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ef4be960ca20fe5fc334f22442bd908adfb92442
opennurbs/opennurbs_subd_eval.cpp
Bozo The Builder ef4be960ca Sync changes from upstream repository 
Co-authored-by: Alain <alain@mcneel.com>
Co-authored-by: Andrew Le Bihan <andy@mcneel.com>
Co-authored-by: croudyj <croudyj@gmail.com>
Co-authored-by: Dale Fugier <dale@mcneel.com>
Co-authored-by: Dale Lear <dalelear@mcneel.com>
Co-authored-by: David Eränen <david.eranen@mcneel.com>
Co-authored-by: Greg Arden <greg@mcneel.com>
Co-authored-by: Mikko Oksanen <mikko@mcneel.com>
Co-authored-by: piac <giulio@mcneel.com>
Co-authored-by: Steve Baer <steve@mcneel.com>
Co-authored-by: TimHemmelman <tim@mcneel.com>
Co-authored-by: Will Pearson <will@mcneel.com>
2023-04-23 04:06:52 -07:00

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#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
#include "opennurbs_subd_data.h"
ON_SubD* ON_SubDSectorType::SectorRingSubD(
double radius,
double sector_angle_radians,
ON_SubD* subd
) const
{
if (subd)
*subd = ON_SubD::Empty;
if (!IsValid())
return ON_SUBD_RETURN_ERROR(nullptr);
const unsigned int R = PointRingCount();
if (R < 3)
return ON_SUBD_RETURN_ERROR(nullptr);
const unsigned int F = FaceCount();
if ( F < 1)
return ON_SUBD_RETURN_ERROR(nullptr);
const unsigned int N = EdgeCount();
if (N < 2)
return ON_SUBD_RETURN_ERROR(nullptr);
if (F != N && F + 1 != N)
return ON_SUBD_RETURN_ERROR(nullptr);
const ON_SubDVertexTag vertex_tag = VertexTag();
const unsigned int ring_ei_delta = 2;
if (nullptr == subd)
subd = new ON_SubD;
ON_SubDVertexTag vertex_tag0;
ON_SubDVertexTag vertex_tag1;
ON_SubDEdgeTag edge_tag0;
ON_SubDEdgeTag edge_tag1;
const bool bSmoothOrDartSector = (ON_SubDVertexTag::Smooth == vertex_tag || ON_SubDVertexTag::Dart == vertex_tag);
switch (vertex_tag)
{
case ON_SubDVertexTag::Smooth:
sector_angle_radians = 2.0*ON_PI;
vertex_tag0 = ON_SubDVertexTag::Smooth;
vertex_tag1 = ON_SubDVertexTag::Smooth;
edge_tag0 = ON_SubDEdgeTag::Smooth;
edge_tag1 = ON_SubDEdgeTag::Smooth;
break;
case ON_SubDVertexTag::Crease:
if ( !(sector_angle_radians > 0.0 && sector_angle_radians < 2.0*ON_PI) )
sector_angle_radians = 0.5*ON_PI;
vertex_tag0 = ON_SubDVertexTag::Crease;
vertex_tag1 = ON_SubDVertexTag::Crease;
edge_tag0 = ON_SubDEdgeTag::Crease;
edge_tag1 = ON_SubDEdgeTag::Crease;
break;
case ON_SubDVertexTag::Corner:
sector_angle_radians = CornerSectorAngleRadians();
vertex_tag0 = ON_SubDVertexTag::Crease;
vertex_tag1 = ON_SubDVertexTag::Crease;
edge_tag0 = ON_SubDEdgeTag::Crease;
edge_tag1 = ON_SubDEdgeTag::Crease;
break;
case ON_SubDVertexTag::Dart:
sector_angle_radians = 2.0*ON_PI;
vertex_tag0 = ON_SubDVertexTag::Crease;
vertex_tag1 = ON_SubDVertexTag::Smooth;
edge_tag0 = ON_SubDEdgeTag::Crease;
edge_tag1 = ON_SubDEdgeTag::Smooth;
break;
default:
return ON_SUBD_RETURN_ERROR(nullptr);
break;
}
unsigned int sector_angle_index
= bSmoothOrDartSector
? ON_UNSET_UINT_INDEX
: ON_SubDSectorType::CornerAngleIndexFromCornerAngleRadians(
ON_SubDSectorType::ClampCornerSectorAngleRadians(sector_angle_radians)
);
if (sector_angle_index <= ON_SubDSectorType::MaximumCornerAngleIndex
&& fabs(ON_SubDSectorType::AngleRadiansFromCornerAngleIndex(sector_angle_index) - sector_angle_radians) <= 1.0e-6
)
{
sector_angle_radians = ON_SubDSectorType::AngleRadiansFromCornerAngleIndex(sector_angle_index);
}
else
{
sector_angle_index = ON_UNSET_UINT_INDEX;
}
const double smooth_edge_w0 = this->SectorCoefficient();
ON_SimpleArray< ON_SubDVertex* > V(R);
ON_SimpleArray< ON_SubDEdge* > E(N);
ON_3dPoint vertexP = ON_3dPoint::Origin;
for (unsigned int vi = 0; vi < R; vi++)
{
ON_SubDVertexTag vertex_tag_vi;
if ( 0 == vi )
vertex_tag_vi = vertex_tag; // center vertex
else if ( 1 == vi )
vertex_tag_vi = vertex_tag0; // first edge
else if ( R == vi+1 && N > F )
vertex_tag_vi = vertex_tag1; // last edge
else
vertex_tag_vi = ON_SubDVertexTag::Smooth; // interior edge or an outer face vertex
if (radius > 0.0)
{
double cos_a, sin_a;
if (sector_angle_index == ON_UNSET_UINT_INDEX)
{
double a = (vi / ((double)(R-1)))*sector_angle_radians;
cos_a = cos(a);
sin_a = sin(a);
}
else
{
ON_SubDMatrix::EvaluateCosAndSin(2*sector_angle_index*vi, (R-1)*ON_SubDSectorType::MaximumCornerAngleIndex,&cos_a,&sin_a);
}
const double r = (1 == (vi%2)) ? radius : (2.0*radius);
vertexP.x = r*cos_a;
vertexP.y = r*sin_a;
}
ON_SubDVertex* vertex = subd->AddVertex( vertex_tag_vi, vertexP);
V.Append(vertex);
}
//V[0]->m_vertex_edge_order = ON_SubD::VertexEdgeOrder::radial;
for (unsigned int vei = 0; vei < N; vei++)
{
ON_SubDEdgeTag edge_tag_vei;
if ( 0 == vei )
edge_tag_vei = edge_tag0; // first edge
else if ( vei+1 == N )
edge_tag_vei = edge_tag1; // last edge
else
edge_tag_vei = ON_SubDEdgeTag::Smooth; // interior edge
