* line_t1,
      ON_3dPoint& circle_point1
      )
{
  // transform to coordinate system where equation of circle
  // is x^2 + y^2 = R^2 and solve for line parameter(s).
  ON_Xform xform;
  xform.ChangeBasis( circle.plane, ON_xy_plane );
  xform.ChangeBasis( ON_xy_plane, circle.plane );
  ON_Line L = line;
  L.Transform(xform);
  double r = fabs(circle.radius);
  double tol = r*ON_SQRT_EPSILON;
  if ( tol < ON_ZERO_TOLERANCE )
    tol = ON_ZERO_TOLERANCE;
  int xcnt;
  if (    fabs(L.from.x - L.to.x) <= tol 
       && fabs(L.from.y - L.to.y) <= tol
       && fabs(L.from.z - L.to.z) > tol )
  {
    xcnt = 0;
  }
  else
  {
    xcnt = Intersect2dLineCircle( L.from, L.to, r, tol, line_t0, line_t1 );
    if ( xcnt == 3 )
      xcnt = 1;
  }
  
  if ( xcnt == 0 )
  {
    if ( L.ClosestPointTo( circle.Center(), line_t0 ) )
    {
      xcnt = 1;
      *line_t1 = *line_t0;
    }
  }
  ON_3dPoint line_point1, line_point0 = line.PointAt(*line_t0);
  circle_point0 = circle.ClosestPointTo(line_point0);
  double d1, d0 = line_point0.DistanceTo(circle_point0);
  if ( xcnt == 2 ) 
  {
    line_point1 = line.PointAt(*line_t1);
    circle_point1 = circle.ClosestPointTo(line_point1);
    d1 = line_point1.DistanceTo(circle_point1);
  }
  else
  {
    line_point1 = line_point0;
    circle_point1 = circle_point0;
    d1 = d0;
  }
  if ( xcnt==2 && (d0 > tol && d1 > tol) )
  {
    xcnt = 1;
    if ( d0 <= d1 ) 
    {
      *line_t1 = *line_t0;
      line_point1 = line_point0;
      circle_point1 = circle_point0;
      d1 = d0;
    }
    else
    {
      *line_t0 = *line_t1;
      line_point0 = line_point1;
      circle_point0 = circle_point1;
      d0 = d1;
    }
  }
  if ( xcnt == 1 && d0 > tol )
  {
    // TODO: iterate to closest point
  }
  return xcnt;
}

// Converts from WCS 3d points to 2d points in annotation
bool ON_Annotation::GeWCStoECSXform( ON_Xform& xform ) const
{
  ON_3dVector z = ON_CrossProduct( m_plane.xaxis, m_plane.yaxis );
  return xform.ChangeBasis( ON_origin, ON_xaxis, ON_yaxis, ON_zaxis,
                            m_plane.origin, m_plane.xaxis, m_plane.yaxis, z );
}

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.........