ON_BoundingBox ON_Arc::BoundingBox() const
{
// TODO - compute tight arc bounding box
// Using these knot[] and cv[] arrays makes this function
// not use any heap memory.
double knot[10];
ON_4dPoint cv[9];
ON_NurbsCurve c;
c.m_knot = knot;
c.m_cv = &cv[0].x;
if ( GetNurbForm(c) )
return c.BoundingBox();
return ON_Circle::BoundingBox();
}
ON_NurbsSurface* ON_Surface::NurbsSurface(
ON_NurbsSurface* pNurbsSurface,
double tolerance,
const ON_Interval* s_subdomain,
const ON_Interval* t_subdomain
) const
{
ON_NurbsSurface* nurbs_surface = pNurbsSurface;
if ( !nurbs_surface )
nurbs_surface = new ON_NurbsSurface();
int rc = GetNurbForm( *nurbs_surface, tolerance );
if ( !rc )
{
if (!pNurbsSurface)
delete nurbs_surface;
nurbs_surface = NULL;
}
return nurbs_surface;
}
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]);
}
if(tbez<0)
tbez=0.0;
else if(tbez>1.0)
tbez=1.0;
//Debug ONLY Code - check the result
// double aa = a[0]*(1-tbez)*(1-tbez) + 2*a[1]*tbez*(1-tbez) + a[2]*tbez*tbez;
// double tantheta= tan(RadianParameter);
// ON_3dPoint bezp;
// bez.Evaluate(tbez, 0, 3, bezp);
// double yx = bezp.y/bezp.x;
*NurbParameter = BezDomain.ParameterAt(tbez);
return true;
}
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;
}