double w0 = (ON_SubDEdgeTag::Smooth == edge_tag_vei) ? smooth_edge_w0 : ON_SubDSectorType::IgnoredSectorCoefficient;
unsigned int ev1i = 1 + vei*ring_ei_delta;
E.Append(
subd->AddEdgeWithSectorCoefficients(
edge_tag_vei,
V[0], w0,
V[ev1i], ON_SubDSectorType::IgnoredSectorCoefficient)
);
}
ON_SubDVertex* f_vertex[4] = {};
ON_SubDEdge* f_edge[4] = {};
ON_SubDEdgePtr f_edgeptr[4] = {};
f_vertex[0] = V[0];
f_vertex[3] = const_cast<ON_SubDVertex*>(E[0]->m_vertex[1]);
f_edge[3] = E[0];
for (unsigned int vfi = 0; vfi < F; vfi++)
{
f_edge[0] = f_edge[3];
f_edge[3] = E[(vfi + 1) % N];
f_vertex[1] = const_cast<ON_SubDVertex*>(f_edge[0]->m_vertex[1]);
f_vertex[3] = const_cast<ON_SubDVertex*>(f_edge[3]->m_vertex[1]);
f_edgeptr[0] = ON_SubDEdgePtr::Create(f_edge[0], 0);
f_edgeptr[3] = ON_SubDEdgePtr::Create(f_edge[3], 1);
f_vertex[2] = V[2 + 2 * vfi];
f_edge[1] = subd->AddEdgeWithSectorCoefficients(ON_SubDEdgeTag::Smooth, f_vertex[1], ON_SubDSectorType::IgnoredSectorCoefficient, f_vertex[2], ON_SubDSectorType::IgnoredSectorCoefficient);
f_edge[2] = subd->AddEdgeWithSectorCoefficients(ON_SubDEdgeTag::Smooth, f_vertex[2], ON_SubDSectorType::IgnoredSectorCoefficient, f_vertex[3], ON_SubDSectorType::IgnoredSectorCoefficient);
f_edgeptr[1] = ON_SubDEdgePtr::Create(f_edge[1], 0);
f_edgeptr[2] = ON_SubDEdgePtr::Create(f_edge[2], 0);
subd->AddFace(f_edgeptr,4);
}
return subd;
}
static bool TestPoint(
const ON_3dPoint* SP,
unsigned int SPi,
ON_3dPoint Q,
unsigned int Pi,
double* e,
unsigned int* ei
)
{
ON_3dPoint P = SP[SPi];
double z = fabs(P[(Pi + 1) % 3]) + fabs(P[(Pi + 1) % 3])+ fabs(Q[(Pi + 1) % 3]) + fabs(Q[(Pi + 1) % 3]);
if (!(0.0 == z))
{
// ON_ERROR("point coordinate is not zero.");
return ON_SUBD_RETURN_ERROR(false);
}
if (fabs(P[Pi]) > 1.0)
{
// ON_ERROR("point coordinate P[Pi] > 1.");
return ON_SUBD_RETURN_ERROR(false);
}
if (fabs(Q[Pi]) > 1.0)
{
// ON_ERROR("point coordinate Q[Pi] > 1.");
return ON_SUBD_RETURN_ERROR(false);
}
double d = fabs(P[Pi] - Q[Pi]);
if (d > e[Pi])
{
e[Pi] = d;
*ei = SPi;
#if defined(ON_DEBUG)
if (d > 0.0001)
{
// almost certainly a bug
ON_SubDIncrementErrorCount();
}
#endif
}
return true;
}
static bool ClearCachedPoints(
unsigned int component_ring_count,
const ON_SubDComponentPtr* component_ring
)
{
if ( component_ring_count < 4 || nullptr == component_ring)
return ON_SUBD_RETURN_ERROR(false);
ON_SubDVertex* vertex = component_ring[0].Vertex();
if ( nullptr == vertex)
return ON_SUBD_RETURN_ERROR(false);
vertex->ClearSavedSubdivisionPoints();
for (unsigned int i = 1; i < component_ring_count; i++)
{
ON_SubDEdge* edge = component_ring[i].Edge();
if ( nullptr == edge)
return ON_SUBD_RETURN_ERROR(false);
edge->ClearSavedSubdivisionPoints();
i++;
if (i >= component_ring_count)
break;
ON_SubDFace* face = component_ring[i].Face();
if ( nullptr == face)
return ON_SUBD_RETURN_ERROR(false);
face->ClearSavedSubdivisionPoints();
}
return true;
}
double ON_SubDMatrix::TestEvaluation() const
{
if ( nullptr == m_S || m_R < 3 )
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
if (!m_sector_type.IsValid())
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const unsigned int F = m_sector_type.FaceCount();
if (0 == F)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const unsigned int N = m_sector_type.EdgeCount();
if (0 == N)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const unsigned int R = m_sector_type.PointRingCount();
if (0 == R)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
if (R != m_R)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const unsigned f_edge_count = m_sector_type.FacetEdgeCount();
if (0 == f_edge_count)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
double rc = TestMatrix();
const double*const* S = m_S;
unsigned int SP_low_precision_index = ON_UNSET_UINT_INDEX;
ON_SimpleArray< ON_3dPoint > _P(R);
ON_3dPoint* SP = _P.Array();
ON_SimpleArray< double > _Scol(R);
double* Scol = _Scol.Array();
ON_SubD subd;
if (&subd != m_sector_type.SectorRingSubD(0.0,0.0,&subd))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const ON_SubDVertex* vertex0 = subd.FirstVertex();
if (nullptr == vertex0)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
if (N != vertex0->m_edge_count)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
if (F != vertex0->m_face_count)
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
ON_SubDSectorIterator sit;
if ( nullptr == sit.Initialize(vertex0) )
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
ON_SimpleArray<const ON_SubDVertex*> vertex_ring_array(subd.VertexCount());
for (const ON_SubDVertex* vertex = vertex0; nullptr != vertex; vertex = vertex->m_next_vertex)
{
vertex_ring_array.Append(vertex);
}
if ( R != vertex_ring_array.UnsignedCount())
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const ON_SubDVertex*const* vertex_ring = vertex_ring_array.Array();
