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opennurbs_curve.cpp
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opennurbs_curve.cpp
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/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
////////////////////////////////////////////////////////////////
*/
#include "opennurbs.h"
#if !defined(ON_COMPILING_OPENNURBS)
// This check is included in all opennurbs source .c and .cpp files to insure
// ON_COMPILING_OPENNURBS is defined when opennurbs source is compiled.
// When opennurbs source is being compiled, ON_COMPILING_OPENNURBS is defined
// and the opennurbs .h files alter what is declared and how it is declared.
#error ON_COMPILING_OPENNURBS must be defined when compiling opennurbs
#endif
ON_VIRTUAL_OBJECT_IMPLEMENT(ON_Curve,ON_Geometry,"4ED7D4D7-E947-11d3-BFE5-0010830122F0");
ON_Curve::ON_Curve() ON_NOEXCEPT
: ON_Geometry()
{}
ON_Curve::ON_Curve(const ON_Curve& src)
: ON_Geometry(src)
{}
ON_Curve& ON_Curve::operator=(const ON_Curve& src)
{
if ( this != &src )
{
this->DestroyCurveTree();
ON_Geometry::operator=(src);
}
return *this;
}
#if defined(ON_HAS_RVALUEREF)
ON_Curve::ON_Curve( ON_Curve&& src ) ON_NOEXCEPT
: ON_Geometry(std::move(src))
{
}
ON_Curve& ON_Curve::operator=( ON_Curve&& src )
{
if ( this != &src )
{
this->DestroyCurveTree();
ON_Geometry::operator=(std::move(src));
}
return *this;
}
#endif
ON_Curve::~ON_Curve()
{
// Do not call the (virtual) DestroyRuntimeCache or
// DestroyCurveTree (which calls DestroyRuntimeCache()
// because it opens the potential for crashes in a
// "dirty" destructors of classes derived from ON_Curve
// that to not use DestroyRuntimeCache() in their
// destructors and to not set deleted pointers to zero.
}
unsigned int ON_Curve::SizeOf() const
{
unsigned int sz = ON_Geometry::SizeOf();
sz += (sizeof(*this) - sizeof(ON_Geometry));
// Currently, the size of m_ctree is not included
// because this is cached runtime information.
// Applications that care about object size are
// typically storing "inactive" objects for potential
// future use and should call DestroyRuntimeCache(true)
// to remove any runtime cache information.
return sz;
}
ON_Curve* ON_Curve::DuplicateCurve() const
{
// ON_CurveProxy overrides this virtual function.
return Duplicate();
}
ON::object_type ON_Curve::ObjectType() const
{
return ON::curve_object;
}
bool ON_Curve::GetDomain(double* s0,double* s1) const
{
bool rc = false;
ON_Interval d = Domain();
if ( d.IsIncreasing() ) {
if(s0) *s0 = d.Min();
if (s1) *s1 = d.Max();
rc = true;
}
return rc;
}
void ON_Curve::DestroyCurveTree()
{
DestroyRuntimeCache(true);
}
bool ON_Curve::GetTightBoundingBox(
ON_BoundingBox& tight_bbox,
bool bGrowBox,
const ON_Xform* xform
) const
{
if ( bGrowBox && !tight_bbox.IsValid() )
{
bGrowBox = false;
}
if ( !bGrowBox )
{
tight_bbox.Destroy();
}
// In general, putting start and end point in the box lets me avoid
// testing lots of nodes.
