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opennurbs_arccurve.cpp
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opennurbs_arccurve.cpp
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//
// Copyright (c) 1993-2022 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_OBJECT_IMPLEMENT(ON_ArcCurve,ON_Curve,"CF33BE2A-09B4-11d4-BFFB-0010830122F0");
ON_ArcCurve::ON_ArcCurve() ON_NOEXCEPT
{}
ON_ArcCurve::~ON_ArcCurve()
{}
ON_ArcCurve::ON_ArcCurve( const ON_ArcCurve& src )
: ON_Curve(src)
, m_arc(src.m_arc)
, m_t(src.m_t)
, m_dim(src.m_dim)
{}
ON_ArcCurve& ON_ArcCurve::operator=( const ON_ArcCurve& src )
{
if ( this != &src )
{
ON_Curve::operator=(src);
m_arc = src.m_arc;
m_t = src.m_t;
m_dim = src.m_dim;
}
return *this;
}
#if defined(ON_HAS_RVALUEREF)
ON_ArcCurve::ON_ArcCurve( ON_ArcCurve&& src) ON_NOEXCEPT
: ON_Curve(std::move(src))
, m_arc(std::move(src.m_arc))
, m_t(src.m_t)
, m_dim(src.m_dim)
{
}
ON_ArcCurve& ON_ArcCurve::operator=( ON_ArcCurve&& src)
{
if ( this != &src )
{
ON_Curve::operator=(std::move(src));
m_arc = std::move(src.m_arc);
m_t = src.m_t;
m_dim = src.m_dim;
}
return *this;
}
#endif
ON_ArcCurve::ON_ArcCurve( const ON_Arc& A )
{
m_arc = A;
m_t.m_t[0] = 0.0;
m_t.m_t[1] = m_arc.Length();
if ( m_t.m_t[1] <= 0.0 )
m_t.m_t[1] = 1.0;
m_dim = 3;
}
ON_ArcCurve::ON_ArcCurve( const ON_Circle& circle )
{
ON_ArcCurve::operator=(circle);
}
ON_ArcCurve::ON_ArcCurve( const ON_Arc& A, double t0, double t1 )
{
m_arc = A;
m_t.m_t[0] = t0;
m_t.m_t[1] = t1;
m_dim = 3;
}
ON_ArcCurve::ON_ArcCurve( const ON_Circle& circle, double t0, double t1 )
{
m_arc = circle;
m_t.m_t[0] = t0;
m_t.m_t[1] = t1;
m_dim = 3;
}
unsigned int ON_ArcCurve::SizeOf() const
{
unsigned int sz = ON_Curve::SizeOf();
sz += sizeof(*this) - sizeof(ON_Curve);
return sz;
}
ON__UINT32 ON_ArcCurve::DataCRC(ON__UINT32 current_remainder) const
{
current_remainder = ON_CRC32(current_remainder,sizeof(m_arc),&m_arc);
current_remainder = ON_CRC32(current_remainder,sizeof(m_t),&m_t);
current_remainder = ON_CRC32(current_remainder,sizeof(m_dim),&m_dim);
return current_remainder;
}
ON_ArcCurve& ON_ArcCurve::operator=( const ON_Arc& A )
{
m_arc = A;
m_t.m_t[0] = 0.0;
m_t.m_t[1] = A.Length();
if ( m_t.m_t[1] == 0.0 )
m_t.m_t[1] = 1.0;
m_dim = 3;
return *this;
}
ON_ArcCurve& ON_ArcCurve::operator=(const ON_Circle& circle)
{
m_arc = circle;
m_t.m_t[0] = 0.0;
m_t.m_t[1] = m_arc.Length();
if ( m_t.m_t[1] <= 0.0 )
m_t.m_t[1] = 1.0;
m_dim = 3;
return *this;
}
int ON_ArcCurve::Dimension() const
{
return m_dim;
}
bool ON_ArcCurve::GetBBox( // returns true if successful
double* boxmin, // minimum
double* boxmax, // maximum
bool bGrowBox
) const
{
bool rc = m_arc.IsValid();
if (rc) {
ON_BoundingBox bbox = m_arc.BoundingBox();
if ( bGrowBox ) {
if ( boxmin[0] > bbox.m_min.x ) boxmin[0] = bbox.m_min.x;
if ( boxmin[1] > bbox.m_min.y ) boxmin[1] = bbox.m_min.y;
if ( boxmax[0] < bbox.m_max.x ) boxmax[0] = bbox.m_max.x;
if ( boxmax[1] < bbox.m_max.y ) boxmax[1] = bbox.m_max.y;
if ( m_dim > 2 ) {
if ( boxmin[2] > bbox.m_min.z ) boxmin[2] = bbox.m_min.z;
if ( boxmax[2] < bbox.m_max.z ) boxmax[2] = bbox.m_max.z;
}
}
else {
boxmin[0] = bbox.m_min.x;
boxmin[1] = bbox.m_min.y;
boxmax[0] = bbox.m_max.x;
boxmax[1] = bbox.m_max.y;
if ( m_dim > 2 ) {
boxmin[2] = bbox.m_min.z;
boxmax[2] = bbox.m_max.z;
}
}
}
return rc;
}
bool
ON_ArcCurve::Transform( const ON_Xform& xform )
{
TransformUserData(xform);