ON_SimpleArray<ON_SubDComponentPtr> component_ring_array;
const unsigned int component_ring_count = ON_SubD::GetSectorComponentRing(sit,component_ring_array);
if ( component_ring_count < 4 || component_ring_count != m_sector_type.ComponentRingCount())
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const ON_SubDComponentPtr* component_ring = component_ring_array.Array();
ON_SimpleArray< ON_3dPoint > _ringP0;
ON_SimpleArray< ON_3dPoint > _ringP1;
for (unsigned int vi = 0; vi < R; vi++)
Scol[vi] = ON_DBL_QNAN;
for (unsigned int vi = 0; vi < R; vi++)
{
double N_vertex_point_precision[3] = { 0 };
double N_outer_point_precision[3] = { 0 };
double N_Scol_precision[3] = { 0 };
for (unsigned int Pi = 0; Pi < 3; Pi++)
{
if (false == ClearCachedPoints(component_ring_count,component_ring))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const_cast<ON_SubDVertex*>(vertex_ring[vi])->m_P[Pi] = 1.0;
if ( R != ON_SubD::GetSectorPointRing(false,component_ring_count,component_ring,_ringP0))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const ON_3dPoint* ringP0 = _ringP0.Array();
// vertex_ring[]->m_P and ringP0[] should be same point lists
for (unsigned int i = 0; i < R; i++)
{
if (0.0 == ringP0[i][(Pi+1)%3] && 0.0 == ringP0[i][(Pi+2)%3])
{
if ( ringP0[i][Pi] == ((i == vi) ? 1.0 : 0.0) )
continue;
}
// vertex_ring[] is not in the expected order or
// there is a bug in ON_SubD::GetSectorPointRing
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
if ( R != ON_SubD::GetSectorSubdivisionPointRing(component_ring, component_ring_count,_ringP1))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
const ON_3dPoint* ringP1 = _ringP1.Array();
for (unsigned int i = 0; i < R; i++)
{
SP[i] = ON_3dPoint::Origin;
for (unsigned int j = 0; j < R; j++)
{
SP[i] += S[i][j] * ringP0[j];
}
}
if (!(SP[vi][Pi] > 0.0))
{
// ON_ERROR("SP[vi][Pi] is not positive.");
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
if (false == TestPoint(SP, 0, ringP1[0], Pi, N_vertex_point_precision, &SP_low_precision_index))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
for (unsigned int j = 1; j < R; j++)
{
if (false == TestPoint(SP, j, ringP1[j], Pi, N_outer_point_precision, &SP_low_precision_index))
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
for (unsigned int i = 0; i < R; i++)
{
double d = fabs(S[i][vi] - ringP1[i][Pi]);
if (d > N_Scol_precision[Pi])
N_Scol_precision[Pi] = d;
}
if (!(N_vertex_point_precision[0] == N_vertex_point_precision[Pi]))
{
ON_ERROR("x,y,z vertex point precisions are not identical.");
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
if (!(N_outer_point_precision[0] == N_outer_point_precision[Pi]))
{
ON_ERROR("x,y,z outer point precisions are not identical.");
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
if (!(N_Scol_precision[0] == N_Scol_precision[Pi]))
{
ON_ERROR("x,y,z S column precisions are not identical.");
return ON_SUBD_RETURN_ERROR(ON_UNSET_VALUE);
}
if (rc < N_vertex_point_precision[0])
rc = N_vertex_point_precision[0];
if (rc < N_outer_point_precision[0])
rc = N_outer_point_precision[0];
if (rc < N_Scol_precision[0])
rc = N_Scol_precision[0];
const_cast<ON_SubDVertex*>(vertex_ring[vi])->m_P[Pi] = 0.0;
}
}
return rc; // basic tests passed.
}
static bool GetSectorLimitPointHelper(
const ON_SubDSectorIterator& sit,
bool& bUndefinedNormalIsPossible,
ON_SubDSectorSurfacePoint& limit_point
)
{
limit_point.m_limitP[0] = ON_DBL_QNAN;
limit_point.m_limitP[1] = ON_DBL_QNAN;
limit_point.m_limitP[2] = ON_DBL_QNAN;
const ON_SubDSectorType sector_type = ON_SubDSectorType::Create(sit);
if (false == sector_type.IsValid())
return ON_SUBD_RETURN_ERROR(false);
const unsigned int R = sector_type.PointRingCount();
if (R < 3)
return ON_SUBD_RETURN_ERROR(false);
double stack_point_ring[41*3];
double* point_ring = stack_point_ring;
const unsigned int point_ring_stride = 3;
unsigned int point_ring_capacity = (unsigned int)(sizeof(stack_point_ring)/(point_ring_stride*sizeof(stack_point_ring[0])));
if (point_ring_capacity < R )
{
point_ring = new(std::nothrow) double[point_ring_stride*R];
if ( nullptr == point_ring)
return ON_SUBD_RETURN_ERROR(false);
point_ring_capacity = R;
}
const unsigned int point_ring_count = ON_SubD::GetSectorPointRing( true, sit, point_ring, point_ring_capacity, point_ring_stride);
if ( R != point_ring_count )
return ON_SUBD_RETURN_ERROR(false);
bool rc = false;
for (;;)
{
const ON_SubDMatrix& SM = ON_SubDMatrix::FromCache(sector_type);
if (R != SM.m_R || nullptr == SM.m_LP)
break;
if (
false == bUndefinedNormalIsPossible
&& ON_SubDVertexTag::Crease == SM.m_sector_type.VertexTag()
&& R >= 5
&& *((const ON_3dPoint*)(point_ring+ point_ring_stride)) == *((const ON_3dPoint*)(point_ring + (R-1)* point_ring_stride))
)
{
// Crease where ends of the creased edges are equal.