ON_3dPoint P = PointAtStart();
if ( xform )
P = (*xform)*P;
tight_bbox.Set( P, bGrowBox );
bGrowBox = true;
P = PointAtEnd();
if ( xform )
P = (*xform)*P;
tight_bbox.Set( P, bGrowBox );
ON_BoundingBox curve_bbox = BoundingBox();
if ( ON_WorldBBoxIsInTightBBox( tight_bbox, curve_bbox, xform ) )
{
// Curve is inside tight_bbox
return true;
}
ON_NurbsCurve N;
if ( 0 == GetNurbForm(N) )
return false;
if ( N.m_order < 2 || N.m_cv_count < N.m_order )
return false;
ON_BezierCurve B;
for ( int span_index = 0; span_index <= N.m_cv_count - N.m_order; span_index++ )
{
if ( !(N.m_knot[span_index + N.m_order-2] < N.m_knot[span_index + N.m_order-1]) )
continue;
if ( !N.ConvertSpanToBezier( span_index, B ) )
continue;
if ( !B.GetTightBoundingBox(tight_bbox,bGrowBox,xform) )
continue;
bGrowBox = true;
}
return (0!=bGrowBox);
}
// overrides virtual ON_Geometry::Transform()
bool ON_Curve::Transform(
const ON_Xform& xform
)
{
if ( !this->ON_Geometry::Transform(xform) )
return false;
this->DestroyCurveTree();
return true;
}
bool ON_Curve::SetDomain( ON_Interval domain )
{
return ( domain.IsIncreasing() && SetDomain( domain[0], domain[1] )) ? true : false;
}
bool ON_Curve::SetDomain( double, double )
{
// this virtual function is overridden by curves that can change their domain.
return false;
}
bool ON_Curve::ChangeClosedCurveSeam( double t )
{
// this virtual function is overridden by curves that can be closed
return false;
}
//virtual
bool ON_Curve::ChangeDimension( int desired_dimension )
{
return (desired_dimension > 0 && desired_dimension == Dimension() );
}
//virtual
bool ON_Curve::GetSpanVectorIndex(
double t, // [IN] t = evaluation parameter
int side, // [IN] side 0 = default, -1 = from below, +1 = from above
int* span_vector_i, // [OUT] span vector index
ON_Interval* span_domain // [OUT] domain of the span containing "t"
) const
{
bool rc = false;
int i;
int span_count = SpanCount();
if ( span_count > 0 ) {
double* span_vector = (double*)onmalloc((span_count+1)*sizeof(span_vector[0]));
rc = GetSpanVector( span_vector );
if (rc) {
i = ON_NurbsSpanIndex( 2, span_count+1, span_vector, t, side, 0 );
if ( i >= 0 && i < span_count ) {
if ( span_vector_i )
*span_vector_i = i;
if ( span_domain )
span_domain->Set( span_vector[i], span_vector[i+1] );
}
else
rc = false;
}
onfree(span_vector);
}
return rc;
}
bool ON_Curve::GetParameterTolerance( // returns tminus < tplus: parameters tminus <= s <= tplus
double t, // t = parameter in domain
double* tminus, // tminus
double* tplus // tplus
) const
{
bool rc = false;
ON_Interval d = Domain();
if ( d.IsIncreasing() )
rc = ON_GetParameterTolerance( d[0], d[1], t, tminus, tplus );
return rc;
}
int ON_Curve::IsPolyline(
ON_SimpleArray<ON_3dPoint>* pline_points, // default = nullptr
ON_SimpleArray<double>* pline_t // default = nullptr
) const
{
// virtual function that is overridden
return 0;
}
bool ON_Curve::IsLinear( double tolerance ) const
{
bool rc = false;
if ( Dimension() == 2 || Dimension() == 3 ) {
const int span_count = SpanCount();
const int span_degree = Degree();
if ( span_count > 0 ) {
ON_SimpleArray<double> s(span_count+1);
s.SetCount(span_count+1);
if ( GetSpanVector( s.Array() ) ) {
if ( tolerance == 0.0 )
tolerance = ON_ZERO_TOLERANCE;
ON_Line line( PointAtStart(), PointAtEnd() );
if ( line.Length() > tolerance ) {
double t, t0, d, delta;
ON_Interval sp;
int n, i, span_index;
rc = true;
t0 = 0; // Domain()[0];
ON_3dPoint P;
for ( span_index = 0; span_index < span_count; span_index++ ) {
sp.Set( s[span_index], s[span_index+1] );
