void SBezier::ClosestPointTo(Vector p, double *t, bool converge) {
int i;
double minDist = VERY_POSITIVE;
*t = 0;
double res = (deg <= 2) ? 7.0 : 20.0;
for(i = 0; i < (int)res; i++) {
double tryt = (i/res);
Vector tryp = PointAt(tryt);
double d = (tryp.Minus(p)).Magnitude();
if(d < minDist) {
*t = tryt;
minDist = d;
}
}
Vector p0;
for(i = 0; i < (converge ? 15 : 5); i++) {
p0 = PointAt(*t);
if(p0.Equals(p, RATPOLY_EPS)) {
return;
}
Vector dp = TangentAt(*t);
Vector pc = p.ClosestPointOnLine(p0, dp);
*t += (pc.Minus(p0)).DivPivoting(dp);
}
if(converge) {
dbp("didn't converge (closest point on bezier curve)");
}
}
bool ON_PolyEdgeCurve::EvSrfTangent(
double t,
bool bIsoDir,
ON_3dPoint& srfpoint,
ON_3dVector& srftangent,
ON_3dVector& srfnormal
) const
{
ON_3dPoint srfpt;
ON_3dVector du, dv, duu, duv, dvv;
bool rc = EvSrfDerivatives(t,srfpoint,du,dv,duu,duv,dvv);
if (rc )
rc = ON_EvNormal( 0, du, dv, duu, duv, dvv, srfnormal ) ? true : false;
if (rc)
{
int segment_index = SegmentIndex(t);
ON_PolyEdgeSegment* seg = SegmentCurve(segment_index);
if ( seg )
{
if ( bIsoDir && seg->IsoType() == ON_Surface::not_iso )
bIsoDir = false;
ON_3dVector crvtangent = TangentAt(t);
ON_3dVector binormal = ON_CrossProduct(crvtangent,srfnormal);
binormal.Unitize();
if ( seg->ReversedTrimDir() )
binormal.Reverse();
// at this point, binormal points "out" and is tangent
// to the surface.
if ( bIsoDir )
{
du.Unitize();
dv.Unitize();
double B_dot_du = binormal*du;
double B_dot_dv = binormal*dv;
if ( fabs(B_dot_dv) > fabs(B_dot_du) )
{
if (B_dot_dv < 0.0)
dv.Reverse();
srftangent = dv;
}
else
{
if (B_dot_du < 0.0)
du.Reverse();
srftangent = du;
}
}
else
srftangent = binormal;
if ( seg && seg->m_face && seg->m_face->m_bRev )
srfnormal.Reverse();
}
else
rc = false;
}
return rc;
}
ON_BOOL32 ON_Ellipse::ClosestPointTo( const ON_3dPoint& point, double* t ) const
{
ON_BOOL32 rc = true;
if ( t ) {
ON_2dPoint uv;
rc = plane.ClosestPointTo( point, &uv.x, &uv.y );
if ( uv.x == 0.0 ) {
if ( uv.y == 0.0 ) {
*t = (radius[0] <= radius[1]) ? 0.0 : 0.5*ON_PI;
return true;
}
if ( uv.y >= radius[1] ) {
*t = 0.5*ON_PI;
return true;
}
if ( uv.y <= -radius[1] ) {
*t = 1.5*ON_PI;
return true;
}
}
else if ( uv.y == 0.0 ) {
if ( uv.x >= radius[0] ) {
*t = 0.0;
return true;
}
if ( uv.x <= -radius[0] ) {
*t = ON_PI;
return true;
}
}
{
// use circluar approximation to get a seed value
double t0, t1;
*t = atan2( uv.y, uv.x );
if ( *t < 0.0 )
{
*t += 2.0*ON_PI;
if ( 2.0*ON_PI <= *t)
{
// == happens when atan2() <= 0.5*ON_EPSILON*2.0*PI
*t = 0.0;
}
}
if ( radius[0] != radius[1] ) {
// set limits for search
if ( uv.x >= 0.0 ) {
if ( uv.y >= 0.0 ) {
// search quadrant I
t0 = 0.0;
t1 = 0.5*ON_PI;
}
else {
// search quadrant IV
t0 = 1.5*ON_PI;
t1 = 2.0*ON_PI;
}
}
else {
if ( uv.y >= 0.0 ) {
// search quadrant II
t0 = 0.5*ON_PI;
t1 = ON_PI;
}
else {
// search quadrant III
t0 = ON_PI;
t1 = 1.5*ON_PI;
}
}
// solve for closest point using Brent's algorithm
{
// 6 October 2003 Dale Lear:
// Fixed several serious bugs here.
// get seed value appropriate for Brent
double p[4], et, d0, d1, dt;
int i;
p[0] = radius[0];
p[1] = radius[1];
p[2] = uv.x;
p[3] = uv.y;
et = *t;
if ( et <= t0 )
et = 0.9*t0 + 0.1*t1;
else if ( et >= t1 )
et = 0.9*t1 + 0.1*t0;
distSqToEllipse( p, t0, &d0, NULL );
distSqToEllipse( p, t1, &d1, NULL );
if ( d0 == 0.0 ) {
*t = (t0 == 2.0*ON_PI) ? 0.0 : t0;
return true;
}
if ( d1 == 0.0 ) {
*t = (t1 == 2.0*ON_PI) ? 0.0 : t1;
return true;
}
if ( d0 > d1 ) {
dt = t0; t0 = t1; t1 = dt;
dt = d0; d0 = d1; d1 = dt;
}
*t = (t0 == 2.0*ON_PI) ? 0.0 : t0;
for ( i = 0; true; i++ ) {
distSqToEllipse( p, et, &dt, NULL );
if ( dt < d0 )
{
*t = (et >= 2.0*ON_PI) ? 0.0 : et;
break;
}
if ( i >= 100 )
{
ON_3dPoint E0 = PointAt(t0);
if ( sqrt(d0) <= ON_ZERO_TOLERANCE
|| sqrt(d0) <= ON_SQRT_EPSILON*E0.DistanceTo(Center())
)
{
// Could not find a seed value for dbrent,
// but t0 is pretty close.
return true;
}
ON_3dVector T = TangentAt(t0);
ON_3dVector V = E0 - point;
if ( V.Unitize() )
{
// Could not find a seed value for dbrent,
// but V and T are orthoganal, so t0 is
// pretty close.
if ( fabs(V*T) <= 0.087155742747658173558064270837474 )
return true;
}
return false; // can't get valid seed - bail out
}
et = (i) ? (0.5*(t0+et)) : 0.5*(t0+t1);
if ( et == t0 )
{
return true;
}
}
rc = ON_FindLocalMinimum( distSqToEllipse, p,
t0, et, t1,
ON_EPSILON, ON_SQRT_EPSILON, 100,
&et );
rc = (rc > 0) ? true : false;
if ( rc )
*t = (et >= 2.0*ON_PI) ? 0.0 : et;
}
}
}
}
return rc;
}