// common overlapping creases (happens when a smooth interior edge is separated (unwelded) into two creases)
bUndefinedNormalIsPossible = true;
}
if (false == SM.EvaluateSurfacePoint(point_ring, R, point_ring_stride, bUndefinedNormalIsPossible, limit_point))
break;
if (
false == bUndefinedNormalIsPossible
&& 0.0 == limit_point.m_limitN[0] && 0.0 == limit_point.m_limitN[1] && 0.0 == limit_point.m_limitN[2]
&& limit_point.IsSet(true)
)
{
// SM.EvaluateSurfacePoint() logged the error - setting bUndefinedNormalIsPossible = true here
// allows the limit point to be cached so the same error doesn't continue to get logged.
bUndefinedNormalIsPossible = true;
}
rc = true;
break;
}
if ( point_ring != stack_point_ring)
delete[] point_ring;
return rc
? true
: ON_SUBD_RETURN_ERROR(false);
}
static ON_SubDSectorSurfacePoint* LimitPointPool(
const ON_SubDSectorSurfacePoint* pReturnToPool // If nullptr, then one is allocated
)
{
static ON_FixedSizePool limit_point_fsp;
if (0 == limit_point_fsp.SizeofElement())
{
if (nullptr != pReturnToPool)
return ON_SUBD_RETURN_ERROR(nullptr);
static ON_SleepLock initialize_lock;
initialize_lock.GetLock();
if (0 == limit_point_fsp.SizeofElement())
limit_point_fsp.Create(sizeof(ON_SubDSectorSurfacePoint), 0, 0);
initialize_lock.ReturnLock();
}
if (nullptr != pReturnToPool)
{
limit_point_fsp.ThreadSafeReturnElement((void*)pReturnToPool);
return nullptr;
}
ON_SubDSectorSurfacePoint* lp = (ON_SubDSectorSurfacePoint*)limit_point_fsp.ThreadSafeAllocateDirtyElement();
if (nullptr == lp)
return ON_SUBD_RETURN_ERROR(nullptr);
return lp;
}
bool ON_SubDVertex::GetSurfacePoint(
const ON_SubDFace* sector_face,
ON_SubDSectorSurfacePoint& limit_point
) const
{
return GetSurfacePoint( sector_face, false, limit_point);
}
bool ON_SubDVertex::GetSurfacePoint(
const ON_SubDFace* sector_face,
bool bUndefinedNormalIsPossible,
ON_SubDSectorSurfacePoint& limit_point
) const
{
bool rc = false;
ON_SubDSectorIterator sit;
const ON_SubDFace* limit_point_sector_face = nullptr;
if (nullptr != sector_face)
{
for (unsigned int vfi = 0; vfi < m_face_count; vfi++)
{
if (sector_face == m_faces[vfi])
{
rc = true;
break;
}
}
if (false == rc)
{
// sector_face is not referenced by this vertex
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
}
if (this->SurfacePointIsSet() )
{
if (nullptr == m_limit_point.m_sector_face && nullptr == m_limit_point.m_next_sector_limit_point)
{
// single sector
limit_point = m_limit_point;
limit_point.m_next_sector_limit_point = nullptr;
return true;
}
if (nullptr == sector_face)
{
// this vertex has multiple sectors
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
if (nullptr == sit.Initialize(sector_face, 0, this))
{
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
limit_point_sector_face = sit.IncrementToCrease(-1);
if (nullptr == limit_point_sector_face)
{
// no creases
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
for (const ON_SubDSectorSurfacePoint* lp = &m_limit_point; nullptr != lp; lp = lp->m_next_sector_limit_point)
{
if (limit_point_sector_face == lp->m_sector_face)
{
limit_point = *lp;
limit_point.m_next_sector_limit_point = nullptr;
return true;
}
}
// cache does not contain this limit point.