n = 2*span_degree+1;
delta = 1.0/n;
for ( i = (span_index)?0:1; i < n; i++ ) {
P = PointAt( sp.ParameterAt(i*delta) );
if ( !line.ClosestPointTo( P, &t ) )
rc = false;
else if ( t < t0 )
rc = false;
else if (t > 1.0 + ON_SQRT_EPSILON)
rc = false;
d = P.DistanceTo( line.PointAt(t) );
if ( d > tolerance )
rc = false;
t0 = t;
}
}
}
}
}
}
return rc;
}
bool ON_Curve::IsEllipse(
const ON_Plane* plane,
ON_Ellipse* ellipse,
double tolerance
) const
{
// virtual function
ON_Arc arc;
bool rc = IsArc(plane,&arc,tolerance)?true:false;
if (rc && ellipse)
{
ellipse->plane = arc.plane;
ellipse->radius[0] = arc.radius;
ellipse->radius[1] = arc.radius;
}
return rc;
}
bool ON_Curve::IsArcAt(
double t,
const ON_Plane* plane,
ON_Arc* arc,
double tolerance,
double* t0,
double* t1
) const
{
double k, k0, k1;
int hint;
if ( !GetDomain(&k0,&k1) )
return false;
if ( 0 != t0 )
*t0 = k0;
if ( 0 != t1 )
*t1 = k1;
if ( !ON_IsValid(t) )
return false;
if ( ! (t <= k1) )
return false;
if ( IsArc(plane,arc,tolerance) )
return true; // entire curve is an arc
// check sub-segments
hint = 0;
for ( k = k0; k0 <= t && GetNextDiscontinuity(ON::continuity::G2_locus_continuous, k0, k1, &k, &hint); k0 = k )
{
if ( !(k > k0) )
break; // sanity check to prevent infinite loops
if( t <= k )
{
if ( 0 != t0 )
*t0 = k0;
if ( 0 != t1 )
*t1 = k1;
ON_CurveProxy subcrv(this,ON_Interval(k0,k));
if ( subcrv.IsArc(plane,arc,tolerance) )
return true;
// NOTE WELL:
// When t == k, we need to check the next segment as well
// (happens when t is the parameter between a line and arc segment.)
// The "k0 <= t" test is in the for() condition will
// terminate the loop when t < k
}
}
return false;
}
bool ON_Curve::IsArc( const ON_Plane* plane, ON_Arc* arc, double tolerance ) const
{
bool rc = false;
double c0, c, t, delta;
int n, i, span_index;
ON_Plane pln;
ON_Arc a;
ON_3dPoint P, C;
if ( !plane ) {
if ( !IsPlanar(&pln,tolerance) )
return false;
plane = &pln;
}
if ( !arc )
arc = &a;
const int span_count = SpanCount();
const int span_degree = Degree();
if ( span_count < 1 )
return false;
ON_SimpleArray<double> d(span_count+1);
d.SetCount(span_count+1);
if ( !GetSpanVector(d.Array()) )
return false;
const bool bIsClosed = IsClosed();
ON_3dPoint P0 = PointAt( d[0] );
t = bIsClosed ? 0.5*d[0] + 0.5*d[span_count] : d[span_count];
ON_3dPoint P1 = PointAt( 0.5*d[0] + 0.5*t );
ON_3dPoint P2 = PointAt( t );
if ( !arc->Create(P0,P1,P2) )
return false;
if ( bIsClosed )
arc->SetAngleRadians(2.0*ON_PI);
ON_Interval arc_domain = arc->Domain();
ON_3dPoint A0 = arc->PointAt(arc_domain[0]);
ON_3dPoint A1 = arc->PointAt(arc_domain[1]);
ON_3dPoint C0 = PointAtStart();
ON_3dPoint C1 = PointAtEnd();
if ( false == ON_PointsAreCoincident(3,0,&A0.x,&C0.x)
|| false == ON_PointsAreCoincident(3,0,&A1.x,&C1.x)
)
{
return false;
}
if ( tolerance == 0.0 )
tolerance = ON_ZERO_TOLERANCE;
rc = true;
c0 = 0.0;
for ( span_index = 0; rc && span_index < span_count; span_index++ ) {
n = 2*span_degree+1;
if ( n < 4 )
n = 4;
delta = 1.0/n;
for ( i = 0; i < n; i++ ) {
t = i*delta;
P = PointAt( (1.0-t)*d[span_index] + t*d[span_index+1] );
if ( !arc->ClosestPointTo(P,&c) ) {
rc = false;
break;
}
if ( c < c0 ) {
rc = false;
break;
}
C = arc->PointAt(c);
if ( C.DistanceTo(P) > tolerance ) {
rc = 0;
break;
}
c0 = c;
}
}
return rc;
}
bool ON_Curve::IsPlanar( ON_Plane* plane, double tolerance ) const
{
bool rc = false;
const int dim = Dimension();
if ( dim == 2 )
{
// all 2d curves use this code to set the plane
// so that there is consistent behavior.