DestroyCurveTree();
return m_arc.Transform( xform );
}
bool ON_ArcCurve::IsValid( ON_TextLog* text_log ) const
{
if ( !m_t.IsIncreasing() )
{
if ( 0 != text_log )
text_log->Print("ON_ArcCurve - m_t=(%g,%g) - it should be an increasing interval.\n",m_t[0],m_t[1]);
return false;
}
if ( !m_arc.IsValid() )
{
if ( 0 != text_log )
text_log->Print("ON_ArcCurve m_arc is not valid\n");
return false;
}
// 7-May-21. GBA. Added conditions to define a degenerate ON_ArcCurve
// Note: these conditions should be enforced by Trim and Split
if (m_arc.radius < ON_ZERO_TOLERANCE )
{
if (0 != text_log)
text_log->Print("ON_ArcCurve m_arc.radius < ON_ZERO_TOLERANCE\n");
return false;
}
ON_3dPoint S = PointAtStart();
ON_3dPoint E = PointAtEnd();
if( S.IsCoincident(E) != IsCircle())
{
if (0 != text_log)
{
if (IsCircle() )
text_log->Print("ON_ArcCurve !Start.IsCoincident(End) an a circle\n");
else
text_log->Print("ON_ArcCurve Start.IsCoincident(End) on open arc curve\n");
}
return false;
}
return true;
}
void ON_ArcCurve::Dump( ON_TextLog& dump ) const
{
dump.Print( "ON_ArcCurve: domain = [%g,%g]\n",m_t[0],m_t[1]);
dump.PushIndent();
dump.Print( "center = ");
dump.Print( m_arc.plane.origin );
dump.Print( "\nradius = %g\n",m_arc.radius);
dump.Print( "length = %g\n",m_arc.Length());
ON_3dPoint start = PointAtStart();
ON_3dPoint end = PointAtEnd();
dump.Print( "start = "); dump.Print(start);
dump.Print( "\nend = "); dump.Print(end); dump.Print("\n");
dump.PopIndent();
}
bool ON_ArcCurve::Write(
ON_BinaryArchive& file // open binary file
) const
{
bool rc = file.Write3dmChunkVersion(1,0);
if (rc)
{
rc = file.WriteArc( m_arc );
if (rc) rc = file.WriteInterval( m_t );
if (rc) rc = file.WriteInt(m_dim);
}
return rc;
}
bool ON_ArcCurve::Read(
ON_BinaryArchive& file // open binary file
)
{
int major_version = 0;
int minor_version = 0;
bool rc = file.Read3dmChunkVersion(&major_version,&minor_version);
if (rc)
{
if (major_version==1)
{
// common to all 1.x versions
rc = file.ReadArc( m_arc );
if (rc)
rc = file.ReadInterval( m_t );
if (rc)
rc = file.ReadInt(&m_dim);
if ( m_dim != 2 && m_dim != 3 )
m_dim = 3;
}
else
rc = 0;
}
return rc;
}
bool ON_ArcCurve::SetDomain( double t0, double t1 )
{
bool rc = false;
if ( t0 < t1 )
{
m_t.Set(t0,t1);
rc = true;
}
DestroyCurveTree();
return rc;
}
bool ON_ArcCurve::ChangeDimension( int desired_dimension )
{
bool rc = (desired_dimension>=2 && desired_dimension<=3);
if ( rc && m_dim != desired_dimension )
{
DestroyCurveTree();
if ( desired_dimension == 2 )
m_dim = 2;
else
m_dim = 3;
}
return rc;
}
ON_Interval ON_ArcCurve::Domain() const
{
return m_t;
}
bool ON_ArcCurve::ChangeClosedCurveSeam(
double t ){
bool rc = false;
if( IsCircle() ){
double angle_delta = m_t.NormalizedParameterAt(t);
angle_delta*= 2*ON_PI;
m_arc.Rotate(angle_delta, m_arc.plane.Normal());
m_t = ON_Interval( t, m_t[1] + t - m_t[0]);
rc = true;
}
return rc;
}
int ON_ArcCurve::SpanCount() const
{
return 1;
}
bool ON_ArcCurve::GetSpanVector( double* s ) const
{
s[0] = m_t[0];
s[1] = m_t[1];
return m_t.IsIncreasing();
}
int ON_ArcCurve::Degree() const
{
return 2;
}
bool
ON_ArcCurve::IsLinear( // true if curve locus is a line segment
double // tolerance - formal parameter intentionally ignored in this virtual function
) const
{
return false; // GBA 23 May 23. This just seems wrong. Maybe we should change this very early in WIP and see if anyone notices.
