int ON_Intersect(
const ON_Line& line,
const ON_Arc& arc,
double* line_t0,
ON_3dPoint& arc_point0,
double* line_t1,
ON_3dPoint& arc_point1
)
{
ON_Circle c = arc;
ON_3dPoint p[2];
double t[2], a[2], s;
ON_BOOL32 b[2] = {false,false};
int i, xcnt = ON_Intersect( line, c, &t[0], p[0], &t[1], p[1] );
if ( xcnt > 0 )
{
// make sure points are on the arc;
ON_Interval arc_domain = arc.DomainRadians();
for ( i = 0; i < xcnt; i++ )
{
b[i] = c.ClosestPointTo(p[i], &a[i]);
if ( b[i] )
{
s = arc_domain.NormalizedParameterAt(a[i]);
if ( s < 0.0 )
{
if ( s >= -ON_SQRT_EPSILON )
{
a[i] = arc_domain[0];
p[i] = c.PointAt(a[i]);
b[i] = line.ClosestPointTo( p[i], &t[i] );
}
else
b[i] = false;
}
else if ( s > 1.0 )
{
if ( s <= 1.0+ON_SQRT_EPSILON )
{
a[i] = arc_domain[1];
p[i] = c.PointAt(a[i]);
b[i] = line.ClosestPointTo( p[i], &t[i] );
}
else
b[i] = false;
}
}
}
if ( !b[0] && !b[1] )
xcnt = 0;
if ( xcnt == 2 )
{
if ( !b[1] )
xcnt = 1;
if ( !b[0] )
{
xcnt = 1;
b[0] = b[1];
t[0] = t[1];
a[0] = a[1];
p[0] = p[1];
b[1] = 0;
}
if ( xcnt == 2 && t[0] == t[1] )
{
xcnt = 1;
b[1] = 0;
ON_3dPoint q = line.PointAt(t[0]);
if ( p[0].DistanceTo(q) > p[1].DistanceTo(q) )
{
a[0] = a[1];
t[0] = t[1];
p[0] = p[1];
}
}
}
if ( xcnt == 1 && !b[0] )
xcnt = 0;
if ( xcnt >= 1 )
{
if ( line_t0 )
*line_t0 = t[0];
arc_point0 = p[0];
}
if ( xcnt == 2 )
{
if ( line_t1 )
*line_t1 = t[1];
arc_point1 = p[1];
}
}
return xcnt;
}
static ON_BOOL32 NurbsCurveArc ( const ON_Arc& arc, int dim, ON_NurbsCurve& nurb )
{
if ( !arc.IsValid() )
return false;
// makes a quadratic nurbs arc
const ON_3dPoint center = arc.Center();
double angle = arc.AngleRadians();
ON_Interval dom = arc.DomainRadians();
const double angle0 = dom[0];
const double angle1 = dom[1];
ON_3dPoint start_point = arc.StartPoint();
//ON_3dPoint mid_point = arc.PointAt(angle0 + 0.5*angle);
ON_3dPoint end_point = arc.IsCircle() ? start_point : arc.EndPoint();
ON_4dPoint CV[9];
double knot[10];
double a, b, c, w, winv;
double *cv;
int j, span_count, cv_count;
a = (0.5 + ON_SQRT_EPSILON)*ON_PI;
if (angle <= a)
span_count = 1;
else if (angle <= 2.0*a)
span_count = 2;
else if (angle <= 3.0*a)
span_count = 4; // TODO - make a 3 span case
else
span_count = 4;
cv_count = 2*span_count + 1;
switch(span_count) {
case 1:
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.50*angle);
CV[2] = end_point;
break;
case 2:
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.25*angle);
CV[2] = arc.PointAt(angle0 + 0.50*angle);
CV[3] = arc.PointAt(angle0 + 0.75*angle);
CV[4] = end_point;
angle *= 0.5;
break;
default: // 4 spans
CV[0] = start_point;
CV[1] = arc.PointAt(angle0 + 0.125*angle);
CV[2] = arc.PointAt(angle0 + 0.250*angle);
CV[3] = arc.PointAt(angle0 + 0.375*angle);
CV[4] = arc.PointAt(angle0 + 0.500*angle);
CV[5] = arc.PointAt(angle0 + 0.625*angle);
CV[6] = arc.PointAt(angle0 + 0.750*angle);
CV[7] = arc.PointAt(angle0 + 0.875*angle);
CV[8] = end_point;
angle *= 0.25;
break;
}
a = cos(0.5*angle);
b = a - 1.0;
//c = (radius > 0.0) ? radius*angle : angle;
c = angle;
span_count *= 2;
knot[0] = knot[1] = angle0; //0.0;
for (j = 1; j < span_count; j += 2) {
CV[j].x += b * center.x;
CV[j].y += b * center.y;
CV[j].z += b * center.z;
CV[j].w = a;
CV[j+1].w = 1.0;
knot[j+1] = knot[j+2] = knot[j-1] + c;
}
knot[cv_count-1] = knot[cv_count] = angle1;
for ( j = 1; j < span_count; j += 2 ) {
w = CV[j].w;
winv = 1.0/w;
a = CV[j].x*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].x = b*w;
}
a = CV[j].y*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].y = b*w;
}
a = CV[j].z*winv;
b = ArcDeFuzz(a);
if ( a != b ) {
CV[j].z = b*w;
}
}
nurb.m_dim = (dim==2) ? 2 : 3;
nurb.m_is_rat = 1;
nurb.m_order = 3;
nurb.m_cv_count = cv_count;
nurb.m_cv_stride = (dim==2 ? 3 : 4);
nurb.ReserveCVCapacity( nurb.m_cv_stride*cv_count );
nurb.ReserveKnotCapacity( cv_count+1 );
for ( j = 0; j < cv_count; j++ ) {
cv = nurb.CV(j);
cv[0] = CV[j].x;
cv[1] = CV[j].y;
if ( dim == 2 ) {
cv[2] = CV[j].w;
}
else {
cv[2] = CV[j].z;
cv[3] = CV[j].w;
}
nurb.m_knot[j] = knot[j];
}
nurb.m_knot[cv_count] = knot[cv_count];
return true;
}