rc = true;
if ( plane )
{
*plane = ON_xy_plane;
//plane->CreateFromFrame( PointAtStart(), ON_3dVector::XAxis, ON_3dVector::YAxis );
}
}
else if ( IsLinear(tolerance) )
{
rc = true;
if ( plane )
{
ON_Line line( PointAtStart(), PointAtEnd() );
if ( !line.InPlane( *plane, tolerance ) )
line.InPlane( *plane, 0.0 );
}
}
else if ( dim == 3 )
{
const int span_count = SpanCount();
if ( span_count < 1 )
return false;
const int span_degree = Degree();
if ( span_degree < 1 )
return false;
ON_SimpleArray<double> s(span_count+1);
s.SetCount(span_count+1);
if ( !GetSpanVector(s.Array()) )
return false;
ON_Interval d = Domain();
// use initial point, tangent, and evaluated spans to guess a plane
ON_3dPoint pt = PointAt(d.ParameterAt(0.0));
ON_3dVector x = TangentAt(d.ParameterAt(0.0));
if ( x.Length() < 0.95 ) {
return false;
}
int n = (span_degree > 1) ? span_degree+1 : span_degree;
double delta = 1.0/n;
int i, span_index, hint = 0;
ON_3dPoint q;
ON_3dVector y;
bool bNeedY = true;
for ( span_index = 0; span_index < span_count && bNeedY; span_index++ ) {
d.Set(s[span_index],s[span_index+1]);
for ( i = span_index ? 0 : 1; i < n && bNeedY; i++ ) {
if ( !EvPoint( d.ParameterAt(i*delta), q, 0, &hint ) )
return false;
y = q-pt;
y = y - (y*x)*x;
bNeedY = ( y.Length() <= 1.0e-6 );
}
}
if ( bNeedY )
y.PerpendicularTo(x);
ON_Plane pln( pt, x, y );
if ( plane )
*plane = pln;
// test
rc = true;
n = 2*span_degree + 1;
delta = 1.0/n;
double h = pln.plane_equation.ValueAt(PointAtEnd());
if ( fabs(h) > tolerance )
rc = false;
hint = 0;
for ( span_index = 0; rc && span_index < span_count; span_index++ ) {
d.Set(s[span_index],s[span_index+1]);
for ( i = 0; rc && i < n; i++ ) {
if ( !EvPoint( d.ParameterAt(i*delta), q, 0, &hint ) )
rc = false;
else {
h = pln.plane_equation.ValueAt(q);
if ( fabs(h) > tolerance )
rc = false;
}
}
}
}
return rc;
}
bool ON_Curve::IsClosed() const
{
bool rc = false;
double *a, *b, *c, *p, w[12];
const int dim = Dimension();
a = 0;
if ( dim > 1 )
{
ON_Interval d = Domain();
a = (dim>3) ? (double*)onmalloc(dim*4*sizeof(*a)) : w;
b = a+dim;
c = b+dim;
p = c+dim;
if ( Evaluate( d.ParameterAt(0.0), 0, dim, a, 1 )
&& Evaluate( d.ParameterAt(1.0), 0, dim, p,-1 )
)
{
// Note: The point compare test should be the same
// as the one used in ON_PolyCurve::HasGap().