}
if (nullptr == (nullptr == sector_face ? sit.Initialize(this) : sit.Initialize(sector_face, 0, this)))
{
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
limit_point_sector_face = sit.IncrementToCrease(-1);
rc = GetSectorLimitPointHelper( sit, bUndefinedNormalIsPossible, limit_point);
if (false == rc)
{
limit_point = ON_SubDSectorSurfacePoint::Unset;
return ON_SUBD_RETURN_ERROR(false);
}
limit_point.m_sector_face = this->IsSingleSectorVertex() ? nullptr : limit_point_sector_face;
ON_SubDSectorSurfacePoint saved_limit_point = limit_point;
saved_limit_point.m_next_sector_limit_point = (ON_SubDSectorSurfacePoint*)1; // causes unnecessary test to be skipped
SetSavedSurfacePoint( bUndefinedNormalIsPossible, saved_limit_point);
return rc;
}
bool ON_SubDVertex::GetSavedSurfacePoint(
double limit_point[3]
) const
{
const bool rc = SurfacePointIsSet();
if (rc)
{
limit_point[0] = m_limit_point.m_limitP[0];
limit_point[1] = m_limit_point.m_limitP[1];
limit_point[2] = m_limit_point.m_limitP[2];
}
return rc;
}
const ON_3dPoint ON_SubDVertex::SurfacePoint() const
{
ON_3dPoint limit_point(ON_3dPoint::NanPoint);
return GetSurfacePoint(&limit_point.x) ? limit_point : ON_3dPoint::NanPoint;
}
const ON_3dVector ON_SubDVertex::SurfaceNormal(
const ON_SubDFace* sector_face,
bool bUndefinedNormalPossible
) const
{
for (;;)
{
if (m_face_count < 1 || nullptr == m_faces)
{
ON_ERROR("No faces on this vertex.");
break;
}
if (nullptr == sector_face && IsCreaseOrCorner())
{
const ON_SubDComponentPtrPair crease_pair = this->CreasedEdgePair(false);
const ON_SubDEdge* e[2] = { crease_pair.First().Edge(), crease_pair.Second().Edge() };
if (nullptr == e[0] || 1 != e[0]->m_face_count || nullptr == e[1] || 1 != e[1]->m_face_count)
{
ON_ERROR("sector_face must be specified in this case.");
break;
}
}
if (nullptr == sector_face)
sector_face = m_faces[0];
ON_SubDSectorSurfacePoint limit_point;
bool rc = ON_SubDVertex::GetSurfacePoint(
sector_face,
bUndefinedNormalPossible,
limit_point
);
if (false == rc)
break;
const ON_3dVector N(limit_point.m_limitN);
if (false == bUndefinedNormalPossible && N.IsZero())
break;
return N;
}
return ON_3dVector::NanVector;
}
const ON_SubDSectorSurfacePoint& ON_SubDVertex::SectorSurfacePointForExperts() const
{
return this->m_limit_point;
}
const ON_Plane ON_SubDVertex::VertexFrame(
ON_SubDComponentLocation subd_appearance
) const
{
if (0 == FaceCount())
return ON_Plane::NanPlane;
const ON_SubDFace* sector_face = Face(0);
if (nullptr == sector_face)
return ON_Plane::NanPlane;
ON_Plane vertex_frame(ON_Plane::NanPlane);
if (ON_SubDComponentLocation::ControlNet == subd_appearance)
{
ON_3dVector V = ON_3dVector::ZeroVector;
for (int vei = 0; vei < m_edge_count; ++vei)
{
const ON_SubDEdge* e = Edge(vei);
if (nullptr == e)
continue;
const ON_SubDVertex* v1 = e->OtherEndVertex(this);
if (nullptr == v1)
continue;
const ON_SubDFace* f = (1 == e->m_face_count) ? e->Face(0) : nullptr;
if (nullptr == f)
continue;
sector_face = f;
V = (v1->ControlNetPoint() - ControlNetPoint()).UnitVector();
break;
}
vertex_frame.CreateFromNormal(ControlNetPoint(), sector_face->ControlNetCenterNormal());
const ON_3dVector X = (V - (V * vertex_frame.zaxis) * vertex_frame.zaxis).UnitVector();
if (X.IsUnitVector())
{
vertex_frame.xaxis = X;
vertex_frame.yaxis = ON_CrossProduct(vertex_frame.zaxis, vertex_frame.xaxis).UnitVector();
}
}
else
{
// If this is a smooth vertex or a crease vertex on the boundary,
// then the sector_face does not matter. Otherwise it picks the
// "side of the crease" for the normal.
ON_SubDSectorSurfacePoint limit_point;
if (FaceCount())
if (false == GetSurfacePoint(sector_face, limit_point))
return ON_Plane::NanPlane;
ON_3dVector Y(ON_CrossProduct(limit_point.m_limitN, limit_point.m_limitT1));
Y.Unitize();
// The normal is more important than the tangent direction.
vertex_frame.CreateFromNormal(ON_3dPoint(limit_point.m_limitP), ON_3dVector(limit_point.m_limitN));
vertex_frame.yaxis = Y;
vertex_frame.xaxis = ON_CrossProduct(vertex_frame.yaxis, vertex_frame.zaxis);
vertex_frame.xaxis.Unitize();
}
return vertex_frame.IsValid() ? vertex_frame : ON_Plane::NanPlane;
}
const ON_Plane ON_SubDEdge::CenterFrame(
ON_SubDComponentLocation subd_appearance
) const
{
// to fix RH-41763, get the limit mesh fragment for an attached face
// and use subd.LimitSurfaceMesh().GetEdgeCenterPointAndNormal()
// to get P and N.
