bool ON_Arc::Create( // arc through 3 3d points
const ON_3dPoint& P, // point P
const ON_3dPoint& Q, // point Q
const ON_3dPoint& R // point R
)
{
ON_Circle c;
double a = 0.0;
for (;;)
{
if ( !c.Create(P,Q,R) )
break;
if ( !c.ClosestPointTo( R, &a ) )
break;
if ( !(a > 0.0) )
break;
if ( !Create( c, ON_Interval(0.0,a) ) )
break;
return true;
}
plane = ON_Plane::World_xy;
radius = 0.0;
m_angle.Set(0.0,0.0);
return false;
}
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;
}
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;
}