//
if ( ON_PointsAreCoincident( dim, false, a, p ) )
{
if ( Evaluate( d.ParameterAt(1.0/3.0), 0, dim, b, 0 )
&& Evaluate( d.ParameterAt(2.0/3.0), 0, dim, c, 0 )
)
{
if ( false == ON_PointsAreCoincident( dim, false, a, b )
&& false == ON_PointsAreCoincident( dim, false, p, c )
&& false == ON_PointsAreCoincident( dim, false, p, b )
&& false == ON_PointsAreCoincident( dim, false, p, c )
)
{
rc = true;
}
}
}
}
if ( dim > 3 && 0 != a )
onfree(a);
}
return rc;
}
bool ON_Curve::IsPeriodic() const
{
// curve types that may be periodic override this virtual function
return false;
}
bool ON_Curve::GetNextDiscontinuity(
ON::continuity c,
double t0,
double t1,
double* t,
int* hint,
int* dtype,
double cos_angle_tolerance,
double curvature_tolerance
) const
{
// this function must be overridden by curve objects that
// can have parametric discontinuities on the interior of the curve.
bool rc = false;
if ( dtype )
*dtype = 0;
if ( t0 != t1 )
{
bool bTestC0 = false;
bool bTestD1 = false;
bool bTestD2 = false;
bool bTestT = false;
bool bTestK = false;
switch(c)
{
case ON::continuity::C0_locus_continuous:
bTestC0 = true;
break;
case ON::continuity::C1_locus_continuous:
bTestC0 = true;
bTestD1 = true;
break;
case ON::continuity::C2_locus_continuous:
bTestC0 = true;
bTestD1 = true;
bTestD2 = true;
break;
case ON::continuity::G1_locus_continuous:
bTestC0 = true;
bTestT = true;
break;
case ON::continuity::G2_locus_continuous:
bTestC0 = true;
bTestT = true;
bTestK = true;
break;
default:
// other values ignored on purpose.
break;
}
if ( bTestC0 )
{
// 20 March 2003 Dale Lear:
// Have to look for locus discontinuities at ends.
// Must test both ends becuase t0 > t1 is valid input.
// In particular, for ON_CurveProxy::GetNextDiscontinuity()
// to work correctly on reversed "real" curves, the
// t0 > t1 must work right.
ON_Interval domain = Domain();
if ( t0 < domain[1] && t1 >= domain[1] )
t1 = domain[1];
else if ( t0 > domain[0] && t1 <= domain[0] )
t1 = domain[0];
if ( (t0 < domain[1] && t1 >= domain[1]) || (t0 > domain[0] && t1 <= domain[0]) )
{
if ( IsClosed() )
{
if ( bTestD1 || bTestT )
{
// need to check locus continuity at start/end of closed curve.
ON_3dPoint Pa, Pb;
ON_3dVector D1a, D1b, D2a, D2b;
if ( Ev2Der(domain[0],Pa,D1a,D2a,1,nullptr)
&& Ev2Der(domain[1],Pb,D1b,D2b,-1,nullptr) )
{
Pb = Pa; // IsClosed() = true means assume Pa=Pb;
if ( bTestD1 )
{
if ( !(D1a-D1b).IsTiny(D1b.MaximumCoordinate()*ON_SQRT_EPSILON ) )
{
if ( dtype )
*dtype = 1;
*t = t1;
rc = true;
}
else if ( bTestD2 && !(D2a-D2b).IsTiny(D2b.MaximumCoordinate()*ON_SQRT_EPSILON) )
{
if ( dtype )
*dtype = 2;
*t = t1;
rc = true;
}
}
else if ( bTestT )
{
ON_3dVector Ta, Tb, Ka, Kb;
ON_EvCurvature( D1a, D2a, Ta, Ka );
ON_EvCurvature( D1b, D2b, Tb, Kb );
if ( Ta*Tb < cos_angle_tolerance )
{
if ( dtype )
*dtype = 1;
*t = t1;
rc = true;
}
else if ( bTestK )
{
// NOTE:
// This test must exactly match the one
// used in ON_NurbsCurve::GetNextDiscontinuity()
if ( !ON_IsG2CurvatureContinuous( Ka, Kb,
cos_angle_tolerance,
curvature_tolerance
)
)
{
if ( dtype )
*dtype = 2;
*t = t1;
rc = true;
}
}
}
}
}
}
else
{
// open curves are not locus continuous at ends.