ON_Plane edge_frame(ON_Plane::NanPlane);
ON_3dPoint center_point(ON_3dPoint::NanPoint);
ON_3dVector center_normal(ON_3dVector::NanVector);
bool rc = false;
// surface center and normal are not available in public opennurbs
center_point = ControlNetCenterPoint();
center_normal = ControlNetCenterNormal(0);
rc = center_point.IsValid() && center_normal.IsUnitVector();
if (rc)
{
if (false == edge_frame.CreateFromNormal(center_point, center_normal))
return ON_Plane::NanPlane;
const ON_3dVector U = ControlNetDirection();
ON_2dVector v(U * edge_frame.xaxis, U * edge_frame.yaxis);
if ( v.Unitize() )
{
if (fabs(v.y) > ON_SQRT_EPSILON&& fabs(v.x) < (1.0 - ON_SQRT_EPSILON))
{
const ON_3dVector X = (v.x * edge_frame.xaxis + v.y * edge_frame.yaxis).UnitVector();
if (X.IsUnitVector())
{
const ON_3dVector Y = ON_CrossProduct(edge_frame.zaxis, X).UnitVector();
if (Y.UnitVector())
{
edge_frame.xaxis = X;
edge_frame.yaxis = Y;
}
}
}
else if (v.x < 0.0)
{
edge_frame.xaxis = -edge_frame.xaxis;
edge_frame.yaxis = -edge_frame.yaxis;
}
}
}
return edge_frame.IsValid() ? edge_frame : ON_Plane::NanPlane;
}
const ON_3dPoint ON_SubDVertex::Point(ON_SubDComponentLocation point_location) const
{
switch (point_location)
{
case ON_SubDComponentLocation::ControlNet:
return this->ControlNetPoint();
break;
case ON_SubDComponentLocation::Surface:
return this->SurfacePoint();
break;
case ON_SubDComponentLocation::Unset:
return ON_3dPoint::NanPoint;
break;
}
return ON_3dPoint::NanPoint;
}
bool ON_SubDVertex::GetSurfacePoint(
double limit_point[3]
) const
{
if (nullptr == limit_point)
return false;
bool rc = SurfacePointIsSet();
if ( rc )
{
limit_point[0] = m_limit_point.m_limitP[0];
limit_point[1] = m_limit_point.m_limitP[1];
limit_point[2] = m_limit_point.m_limitP[2];
}
else
{
ON_SubDSectorSurfacePoint lp;
rc = GetSurfacePoint(Face(0), true, lp);
if (rc)
{
limit_point[0] = lp.m_limitP[0];
limit_point[1] = lp.m_limitP[1];
limit_point[2] = lp.m_limitP[2];
}
else
{
limit_point[0] = ON_DBL_QNAN;
limit_point[1] = ON_DBL_QNAN;
limit_point[2] = ON_DBL_QNAN;
}
}
return rc;
}
static bool SetLimitPointSectorCheck(
const ON_SubDVertex* vertex,
ON_SubDSectorSurfacePoint& limit_point
)
{
const unsigned int vertex_face_count = vertex->m_face_count;
if ( vertex_face_count < 1 || nullptr == vertex->m_faces)
return ON_SUBD_RETURN_ERROR(false);
ON_SubDSectorIterator sit;
const ON_SubDFace* limit_point_sector_face = limit_point.m_sector_face;
if (nullptr != limit_point_sector_face)
{
bool rc = false;
for (unsigned int vfi = 0; vfi < vertex_face_count; vfi++)
{
if (limit_point_sector_face == vertex->m_faces[vfi])
{
rc = true;
break;
}
}
if (false == rc)
return ON_SUBD_RETURN_ERROR(false); // sector_face is not referenced by this vertex
if (nullptr == sit.Initialize(limit_point_sector_face, 0, vertex))
return ON_SUBD_RETURN_ERROR(false);
}
else if (nullptr == sit.Initialize(vertex))
return ON_SUBD_RETURN_ERROR(false);
limit_point_sector_face = sit.IncrementToCrease(-1);
unsigned int sector_face_count = 0;
const ON_SubDFace* sector_face0 = sit.CurrentFace();
for (const ON_SubDFace* sector_face = sector_face0; nullptr != sector_face && sector_face_count <= vertex_face_count; sector_face = sit.NextFace(ON_SubDSectorIterator::StopAt::AnyCrease))
{
if (sector_face == sector_face0 && sector_face_count == vertex_face_count && vertex->IsSmoothOrDart())
{
// interior vertex
limit_point_sector_face = nullptr;
break;
}
sector_face_count++;
}
if (sector_face_count > vertex_face_count)
{
// error in topology information
return ON_SUBD_RETURN_ERROR(false);
}
if (sector_face_count == vertex_face_count)
{
// vertex has 1 sector (bounded or interior)
limit_point_sector_face = nullptr;
}
else if (nullptr == limit_point_sector_face )
{
// vertex has multiple sectors and
// limit_point.m_sector_face must be the "first" face in the sector
return ON_SUBD_RETURN_ERROR(false);
}
limit_point.m_sector_face = limit_point_sector_face;
return true;
}
bool ON_SubDVertex::SetSavedSurfacePoint(
bool bUndefinedNormalIsPossible,
ON_SubDSectorSurfacePoint limit_point
) const
{
const bool bSkipSectorCheck = (1U == (ON__UINT_PTR)limit_point.m_next_sector_limit_point);
limit_point.m_next_sector_limit_point = nullptr;
if ( limit_point.IsSet(bUndefinedNormalIsPossible)
&& (bSkipSectorCheck || SetLimitPointSectorCheck(this,limit_point))
)
{
if (nullptr == limit_point.m_sector_face
|| ON_UNSET_VALUE == m_limit_point.m_limitP[0]
|| false == Internal_SurfacePointFlag()
)
{
// vertex has 1 sector or this is the first cached limit point
this->ClearSavedSurfacePoints();
m_limit_point = limit_point;
m_limit_point.m_next_sector_limit_point = nullptr;
}
else
{
// get a point from the pool
ON_SubDSectorSurfacePoint* lp = LimitPointPool(nullptr);
if ( nullptr == lp)
return ON_SUBD_RETURN_ERROR(false);
// set the point
*lp = limit_point;
// first limit point location wins
ON_SubDMeshFragment::SealPoints(true, m_limit_point.m_limitP, lp->m_limitP);
// it is expected that the limit normal and tangents will be substantually different.
lp->m_next_sector_limit_point = nullptr;
// append the point to the vertex's linked list.