// I think this is the correct implementation
// return m_arc.IsLinear(tolerance);
}
bool
ON_ArcCurve::IsArc( // true if curve locus in an arc or circle
const ON_Plane* plane, // if not nullptr, test is performed in this plane
ON_Arc* arc, // if not nullptr and true is returned, then arc
// arc parameters are filled in
double tolerance // tolerance to use when checking linearity
) const
{
bool rc = (plane) ? IsInPlane(*plane,tolerance) : true;
if (arc)
*arc = m_arc;
if (rc)
rc = IsValid();
return rc;
}
bool
ON_ArcCurve::IsPlanar(
ON_Plane* plane, // if not nullptr and true is returned, then plane parameters
// are filled in
double tolerance // tolerance to use when checking linearity
) const
{
if ( m_dim == 2 )
{
return ON_Curve::IsPlanar(plane,tolerance);
}
if ( plane )
*plane = m_arc.plane;
return true;
}
bool
ON_ArcCurve::IsInPlane(
const ON_Plane& plane, // plane to test
double tolerance // tolerance to use when checking linearity
) const
{
return m_arc.IsInPlane( plane, tolerance );
}
bool
ON_ArcCurve::IsClosed() const
{
return m_arc.IsCircle();
}
bool
ON_ArcCurve::IsPeriodic() const
{
return m_arc.IsCircle();
}
bool
ON_ArcCurve::Reverse()
{
bool rc = m_arc.Reverse();
if (rc)
{
m_t.Reverse();
DestroyCurveTree();
}
return true;
}
bool ON_ArcCurve::SetStartPoint(ON_3dPoint start_point)
{
if (ON_Curve::SetStartPoint(start_point))
return true;
if (IsCircle())
return false;
bool rc = false;
if ( m_dim == 3 || start_point.z == 0.0 )
{
ON_3dPoint P;
ON_3dVector T;
double t = Domain()[1];
Ev1Der( t, P, T );
T = -T;
ON_Arc a;
rc = a.Create( P, T, start_point );
if ( rc )
{
a.Reverse();
m_arc = a;
}
else {
ON_3dPoint end_point = PointAt(Domain()[1]);
if (end_point.DistanceTo(start_point) < ON_ZERO_TOLERANCE*m_arc.Radius()){
//make arc into circle
m_arc.plane.xaxis = end_point - m_arc.Center();
m_arc.plane.xaxis.Unitize();
m_arc.plane.yaxis = ON_CrossProduct(m_arc.Normal(), m_arc.plane.xaxis);
m_arc.plane.yaxis.Unitize();
m_arc.SetAngleRadians(2.0*ON_PI);
rc = true;
}
}
}
DestroyCurveTree();
return rc;
}
bool ON_ArcCurve::SetEndPoint(ON_3dPoint end_point)
{
if (ON_Curve::SetEndPoint(end_point))
return true;
if (IsCircle())
return false;
bool rc = false;
if ( m_dim == 3 || end_point.z == 0.0 )
{
ON_3dPoint P;
ON_3dVector T;
double t = Domain()[0];
Ev1Der( t, P, T );
ON_Arc a;
rc = a.Create( P, T, end_point );
if ( rc )
{
m_arc = a;
}
else {
ON_3dPoint start_point = PointAt(Domain()[0]);
if (end_point.DistanceTo(start_point) < ON_ZERO_TOLERANCE*m_arc.Radius()){
//make arc into circle
m_arc.plane.xaxis = start_point - m_arc.Center();
m_arc.plane.xaxis.Unitize();
m_arc.plane.yaxis = ON_CrossProduct(m_arc.Normal(), m_arc.plane.xaxis);
m_arc.plane.yaxis.Unitize();
m_arc.SetAngleRadians(2.0*ON_PI);
rc = true;
}
}
}
DestroyCurveTree();
return rc;
}
bool ON_ArcCurve::Evaluate( // returns false if unable to evaluate
double t, // evaluation parameter
int der_count, // number of derivatives (>=0)
int v_stride, // v[] array stride (>=Dimension())
double* v, // v[] array of length stride*(ndir+1)
int, // side - formal parameter intentionally ignored in this virtual function
int* // hint - formal parameter intentionally ignored in this virtual function
) const
{
// The issue here is that ON_PI is a rational approximation of the "real" pi.