if (dtype )
*dtype = 0; // locus C0 discontinuity
*t = t1;
rc = true;
}
}
}
}
return rc;
}
bool ON_Curve::IsContinuous(
ON::continuity desired_continuity,
double t,
int* hint, // default = nullptr,
double point_tolerance, // default=ON_ZERO_TOLERANCE
double d1_tolerance, // default==ON_ZERO_TOLERANCE
double d2_tolerance, // default==ON_ZERO_TOLERANCE
double cos_angle_tolerance, // default==ON_DEFAULT_ANGLE_TOLERANCE_COSINE
double curvature_tolerance // default==ON_SQRT_EPSILON
) const
{
ON_Interval domain = Domain();
if ( !domain.IsIncreasing() )
{
return true;
}
ON_3dPoint Pm, Pp;
ON_3dVector D1m, D1p, D2m, D2p, Tm, Tp, Km, Kp;
bool bIsClosed = false;
// 20 March 2003 Dale Lear
// I added this preable to handle the new
// locus continuity values.
double t0 = t;
double t1 = t;
switch(desired_continuity)
{
case ON::continuity::C0_locus_continuous:
case ON::continuity::C1_locus_continuous:
case ON::continuity::C2_locus_continuous:
case ON::continuity::G1_locus_continuous:
case ON::continuity::G2_locus_continuous:
if ( t <= domain[0] )
{
// By convention - see comments by ON::continuity enum.
return true;
}
if ( t == domain[1] )
{
if ( !IsClosed() )
{
// open curves are not locus continuous at the end parameter
// see comments by ON::continuity enum
return false;
}
else
{
if ( ON::continuity::C0_locus_continuous == desired_continuity )
{
return true;
}
bIsClosed = true;
}
t0 = domain[0];
t1 = domain[1];
}
break;
case ON::continuity::unknown_continuity:
case ON::continuity::C0_continuous:
case ON::continuity::C1_continuous:
case ON::continuity::C2_continuous:
case ON::continuity::G1_continuous:
case ON::continuity::G2_continuous:
case ON::continuity::Cinfinity_continuous:
case ON::continuity::Gsmooth_continuous:
default:
// does not change pre 20 March behavior - just skips the out
// of domain evaluation on parametric queries.
if ( t <= domain[0] || t >= domain[1] )
return true;
break;
}
// at this point, no difference between parametric and locus tests.