const ON_SubDSectorSurfacePoint* p = &m_limit_point;
while(nullptr != p->m_next_sector_limit_point)
{
p = p->m_next_sector_limit_point;
}
const_cast<ON_SubDSectorSurfacePoint*>(p)->m_next_sector_limit_point = lp;
}
Internal_SetSavedSurfacePointFlag(true);
return true;
}
return ON_SUBD_RETURN_ERROR(false);
}
void ON_SubDVertex::ClearSavedSurfacePoints() const
{
// clear vertex specific cache
Internal_ClearSurfacePointFlag();
if (nullptr != m_limit_point.m_next_sector_limit_point)
{
// return multiple sector limit points to pool
const ON_SubDSectorSurfacePoint* next_p = m_limit_point.m_next_sector_limit_point;
m_limit_point.m_next_sector_limit_point = nullptr;
for (const ON_SubDSectorSurfacePoint* p = next_p; nullptr != p; p = next_p)
{
next_p = p->m_next_sector_limit_point;
LimitPointPool(p);
}
}
m_limit_point = ON_SubDSectorSurfacePoint::Unset;
}
void ON_SubDVertex::ClearSavedSubdivisionPoints() const
{
// clear vertex specific limit point cache
ClearSavedSurfacePoints();
// clear general subdivision point cache
ON_SubDComponentBase::Internal_ClearSubdivisionPointAndSurfacePointFlags();
}
void ON_SubDVertex::ClearSavedSubdivisionPoints(bool bClearNeighborhood) const
{
ClearSavedSubdivisionPoints();
if (false == bClearNeighborhood)
return;
for (unsigned short vei = 0; vei < m_edge_count; ++vei)
{
const ON_SubDEdge* e = ON_SUBD_EDGE_POINTER(m_edges[vei].m_ptr);
if (nullptr == e)
continue;
e->ClearSavedSubdivisionPoints();
const ON_SubDVertex* other_v = e->OtherEndVertex(this);
if (nullptr != other_v)
other_v->ClearSavedSubdivisionPoints();
}
for (unsigned short vfi = 0; vfi < m_face_count; ++vfi)
{
const ON_SubDFace* f = m_faces[vfi];
if (nullptr == f)
continue;
f->ClearSavedSubdivisionPoints();
const ON_SubDEdgePtr* eptr = f->m_edge4;
for (unsigned short fei = 0; fei < f->m_edge_count; ++fei, ++eptr)
{
if (4 == fei)
{
eptr = f->m_edgex;
if (nullptr == eptr)
break;
}
const ON_SubDEdge* e = ON_SUBD_EDGE_POINTER(eptr->m_ptr);
if (nullptr == e)
continue;
e->ClearSavedSubdivisionPoints();
if (nullptr != e->m_vertex[0])
e->m_vertex[0]->ClearSavedSubdivisionPoints();
if (nullptr != e->m_vertex[1])
e->m_vertex[1]->ClearSavedSubdivisionPoints();
}
}
}
bool ON_SubDVertex::SurfacePointIsSet() const
{
const bool rc = Internal_SurfacePointFlag();
if (false == rc)
{
this->ClearSavedSurfacePoints();
}
return rc;
}
void ON_SubDEdge::ClearSavedSubdivisionPoints() const
{
// considering using a global pool for the limit curve cache - not yet.
ON_SubDComponentBase::Internal_ClearSubdivisionPointAndSurfacePointFlags();
}
void ON_SubDEdge::ClearSavedSubdivisionPoints(bool bClearNeighborhood) const
{
ClearSavedSubdivisionPoints();
if (false == bClearNeighborhood)
return;
for (unsigned evi = 0; evi < 2; ++evi)
{
const ON_SubDVertex* v = m_vertex[evi];
if (nullptr == v)
continue;
v->ClearSavedSubdivisionPoints();
}
const ON_SubDFacePtr* fptr = this->m_face2;
for (unsigned short efi = 0; efi < m_face_count; ++efi, ++fptr)
{
if (2 == efi)
{
fptr = this->m_facex;
if (nullptr == fptr)
break;
}
const ON_SubDFace* f = ON_SUBD_FACE_POINTER(fptr->m_ptr);
if (nullptr != f)
f->ClearSavedSubdivisionPoints();
}
}
const ON_SubDMeshFragment * ON_SubDFace::MeshFragments() const
{
// NOTE:
// Clearing the ON_SubDComponentBase::SavedPointsFlags::SurfacePointBit bit
// on m_saved_points_flags is used to mark mesh fragmants as dirty.
// They need to be regerated before being used.
return (0 != ON_SUBD_CACHE_LIMITLOC_FLAG(m_saved_points_flags)) ? m_mesh_fragments : nullptr;
}
void ON_SubDFace::ClearSavedSubdivisionPoints() const
{
// considering using a global pool for the limit fragment cache - not yet.
ON_SubDComponentBase::Internal_ClearSubdivisionPointAndSurfacePointFlags();
}
void ON_SubDFace::ClearSavedSubdivisionPoints(bool bClearNeighborhood) const
{
ClearSavedSubdivisionPoints();
if (false == bClearNeighborhood)
return;
const ON_SubDEdgePtr* eptr = this->m_edge4;
for (unsigned short fei = 0; fei < this->m_edge_count; ++fei, ++eptr)
{
if (4 == fei)
{
eptr = this->m_edgex;
if (nullptr == eptr)
break;
}
const ON_SubDEdge* e = ON_SUBD_EDGE_POINTER(eptr->m_ptr);
if (nullptr == e)
continue;
e->ClearSavedSubdivisionPoints();
for (unsigned evi = 0; evi < 2; ++evi)
{
const ON_SubDVertex* v = e->m_vertex[evi];
if (nullptr == v)
continue;
v->ClearSavedSubdivisionPoints();
}
}
}
unsigned int ON_SubDVertex::VertexId() const
{
return m_id;
}
unsigned int ON_SubDEdge::EdgeId() const
{
return m_id;
}
unsigned int ON_SubDFace::FaceId() const
{
return m_id;
}
const ON_3dPoint ON_SubDFace::ControlNetCenterPoint() const
{
if (m_edge_count < 3)
return ON_3dPoint::NanPoint;
ON_3dPoint center(0.0, 0.0, 0.0);
const ON_SubDEdgePtr* eptr = m_edge4;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi, ++eptr)
{
if (4 == fvi)
{
eptr = m_edgex;
if ( nullptr == eptr)
return ON_3dPoint::NanPoint;
}
const ON_SubDVertex* v = eptr->RelativeVertex(0);
if ( nullptr == v)
return ON_3dPoint::NanPoint;
center += v->ControlNetPoint();
}
const double c = (double)m_edge_count;
center.x /= c;
center.y /= c;
center.z /= c;
return center;
}
const ON_3dVector ON_SubDFace::ControlNetCenterNormal() const
{
if (4 == m_edge_count)
{
// faster code for most common case
const ON_SubDVertex* v[4] = { m_edge4[0].RelativeVertex(0),m_edge4[1].RelativeVertex(0),m_edge4[2].RelativeVertex(0),m_edge4[3].RelativeVertex(0)};
if (nullptr == v[0] || nullptr == v[1] || nullptr == v[2] || nullptr == v[3])
return ON_3dVector::NanVector;
const ON_3dVector A = ON_3dPoint(v[2]->m_P) - ON_3dPoint(v[0]->m_P);
const ON_3dVector B = ON_3dPoint(v[3]->m_P) - ON_3dPoint(v[1]->m_P);
const ON_3dVector N = ON_CrossProduct(A, B);
return N.UnitVector();
}
if (3 == m_edge_count)
{
// faster code for 2nd most common case
const ON_SubDVertex* v[3] = { m_edge4[0].RelativeVertex(0),m_edge4[1].RelativeVertex(0),m_edge4[2].RelativeVertex(0)};
if (nullptr == v[0] || nullptr == v[1] || nullptr == v[2])
return ON_3dVector::NanVector;
const ON_3dPoint C0(v[0]->m_P);
const ON_3dVector A = ON_3dPoint(v[1]->m_P) - C0;
const ON_3dVector B = ON_3dPoint(v[2]->m_P) - C0;
const ON_3dVector N = ON_CrossProduct(A, B);
return N.UnitVector();
}
// less common cases
const ON_3dPoint C = ControlNetCenterPoint();
if (false == (C.x == C.x))
return ON_3dVector::NanVector;
// If the face is planar (convex or non-convex), this will return
// the plane's normal with the correct orientation.