// Ideally sin(N*pi) would be zero and the bugs of July 2012 and RH-26341 that are
// discussed below would not exist. When N is large, N*ON_PI isn't close by any
// measure to a multiple of "real" pi. But, for smallish N that we are likely to
// encounter in practice, we want sin(N*ON_PI) to be zero in this evaluator.
// The multiple 4 is used because we felt is was reasonable for somebody to want
// this evaluator to apply the same special case handing to a and a + 2.0*ON_PI
// when fabs(a) <= 2.0*ON_PI.
static const double sin_of_pi = fabs(sin(4.0*ON_PI)) > fabs(sin(ON_PI))
? fabs(sin(4.0*ON_PI)) // the fabs(sin(4.0*ON_PI)) values is used in the tests we performed.
: fabs(sin(ON_PI));
static const double cos_of_pi_over_2 = fabs(cos(4.5*ON_PI)) > fabs(cos(0.5*ON_PI))
? fabs(cos(4.5*ON_PI)) // the fabs(cos(4.5*ON_PI)) values is used in the tests we performed.
: fabs(cos(0.5*ON_PI));
ON_3dVector d;
bool rc = false;
if ( m_t[0] < m_t[1] )
{
double rat = m_arc.DomainRadians().Length()/m_t.Length();
double scale = 1.0;
double a = m_arc.DomainRadians().ParameterAt( m_t.NormalizedParameterAt(t) );
// 12 July 2012 Dale Lear
// When evaluating circles centered at the origin
// a = ON_PI = 3.1415926535897931, c = -1.0 and s = 1.2246467991473532e-016.
// As a result the y coordinates that "should" be zero comes out as
// radius*1.2246467991473532e-016. When the radius is large (1.0e9 in the
// bug I was looking at), the y coordinate is big enough to cause other problems.
// When I added this comment I failed to insert the bug number, so I cannot
// provide more details as of May 6, 2014 and the changes for bug RH-26341.
double c = cos(a);
double s = sin(a);
// This test turned out to be too crude. The bug RH-26341
// is one example. The issue is that the trig function with the
// largest derivative has more precise sensitivity to changes in
// angle and in order to get as precise an evaluation as possible,
// it is important to allow non-zero values of one trig function
// even when the other is being rounded to +1 or -1.
//
////if ( fabs(c) < ON_EPSILON || fabs(s) > 1.0-ON_EPSILON )
////{
//// c = 0.0;
//// s = s < 0.0 ? -1.0 : 1.0;
////}
////else if ( fabs(s) < ON_EPSILON || fabs(c) > 1.0-ON_EPSILON )
////{
//// s = 0.0;
//// c = c < 0.0 ? -1.0 : 1.0;
////}
if (fabs(c) <= cos_of_pi_over_2)
{
c = 0.0;
s = s < 0.0 ? -1.0 : 1.0;
}
else if (fabs(s) <= sin_of_pi)
{
s = 0.0;
c = c < 0.0 ? -1.0 : 1.0;
}
c *= m_arc.radius;
s *= m_arc.radius;
ON_3dPoint p = m_arc.plane.origin + c*m_arc.plane.xaxis + s*m_arc.plane.yaxis;
v[0] = p.x;
v[1] = p.y;
if ( m_dim == 3 )
v[2] = p.z;
for ( int di = 1; di <= der_count; di++ ) {
scale*=rat;
a = c;
c = -s;
s = a;
d = c*m_arc.plane.xaxis + s*m_arc.plane.yaxis;
v += v_stride;
v[0] = d.x*scale;
v[1] = d.y*scale;
if ( m_dim == 3 )
v[2] = d.z*scale;
}
rc = true;
}
return rc;
}
bool ON_ArcCurve::Trim( const ON_Interval& trimt )
{
bool rc = false;
if (trimt.IsIncreasing())
{
if (m_t.Includes(trimt, true))
{
ON_Interval normt = m_t.NormalizedParameterAt(trimt);
ON_3dPoint S = PointAt(trimt[0]);
ON_3dPoint E = PointAt(trimt[1]);
ON_Interval angle = m_arc.DomainRadians().ParameterAt(normt);
// 7-May-21. GBA. New definition of IsValid() enforced.