desired_continuity = ON::ParametricContinuity((int)desired_continuity);
// this is slow and uses evaluation
// virtual overrides on curve classes that can have multiple spans
// are much faster because the avoid evaluation
switch ( desired_continuity )
{
case ON::continuity::unknown_continuity:
break;
case ON::continuity::C0_continuous:
if ( !EvPoint( t1, Pm, -1, hint ) )
return false;
if ( !EvPoint( t0, Pp, 1, hint ) )
return false;
if ( bIsClosed )
Pm = Pp;
if ( !(Pm-Pp).IsTiny(point_tolerance) )
return false;
break;
case ON::continuity::C1_continuous:
if ( !Ev1Der( t1, Pm, D1m, -1, hint ) )
return false;
if ( !Ev1Der( t0, Pp, D1p, 1, hint ) )
return false;
if ( bIsClosed )
Pm = Pp;
if ( !(Pm-Pp).IsTiny(point_tolerance) || !(D1m-D1p).IsTiny(d1_tolerance) )
return false;
break;
case ON::continuity::G1_continuous:
if ( !EvTangent( t1, Pm, Tm, -1, hint ) )
return false;
if ( !EvTangent( t0, Pp, Tp, 1, hint ) )
return false;
if ( bIsClosed )
Pm = Pp;
if ( !(Pm-Pp).IsTiny(point_tolerance) || Tm*Tp < cos_angle_tolerance )
return false;
break;
case ON::continuity::C2_continuous:
if ( !Ev2Der( t1, Pm, D1m, D2m, -1, hint ) )
return false;
if ( !Ev2Der( t0, Pp, D1p, D2p, 1, hint ) )
return false;
if ( bIsClosed )
Pm = Pp;
if ( !(Pm-Pp).IsTiny(point_tolerance) || !(D1m-D1p).IsTiny(d1_tolerance) || !(D2m-D2p).IsTiny(d2_tolerance) )
return false;
break;
case ON::continuity::G2_continuous:
case ON::continuity::Gsmooth_continuous:
if ( !EvCurvature( t1, Pm, Tm, Km, -1, hint ) )
return false;
if ( !EvCurvature( t0, Pp, Tp, Kp, 1, hint ) )
return false;
if ( !bIsClosed && !(Pm-Pp).IsTiny(point_tolerance) )
return false;
if ( Tm*Tp < cos_angle_tolerance )
return false; // tangent discontinuity
if ( desired_continuity == ON::continuity::Gsmooth_continuous )
{
if ( !ON_IsGsmoothCurvatureContinuous(Km,Kp,cos_angle_tolerance,curvature_tolerance) )
return false;
}
else
{
if ( !ON_IsG2CurvatureContinuous(Km,Kp,cos_angle_tolerance,curvature_tolerance) )
return false;
}
break;
case ON::continuity::C0_locus_continuous:
case ON::continuity::C1_locus_continuous:
case ON::continuity::C2_locus_continuous:
case ON::continuity::G1_locus_continuous:
case ON::continuity::G2_locus_continuous:
case ON::continuity::Cinfinity_continuous:
break;
}
return true;
}
ON_3dPoint ON_Curve::PointAt( double t ) const
{
ON_3dPoint p(0.0,0.0,0.0);
if ( !EvPoint(t,p) )
p = ON_3dPoint::UnsetPoint;
return p;
}
ON_3dPoint ON_Curve::PointAtStart() const
{
return PointAt(Domain().Min());
}
ON_3dPoint ON_Curve::PointAtEnd() const
{
return PointAt(Domain().Max());
}
bool ON_Curve::SetStartPoint(ON_3dPoint start_point)
{
ON_3dPoint S = PointAtStart();
return (S == start_point) ? true : false;
}
bool ON_Curve::SetEndPoint(ON_3dPoint end_point)
{
ON_3dPoint E = PointAtEnd();
return (E == end_point) ? true : false;
}
ON_3dVector ON_Curve::DerivativeAt( double t ) const
{
ON_3dPoint p(0.0,0.0,0.0);
ON_3dVector d(0.0,0.0,0.0);
Ev1Der(t,p,d);
return d;
}
ON_3dVector ON_Curve::TangentAt( double t ) const
{
ON_3dPoint point;
ON_3dVector tangent;
EvTangent( t, point, tangent );
return tangent;
}
ON_3dVector ON_Curve::CurvatureAt( double t ) const
{
ON_3dPoint point;
ON_3dVector tangent, kappa;
EvCurvature( t, point, tangent, kappa );
return kappa;
}
bool ON_Curve::EvTangent(
double t,
ON_3dPoint& point,
ON_3dVector& tangent,
int side,
int* hint
) const
{
ON_3dVector D1, D2;//, K;
tangent = ON_3dVector::ZeroVector;
int rc = Ev1Der( t, point, tangent, side, hint );
if ( rc && !tangent.Unitize() )
{
if ( Ev2Der( t, point, D1, D2, side, hint ) )
{