// Otherwise this will return a good choice of normal for
// a non-planar face.
ON_3dVector A;
ON_3dVector B = ControlNetPoint(m_edge_count - 1) - C;
ON_3dVector N = ON_3dVector::ZeroVector;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi)
{
A = B;
B = ControlNetPoint(fvi) - C;
N += ON_CrossProduct(A, B); // do not untize this and then the code works for non-convex faces too.
}
return N.UnitVector();
}
bool ON_SubDFace::IsConvex() const
{
const ON_3dVector N = ControlNetCenterNormal();
if (N.IsNotZero())
{
if (3 == m_edge_count)
return true;
ON_3dPoint P = ControlNetPoint(m_edge_count - 2);
ON_3dPoint Q = ControlNetPoint(m_edge_count - 1);
ON_3dVector A;
ON_3dVector B = Q - P;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi)
{
P = Q;
Q = ControlNetPoint(fvi);
A = B;
B = Q - P;
const ON_3dVector AxB = ON_CrossProduct(A, B);
const double d = AxB*N;
if ( false == (d > 0.0) && false == AxB.IsZero() )
return false;
}
return true;
}
return false;
}
bool ON_SubDFace::IsNotConvex() const
{
const ON_3dVector N = ControlNetCenterNormal();
if (N.IsNotZero())
{
if (3 == m_edge_count)
return false;
bool bIsNotConvex = false;
ON_3dPoint P = ControlNetPoint(m_edge_count - 2);
ON_3dPoint Q = ControlNetPoint(m_edge_count - 1);
ON_3dVector A;
ON_3dVector B = Q - P;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi)
{
P = Q;
Q = ControlNetPoint(fvi);
A = B;
B = Q - P;
const ON_3dVector AxB = ON_CrossProduct(A, B);
const double d = AxB * N;
if (false == (d == d))
return false; // nan
if (false == (d > 0.0) && false == AxB.IsZero())
bIsNotConvex = true;
}
return bIsNotConvex;
}
return false;
}
bool ON_SubDFace::IsPlanar(double planar_tolerance) const
{
const ON_3dPoint C = ControlNetCenterPoint();
const ON_3dVector N = ControlNetCenterNormal();
if (C.IsValid() && N.IsNotZero())
{
if (3 == m_edge_count)
return true;
if (false == (planar_tolerance >= 0.0))
planar_tolerance = ON_ZERO_TOLERANCE;
const ON_SubDEdgePtr* eptr = m_edge4;
double d0 = 0.0;
double d1 = 0.0;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi, ++eptr)
{
if (4 == fvi)
{
eptr = m_edgex;
if (nullptr == eptr)
return false;
}
const ON_SubDVertex* v = eptr->RelativeVertex(0);
if (nullptr == v)
return false;
const double d = (ON_3dPoint(v->m_P) - C)*N;
if (false == (d == d))
return false; // nan
if (d < d0)
d0 = d;
else if (d > d1)
d1 = d;
else
continue;
if ((d1 - d0) > planar_tolerance)
return false;
}
return true;
}
return false;
}
bool ON_SubDFace::IsNotPlanar(double planar_tolerance) const
{
const ON_3dPoint C = ControlNetCenterPoint();
const ON_3dVector N = ControlNetCenterNormal();
if (C.IsValid() && N.IsNotZero())
{
if (3 == m_edge_count)
return false;
if (false == (planar_tolerance >= 0.0))
planar_tolerance = ON_ZERO_TOLERANCE;
const ON_SubDEdgePtr* eptr = m_edge4;
double d0 = 0.0;
double d1 = 0.0;
bool bNotPlanar = false;
for (unsigned short fvi = 0; fvi < m_edge_count; ++fvi, ++eptr)
{
if (4 == fvi)
{
eptr = m_edgex;
if (nullptr == eptr)
return false;
}
const ON_SubDVertex* v = eptr->RelativeVertex(0);
if (nullptr == v)
return false;
const double d = (ON_3dPoint(v->m_P) - C)*N;
if (false == (d == d))
return false; // nan
if (d < d0)
d0 = d;
else if (d > d1)
d1 = d;
else
continue;
if ((d1 - d0) > planar_tolerance)
bNotPlanar = true;
}
return bNotPlanar;
}
return false;
}
const ON_Plane ON_SubDFace::ControlNetCenterFrame() const
{
const ON_3dPoint C = ControlNetCenterPoint();
const ON_3dVector N = ControlNetCenterNormal();
if (C.IsValid() && N.IsNotZero())
{
// TODO - better choices for x and y axes
ON_Plane center_frame;
if (center_frame.CreateFromNormal(C, N))
return center_frame;
}
return ON_Plane::NanPlane;
}
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