// Resulting ON_Arc and ON_ArcCurve must pass IsValid()
if (angle.Length() > ON_ZERO_TOLERANCE && !S.IsCoincident(E)
&& m_arc.SetAngleIntervalRadians(angle))
{
m_t = trimt;
DestroyCurveTree();
rc = true;
}
}
/* Allow trim where nothing is removed RH-64768 */
else if (m_t == trimt)
rc = true;
}
return rc;
}
bool ON_ArcCurve::Extend(
const ON_Interval& domain
)
{
if (IsClosed()) return false;
double s0, s1;
bool changed = false;
GetDomain(&s0, &s1);
if (domain[0] < s0){
s0 = domain[0];
changed = true;
}
if (domain[1] > s1){
s1 = domain[1];
changed = true;
}
if (!changed) return false;
DestroyCurveTree();
double a0 = m_arc.Domain().ParameterAt(Domain().NormalizedParameterAt(s0));
double a1 = m_arc.Domain().ParameterAt(Domain().NormalizedParameterAt(s1));
if (a1 > a0+2.0*ON_PI) {
a1 = a0+2.0*ON_PI;
s1 = Domain().ParameterAt(m_arc.Domain().NormalizedParameterAt(a1));
}
m_arc.Trim(ON_Interval(a0, a1));
SetDomain(s0, s1);
return true;
}
bool ON_ArcCurve::Split(
double t,
ON_Curve*& left_side,
ON_Curve*& right_side
) const
{
// make sure t is strictly inside the arc's domain
ON_Interval arc_domain = Domain();
ON_Interval arc_angles = m_arc.DomainRadians();
if ( !arc_domain.Includes(t) )
return false;
double a = (arc_domain == arc_angles)
? t
: arc_angles.ParameterAt(arc_domain.NormalizedParameterAt(t));
if ( !arc_angles.Includes(a) )
return false;
// make sure input curves are ok.
ON_ArcCurve* left_arc = 0;
ON_ArcCurve* right_arc = 0;
if ( 0 != left_side )
{
if ( left_side == right_side )
return false;
left_arc = ON_ArcCurve::Cast(left_side);
if ( 0 == left_arc )
return false;
left_arc->DestroyCurveTree();
}
if ( 0 != right_side )
{
right_arc = ON_ArcCurve::Cast(right_side);
if ( 0 == right_arc )
return false;
right_arc->DestroyCurveTree();
}
if ( 0 == left_arc )
{
left_arc = new ON_ArcCurve( *this );
}
else if ( this != left_arc )
{
left_arc->operator=(*this);
}
if ( 0 == right_arc )
{
right_arc = new ON_ArcCurve( *this );
}
else if ( this != right_arc )
{
right_arc->operator=(*this);
}
bool rc = false;
if ( this != left_arc )
{
rc = left_arc->Trim( ON_Interval( arc_domain[0], t ) );
if (rc)
rc = right_arc->Trim( ON_Interval( t, arc_domain[1] ) );
}
else
{
rc = right_arc->Trim( ON_Interval( t, arc_domain[1] ) );
if (rc)
rc = left_arc->Trim( ON_Interval( arc_domain[0], t ) );
}
if ( rc )
{
if ( 0 == left_side )
left_side = left_arc;
if ( 0 == right_side )
right_side = right_arc;
}
else
{
if ( 0 == left_side && this != left_arc )
{
delete left_arc;
left_arc = 0;
}
if ( 0 == right_side && this != right_arc )
{
delete right_arc;
right_arc = 0;
}
}
return rc;
}
static double ArcDeFuzz( double d )
{
// 0.0078125 = 1.0/128.0 exactly
// Using 2^n scale factors insures no loss of precision
// but preserves fractional values that are multiples of 1/128.
//
// Fuzz tol should be scale * 2^m * ON_EPSILON for m >= 1
double f, i;
f = modf( d*128.0, &i );
if ( f != 0.0 && fabs(f) <= 1024.0*ON_EPSILON ) {
d = i*0.0078125;
}
return d;
}
static bool 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;
}
int ON_Arc::GetNurbForm( ON_NurbsCurve& nurbscurve ) const
{
bool rc = NurbsCurveArc ( *this, 3, nurbscurve );
return (rc) ? 2 : 0;
}
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 necessary 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==nullptr)
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;
return true;
}
bool ON_Arc::GetNurbFormParameterFromRadian(double RadianParameter, double* NurbParameter ) const
{
if(!IsValid() || NurbParameter==nullptr)
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;
}